tag:blogger.com,1999:blog-89428113431291485302024-03-19T10:34:34.648-07:00Ivan Bezdomny's Baseball BlogMy writings about baseball, with a strong statistical & machine learning slant.Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.comBlogger53125tag:blogger.com,1999:blog-8942811343129148530.post-70336440089270255792011-04-27T16:42:00.000-07:002011-04-28T12:02:58.689-07:00Basketball project, groundball pitchers & status update<div dir="ltr" style="text-align: left;" trbidi="on">
As you can see, this blog has been inactive for a while. Not to say that *I* have been inactive. Rather, I have focused my sports cycles on basketball. Simply put, I created a system to write <a href="http://bball-live.com/live/">live commentary on NBA games</a>. It's been on Twitter for awhile now, and I have a website with <a href="http://bball-live.com/live/">live summaries</a>, as well, although it's in Alpha :-)<br />
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If you want to follow along on Twitter, check out my accounts for some of the top NBA teams in the playoffs. <a href="http://twitter.com/LakersLines">Lakers</a> <a href="http://twitter.com/CelticsCorner3">Celtics</a> <a href="http://twitter.com/Heat_Homer">Heat</a> <a href="http://twitter.com/Magic4thQuarter">Magic</a> <a href="http://twitter.com/RetweetaBulls">Bulls</a> <a href="http://twitter.com/SpursOTheMoment">Spurs</a> <strike><a href="http://twitter.com/KnicksNotes">Knicks</a></strike> <a href="http://twitter.com/DirksDaggers">Mavs</a> <a href="http://twitter.com/BlazersBanter">Blazers</a> <a href="http://twitter.com/OKC_OMG">OKC Thunder</a><br />
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I've been meaning to return to some of the baseball analysis, but man I've been busy. I saw an article I wrote about <a href="http://bezdomnybaseball.blogspot.com/2010/08/incomplete-thoughts-on-ground-ball.html">ground ball pitchers</a> got some <a href="http://www.baseballthinkfactory.org/files/newsstand/discussion/ivan_bezdomnys_baseball_blog/">traction on Baseball Think Factory.</a> I'm sure glad I called it<br />
"incomplete thoughts on groundball pitchers," since a lot of people seemed to disagree with my conclusion. And perhaps they are right. There have certainly been lots of good pitchers who depend on ground balls more than on strikeouts. It's an interesting discussion to return to, at some point. </div>Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com1tag:blogger.com,1999:blog-8942811343129148530.post-49562764084975104232010-11-16T00:35:00.000-08:002010-11-16T00:35:48.195-08:00Why R makes more sense than R^2 (in looking at correlations in baseball)I've been so far removed from baseball that I have not read Tom Tango's "The Book" blog in some time. Thankfully I recently ran into one of his posts anyway.<div>
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Here, Tom gives a succinct <i>qualitative</i> explanation of the difference between <b>r</b> and <b>r^2</b> (<b>r</b> squared) in studies of statistical correlation. If half the data points are a direct match for a simple linear rule (e.g. equality) and the other half of the data points are random (within the same range), then your <b>r</b> is <b>1/2</b> and your <b>r^2</b> is <b>1/4</b>. It is more natural to say that the correlation is <b>1/2</b>. That makes sense. The <b>1/4</b> deals with variance, which is not an intuitive concept. Tom's full article is here:</div>
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<a href="http://www.insidethebook.com/ee/index.php/site/comments/r_v_r_squared/">http://www.insidethebook.com/ee/index.php/site/comments/r_v_r_squared/</a></div>
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This makes me feel a whole lot clearer about the results of my fastball speed vs pitcher strikeout rates studies from last year. I looked at a variety of non-performance characteristics for pitchers, and how those helped to explain the pitchers' strikeout rates. Non-performance means that I looked at physical characteristics like age, height, weight, and (left) handedness. I also looked at which pitches they threw, how often, and how hard. By far the most relevant characteristics were fastball speed and handedness. I got about a <b>0.6</b> correlation (ie <b>r</b>) between those two factors and strikeout rates. That looked pretty important. However <b>0.3 r^2</b> sounded less significant.</div>
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What that means that is that fastball speed and handedness explain "only" 36% of the inter-pitcher <i>variance</i> in strikeout rates, but they explain about 60% of the difference in terms of <i>standard deviation</i>. Or at least that's how I will think of it from now on. What I found was significant, and I believe interesting. It has not gotten much run in the nerd baseball press, but perhaps this is because I did not promote it. That won't change. But if you are interested, look for some of my articles from the winter of 2009-2010. I have not seen anyone write about this before or since. Although I haven't checked recently.</div>
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For what it's worth, it seems like teams are valuing (left) handedness and fastball speed more highly in prospects than ever before. This is not surprising; sports always tends to evolve that way. As money increases and the talent pool grows, rare ability and "natural" talents takes precedence over common ability and "refined" talents and experience. Just consider players like Amar'e Stoudemire in the NBA. That is why I thought that <a href="http://bezdomnybaseball.blogspot.com/2010/02/why-reds-paid-30-million-for-aroldis.html">Aroldis Chapman was a bargain for the Reds</a>, purely based on his fastball speed and handedness.</div>
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At some point, I should go back and see how the rest of my predictions fared, including my <a href="http://bezdomnybaseball.blogspot.com/2010/04/vorp-era-and-fip-projections-keeping-it.html">2010 IP and ERA projections for all MLB pitchers</a>. But that would require more effort than writing a short article like this one.</div>Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com0tag:blogger.com,1999:blog-8942811343129148530.post-5889364727651321712010-09-10T15:40:00.000-07:002010-09-10T15:40:07.940-07:00Tim Lincecum: home runs, strikeouts and fastball speedWhatever happened to <a href="http://www.fangraphs.com/statss.aspx?playerid=5705&position=P">Tim Lincecum</a>? His 3.69 ERA over 185 IP is pretty good and his FIP of 3.33 is even better, but both are a well below his 2008-2009 level, when he deservedly won two NL Cy Young awards. His strikeout rates are down. His walks are up. He is also allowing more home runs.<br />
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By far the biggest difference between 2008-2009 and 2010 for Lincecum have been his home runs given up. He gave up home runs on 6% of fly balls in 2008-2009, but 10% of fly balls in 2010. Tim's xFIP (FIP with league-average for HR per fly ball) is only slightly up from 2008-2009.<br />
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So if someone asked you: "what's wrong with Tim Lincecum in 2010?" you would tell him that his luck with fly balls going out has turned for the worse. Then you would debate how much a pitcher controls his HR/fly ball rates. But other than home runs given up, has anything else changed about Timmy the Freak?<br />
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Eric Seidman of Baseball Prospectus recently wrote <a href="http://www.baseballprospectus.com/article.php?articleid=11928">an article on Lincecum</a>, attempting to break down the differences in his repertoire between 2010 and 2008-2009. It's unclear what changed, other than the drop in fastball speed, and also a decrease in fastball movement. Seidman goes on to suggest that, if Lincecum's fastball is slower an "has less bite," then it may make the rest of his pitches less effective, even if they are the same pitches as before.
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There are a lot of moving parts here, so let's just look at his declining fastball speed compared to his declining strikeout rates. Of all the changes, these are the most easily noticeable "cause" and "effect." Numbers from <a href="http://www.fangraphs.com/statss.aspx?playerid=5705&position=P">Lincecum's FanGraphs profile</a>.<br />
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<table border="2">
<tbody>
<tr>
<th>Year</th>
<th>SO/9 </th>
<th>average FB</th>
<th>% fastballs</th>
</tr>
<tr>
<td>2007</td>
<td>9.2</td>
<td>94.2</td>
<td>69%</td>
</tr>
<tr>
<td>2008</td>
<td>10.5</td>
<td>94.1</td>
<td>66%</td>
</tr>
<tr>
<td>2009</td>
<td>10.4</td>
<td>92.4</td>
<td>56%</td>
</tr>
<tr>
<td>2010</td>
<td>9.7</td>
<td>91.3</td>
<td>55%</td>
</tr>
</tbody></table>
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The trend is weak, but is looks like Tim Lincecum's strikeout rates are declining with his fastball slowing down. Lincecum improved as a strikeout pitcher from his 2007 rookie year, but is now probably maximizing his strikeout ability, relative to his physical skills. As the physical skills decline, so will his ability to strike batters out.<br />
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Why am I looking at fastball speed in predicting strikeout rates, and not various other pitcher skills or characteristics?<br />
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In a series of studies I did last winter I found that, of all the non-performance pitcher attributes, fastball speed was by far the most predictive in terms of predicting strikeout rates. I can predict a pitcher's strikeout rate (given a reasonable IP cutoff) with R=0.52, given just his average fastball speed. The predictive power only goes up to R=0.59 if I also look at what other pitches he throws, his league, his age, his weight, and whether or not his is left handed. Of those factors, the league and handedness are by far the most helpful. See my <a href="http://bezdomnybaseball.blogspot.com/2010/02/why-strikeout-rates-from-pitch-data-are.html">old article</a> here for more details.<br />
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The most important relationship that I discovered in my research was that 1. fastball speed predicts strikeout rates to a significant degree 2. the relationship is non-linear.<br />
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Here are fastball speeds vs strikeout rates 2002-2009 pitchers. Strikeout rates are fit by a quadratic function (ie square of the fastball speed). Note the discrepancies by league:<br />
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<a href="http://picasaweb.google.com/lh/photo/nmCizRJYQNxBesfDB4bROhMXdkPFxccfzJHjXrBvTfE?feat=embedwebsite"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIvtqxbZgmrzn0lalNuP_MrzMEUI2q0h08C0XavqCD4jUrSw6B0TpHV-XSYcFCpd1CRPuUxu2Hg_lZ9JwIHooMy8Jy0gPm5Jdx0lnq3JW7fQLETPcEMmCfUvQfHVlHzWBsp6-sYVswfgQ/s400/SO9-vs-FB-starters-AL-NL.gif" /></a>
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A fastball velocity drop from 95 mph to 90 mph in the NL (in blue) is worth a strikeout rate drop from 9.0 SO/9 to 6.5 SO/9. That's a big difference. For a starting pitcher, that's a drop from being an elite strikeout pitcher to being league average.<br />
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Tim Lincecum has dropped from a 94.1 mph pitcher to a 91.5 mph pitcher. According to the graph above, that should be worth a strikeout drop of about 8.5 - 7.0 = 1.5 SO/9. Even for someone who strikes out ten batters per nine innings, a 1.5 SO/9 drop is enough to taking him down from elite pitcher to just very good.<br />
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Tim Lincecum is not a typical pitcher. He over-achieved his fastball-based strikeout projection at 94 mph, and he's over-achieving his strikeout projection at 91.5 mph. But the strikeout drop is still there. If Lincecum's fastball declines further, he won't any longer be a ten strikeout per nine innings pitcher. To record sub-3.00 ERA's, he'll have to bring down his walk rates from around 3.0 BB/9 to more of a <a href="http://www.fangraphs.com/statss.aspx?playerid=1636&position=P">Cliff Lee</a> type level, or he will have to get lucky with keeping fly balls in the park at well below the league average.<br />
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He is not so old that decreases in fastball speed are inevitable, but I'm guessing that Tim Lincecum is too young to increase his fastball speed, the way that <a href="http://www.fangraphs.com/statss.aspx?playerid=1943&position=P#pitchtype">Zach Greinke</a> did 2005-2007. Nor does he have the strikeout rate advantage of being left-handed (worth about +1.5 SO/9 for the same fastball speed, <a href="http://bezdomnybaseball.blogspot.com/2010/02/in-my-last-post-brian-cashman-to-stop.html">according to my stud</a>y).<br />
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There are many components that go into being a great pitcher. But strikeout rates and walk rates are the two factors that pitchers have the most control over. I'm not saying that Lincecum's 10.0 SO/9 rates from the last couple years were a fluke. But he will have trouble maintaining those into the future as his fastball speed has already declined. Look for him do decrease his walks. If he is not able to do so without further decreasing the strikeout rates, Tim Lincecum can't be considered the best pitcher in baseball going forward.Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com1tag:blogger.com,1999:blog-8942811343129148530.post-7173036440125733382010-08-24T13:13:00.000-07:002010-08-24T13:13:07.978-07:00Incomplete thoughts on ground-ball pitchersI've been out of the baseball loop, focusing on my basketball project. But I still slavishly read Bill James's site, and he brought up a point relevant to my research on pitcher types. In answering a question about Brandon Webb, <a href="http://www.billjamesonline.net/DisplayAnswers.aspx">Bill said</a>:<br />
<blockquote>
I've said it a thousand times, but. . .I don't believe in ground ball pitchers. I don't trust them, I don't want them, and I don't believe one should ever invest money in them. In theory, a ground ball pitcher with a good strikeout rate is the best of both worlds. But the problem is, there just aren't any pitchers like that who are consistently good; they all either get hurt or they lose home plate. The only pitcher like that who has had a great career in the last 30 years was Kevin Brown. The overwhelming majority of the consistently good pitchers are the guys who live off of the high fastball--Clemens, Schilling, the Unit, Pedro, Santana, King Felix, Verlander, Sabathia, etc.
</blockquote>
When I left off my baseball research, I left off with a classification of pitchers by the type of pitches that they throw. Dave Allen pointed out that I should look at pitchers who throw two-seam fastballs, as those pitchers have become the subject of much sabermetric discussion. Two-seam fastballs induce ground balls like no other pitch, and the value of ground balls for pitchers has become a hotly debated topic. (By hot, I mean that multiple analysts are competing to show how much value ground balls really have for pitchers.)<br />
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I created a new category of pitchers, centered around those that throw a high percentage of two-seam fastballs. Indeed, this category of pitchers had very high ground ball rates (something like 6% higher than average), but also lower strikeout rates (about 0.5 K/9 less than average). I was going to write an article about whether or not this "tradeoff" is worth it.<br />
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But Bill James brings up a better point. Who are the great two-seam fastball ground ball pitchers out there?
Clearly Brandon Webb has to be the most famous example. But let's consider the others. I only had reliable two-seamed fastball data for 2009, so all examples have to be from last year. Here are the most name-recognizable pitchers who classified as "type 8: two-seam fastball pitcher" by my scheme. All data courtesy of PF/X posted on FanGraphs.<br />
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<table border="2">
<tbody>
<tr>
<th>Pitcher</th>
<th>2009 FT%</th>
<th>2010 FT%</th>
</tr>
<tr>
<td>Joel Piniero</td>
<td>28%</td>
<td>49%</td>
</tr>
<tr>
<td>Brian Matusz</td>
<td>14%</td>
<td>21%</td>
</tr>
<tr>
<td>Scott Kazmir</td>
<td>10%</td>
<td>0%</td>
</tr>
<tr>
<td>Rick Porcello</td>
<td>22%</td>
<td>52%</td>
</tr>
<tr>
<td>Francisco Liriano</td>
<td>12%</td>
<td>46%</td>
</tr>
<tr>
<td>Fausto Carmona</td>
<td>9%</td>
<td>33%</td>
</tr>
<tr>
<td>Chien-Ming Wang</td>
<td>23%</td>
<td>NA</td>
</tr>
<tr>
<td>Carlos Silva</td>
<td>43%</td>
<td>50%</td>
</tr>
</tbody></table>
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Ignoring Scott Kazmir, who no longer throws two-seam fastballs, and the hobbled CM Wang, is there anything we can generalize about the two-seam fastball pitchers?
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First of all, none of them are backing off the pitch. This is selective, since I chose the most recognizable proponents of the pitch, and PF/X pitch classifications are not consistent year to year. Still, I think this suggests that two-seam fastball pitchers are on the rise. How is it affecting their stats?
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All of these pitchers are recording high GB% stats on the season, except for Brian Matusz. Joel Pineiro leads with 56%, and none of these guys except Matusz are below 45% (league average is in the low 40% range). Accounting for randomness, these pitchers are all getting high ground ball rates, in part due to their use of the two-seam fastball. However none of them except for Liriano are having top-level season. Here are the 2010 strikeout rates (K/9) for those pitchers:
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<br />
<table border="2">
<tbody>
<tr>
<th>Pitcher</th>
<th>2010 K/9</th>
</tr>
<tr>
<td>Joel Piniero</td>
<td>5.7</td>
</tr>
<tr>
<td>Brian Matusz</td>
<td>6.9</td>
</tr>
<tr>
<td>Rick Porcello</td>
<td>4.5</td>
</tr>
<tr>
<td>Francisco Liriano</td>
<td><b>9.8</b></td>
</tr>
<tr>
<td>Fausto Carmona</td>
<td>4.8</td>
</tr>
<tr>
<td>Carlos Silva</td>
<td>6.3</td>
</tr>
</tbody></table>
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Not surprisingly, Francisco Liriano has a 3.45 ERA, despite a very unlucky 0.350 BABIP. He is having a "Kevin Brown" season, as Bill James would describe it, with both high GB% and high strikeout rate.
However the other pitchers have league-average strikeout rates at best. Fausto Carmona has the stuff (93 mph average fastball) to be a high-strikeout pitcher, but he has never realized that potential (even during his 19-win season in 2007, he was a low-strikeout pitcher). It is very unlikely he will become even a league-average strikeout pitcher at this point in his career. Joel Pineiro was dominant earlier this season when he was getting 70% ground balls, but his ERA and FIP have settled around 4.0 now that his ground ball rate is a more sustainable 56%. Without above-average strikeout rates, a pitcher's long term ceiling might be that 4.0 ERA. Not bad, and worth a couple of WAR, but not in the elite pitcher echelon.
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Brian Matusz in an interesting case. He was a high strikeout guy in the minors, and has had a league-average strikeout rate over his first 200 major league innings. He throws a two-seam fastball according to PF/X, but he doesn't get high ground ball rates. I'm not sure what's going on there. Maybe he just doesn't belong in this list.
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Overall, though, I think Bill James's point is well taken. You can't be a great pitcher on ground balls alone, at least not over a course of several years. You need to have strikeouts. Francisco Liriano might be the next pitcher to maintain high GB rates with high strikeout totals. But he'll have to prove it over more than one season.<br />
<h3>
Projecting Liriano in April</h3>
I'm happy to see Liriano having a great season. He's endured a few injury setbacks, and I'm happy to see him finally come back to form. Also, my pitcher projections were very favorable for him, and it's always pleasant to be right on something like this.
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In the <a href="http://spreadsheets.google.com/pub?key=t5bbK1PY29qKUrqPc3_jVjg&output=html">projection I published in April</a>, here is what my system predicted for Francisco Liriano in 2010:<br />
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<ul>
<li>159.6 IP; 20.9 VORP; 4.31 ERA; 4.24 FIP</li>
</ul>
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Of course, he has been much better than that. But it was bold of my system to project him for a full season, and to be in the top 50 most valuable pitchers in MLB. In 2009, he was 5-13 with a 5.80 ERA in 136 IP. I think this is a real win for my injury-based projection adjustments.
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With the season finishing up, I will go my predictions more systematically. As you can see from the link above, I was off on quite a few of them. I was probably more pessimistic on Cliff Lee than most (in part due to his injury in camp). I got fooled on Javier Vazquez. And I thought John Lackey would be a workhorse, rather than a dud.
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But this is all a topic for a future post. Til then...Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com0tag:blogger.com,1999:blog-8942811343129148530.post-35501216483716664652010-07-28T00:39:00.000-07:002010-07-28T00:50:48.518-07:00Andre Dawson, Bert Blyleven, Johnny Damon and Miguel Cabrera<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Jorge Posada is one of my favorite Yankees. I've always been a big Andy Pettitte fan, and generally considered myself one of </span><i><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">those</span></i><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> kind of Yankees fans. But this isn't about Andy Pettitte. Or even about Posada, for that matter.</span><p>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Jorge Posada came up when he was 23, but he didn't become a regular until he was 26. Since then, he's been the top offensive catcher in the AL just about every year. And although I'm sure no one was talking about it in 2000, Jorge Posada compares favorably to the Hall of Fame's current battery of backstops. He hasn't been Johnny Bench or Mike Piazza or Garry Carter, but he was pretty damn good for the past decade and change, and he ain't done yet.</span><p>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">When I checked </span><a href="http://www.baseball-reference.com/players/p/posadjo01.shtml"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Jorge's profile</span></a><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> on Baseball Reference, I wasn't surprised to see his closest comps to that of Carlton Fisk, but I was a little surprised that he only ranked 26th on the list of WAR (wins above replacement) among currently active players. I clicked ahead to see the</span><a href="http://www.baseball-reference.com/leaders/WAR_active.shtml"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> top 50 active players by career WAR</span></a><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">. Man it's a hell of a list. This got me thinking.</span><br />
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Last year Bill James wrote an article called "The Expansion Time Bomb." [Unfortunately it's behind the paywall on his site.] Bill argued that, as baseball has expanded since 1969, so too has the number of players reaching levels "historical achievement" that typically define a Hall of Fame career. In other words, in an expanded league, there will be more players with 3,000 hits, more players with 500 home runs hitters, more 300 game winners, and otherwise more milestones being reached. This seems intuitively true, but it is also very hard to argue, and harder to verify. Still, his main argument is an interesting one (which I paraphrase below):</span><br />
<blockquote>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Most supporters want the Hall of Fame to be an exclusive club. This inherently means restricting membership to a small number of entries per year (or decade, or other time period). As expansion has led to more players with historical levels of achievement, Hall of Fame standards will tighten to levels much more narrow than those used in the past.</span></blockquote>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">We'll come back to this thought in a minute. First, let's look at the current top 50 in baseball by career WAR. How many of them are Hall of Fame players? (By the way, WAR is simply a measurement of career "wins added" above a replacement-level player. The merits of WAR are not important here. It is just a way to place all active players, regardless of position, on a rough universal career ranking.)</span><p>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">For each player, I rate his Hall of Fame chances as "yes," "probably," "maybe," or "no." I assume a conservative estimate for the rest of his career. In other words, will he make the Hall of Fame, based on today's standards, if he doesn't do much for the rest of his career? I'm ignoring steroids and just focusing on performance.</span><p>
<ol>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Alex Rodriguez (34) - </span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="color: #38761d;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Yes</span></span></span></li>
<li><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="border-collapse: collapse;"></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Albert Pujols (30) - </span><span class="Apple-style-span" style="color: #38761d;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Yes</span></span></span></li>
<li><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="border-collapse: collapse;"></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Chipper Jones (38) - </span><span class="Apple-style-span" style="color: #38761d;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Yes</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #38761d;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Ken Griffey (40) - </span><span class="Apple-style-span" style="color: #38761d;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Yes</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #38761d;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Derek Jeter (36) - </span><span class="Apple-style-span" style="color: #38761d;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Yes</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #38761d;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Jim Edmonds (40) - </span><span class="Apple-style-span" style="color: #b45f06;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Probably</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #b45f06;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Jim Thome (39) - </span><span class="Apple-style-span" style="color: #b45f06;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Probably</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #b45f06;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Manny Ramirez (38) - </span><span class="Apple-style-span" style="color: #38761d;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Yes</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #38761d;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Ivan Rodriguez (38) - </span><span class="Apple-style-span" style="color: #38761d;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Yes</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #38761d;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Scott Rolen (35) - </span><span class="Apple-style-span" style="color: #bf9000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Maybe</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #bf9000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Andruw Jones (33) - </span><span class="Apple-style-span" style="color: #990000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">No</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #990000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Vladimir Guerrero (35) - </span><span class="Apple-style-span" style="color: #38761d;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Yes</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #38761d;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Todd Helton (36) - </span><span class="Apple-style-span" style="color: #b45f06;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Probably</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #b45f06;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Bobby Abreu (36) - </span><span class="Apple-style-span" style="color: #bf9000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Maybe</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #bf9000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Carlos Beltran (33) - </span><span class="Apple-style-span" style="color: #b45f06;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Probably</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #b45f06;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Jason Giambi (39) - </span><span class="Apple-style-span" style="color: #990000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">No</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #990000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Ichiro Suzuki (36) - </span><span class="Apple-style-span" style="color: #38761d;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Yes</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #38761d;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Mariano Rivera (40) - </span><span class="Apple-style-span" style="color: #38761d;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Yes</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #38761d;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Roy Halladay (33) - </span><span class="Apple-style-span" style="color: #b45f06;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Probably</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #b45f06;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Andy Pettitte (38) - </span><span class="Apple-style-span" style="color: #bf9000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Maybe</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #bf9000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Johnny Damon (36) - </span><span class="Apple-style-span" style="color: #bf9000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Maybe</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #bf9000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Mike Cameron (37) - </span><span class="Apple-style-span" style="color: #990000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">No</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #990000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Jamie Moyer (47) - </span><span class="Apple-style-span" style="color: #990000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">No</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #990000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">J.D. Drew (34) - </span><span class="Apple-style-span" style="color: #990000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">No</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #990000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Johan Santana (31) - </span><span class="Apple-style-span" style="color: #b45f06;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Probably</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #b45f06;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Jorge Posada (38) - </span><span class="Apple-style-span" style="color: #bf9000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Maybe</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #bf9000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Lance Berkman (34) - </span><span class="Apple-style-span" style="color: #bf9000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Maybe</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #bf9000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Tim Hudson (34) - </span><span class="Apple-style-span" style="color: #990000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">No</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #990000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Omar Vizquel (43) - </span><span class="Apple-style-span" style="color: #b45f06;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Probably</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #b45f06;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Roy Oswalt (32) - </span><span class="Apple-style-span" style="color: #b45f06;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Probably</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #b45f06;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Mark Buehrle (31) - </span><span class="Apple-style-span" style="color: #bf9000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Maybe</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #bf9000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">CC Sabathia (29) - </span><span class="Apple-style-span" style="color: #b45f06;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Probably</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #b45f06;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Adrian Beltre (31) - </span><span class="Apple-style-span" style="color: #cc0000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">No</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #cc0000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Miguel Tejada (36) - </span><span class="Apple-style-span" style="color: #990000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">No</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #990000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Javier Vazquez (34) - </span><span class="Apple-style-span" style="color: #990000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">No</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #990000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Jason Kendall (36) - </span><span class="Apple-style-span" style="color: #990000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">No</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #990000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Chase Utley (31) - </span><span class="Apple-style-span" style="color: #b45f06;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Probably</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #b45f06;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Magglio Ordonez (36) - </span><span class="Apple-style-span" style="color: #990000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">No</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #990000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Joe Mauer (27) - </span><span class="Apple-style-span" style="color: #b45f06;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Probably</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #b45f06;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Eric Chavez (32) - </span><span class="Apple-style-span" style="color: #cc0000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">No</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #cc0000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Mark Teixeira (30) - </span><span class="Apple-style-span" style="color: #bf9000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Maybe</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Troy Glaus (33) - </span><span class="Apple-style-span" style="color: #990000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">No</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #990000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Barry Zito (32) - </span><span class="Apple-style-span" style="color: #990000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">No</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #990000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Placido Polanco (34) - </span><span class="Apple-style-span" style="color: #990000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">No</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #990000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Carlos Zambrano (29) - </span><span class="Apple-style-span" style="color: #990000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">No</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #990000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Tim Wakefield (43) - </span><span class="Apple-style-span" style="color: #990000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">No</span></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> </span></span></li>
<li><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="border-collapse: collapse;"></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Rafael Furcal (32) - </span><span class="Apple-style-span" style="color: #990000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">No</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #990000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Edgar Renteria (33) - </span><span class="Apple-style-span" style="color: #990000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">No</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #990000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">David Wright (27) - </span><span class="Apple-style-span" style="color: #bf9000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Maybe</span></span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="color: #bf9000;"></span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Miguel Cabrera (27) - </span><span class="Apple-style-span" style="color: #b45f06;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Probably</span></span></span></li>
</ol>
<span class="Apple-style-span" style="border-collapse: collapse; font-family: Georgia, 'Times New Roman', serif;">You will surely disagree with some of my assessments. But let's consider the overall picture. How many future Hall of Famers are active in 2010? I'll assign the following counts per rating:</span><p>
<ul>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="color: #38761d;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Yes </span></span></span><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">= 1.0</span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="color: #b45f06;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Probably</span></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> = 0.7</span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="color: #bf9000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Maybe</span></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> = 0.3</span></span></li>
<li><span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="color: #990000;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">No</span></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> = 0.0</span></span></li>
</ul>
<span class="Apple-style-span" style="border-collapse: collapse; font-family: Georgia, 'Times New Roman', serif;">Ken Griffey counts as one Hall of Famer; Roy Oswalt counts as 0.7 Hall of Famers. My main man Jorge counts as 0.3 Hall of Famers. Between himself, Bobby Abreu, and David Wright, there will most likely be one Hall of Fame career. Remember, I'm being a little conservative here.</span><p>
<span class="Apple-style-span" style="border-collapse: collapse;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"></span></span>Out of the fifty players, we get twenty one Hall of Famers, breaking down as follows:
<blockquote>
10 * Yes + 12 * Probably + 9 * Maybe + 19 * No = 21.1 Hall of Famers</blockquote>
<p>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">A Hall of Fame career is typically 16 to 20 years, so in theory, this list represents 16 to 20 years' worth of Hall of Famers, assuming these are evenly distributed through time. However, the list does not include a single player under 27. Hanley Ramirez, Zack Greinke and Tim Lincecum are not accomplished enough yet to be considered possible Hall of Famers for this discussion. Therefore, let's say that the top fifty players by WAR includes all possible Hall of Famers over fifteen years (ie age 27 to age 42).</span><p>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">If my list is reasonably accurate, this suggests that we will induct twenty one players over every fifteen years, if the future performance is much like the recent past.</span><p>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">To me, that sounds very reasonable. With an average of 1.4 new qualified candidate per year, the Hall of Fame would be electing zero to three players every year. Yes, they will be electing more candidates per year than in the recent, but not by much. It will he harder for borderline candidates to get in, but there would never be backlogs of qualified recent candidates running ten deep. There will be years with no obvious Hall of Famers on the ballot, and in those years, weaker candidates will still have a chance to be elected.</span><p>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">While I still think that Bill James's argument sounds appealing, I just don't see the glut of Hall of Fame level performers driving up future Hall of Fame standards significantly. Instead, we will see more years with one or two good new candidates, and fewer multiyear stretches where the best candidate on the ballot is Phil Neikro or Jim Rice. But those borderline cases will still get plenty of consideration. When he is up for Cooperstown, Johnny Damon will have more competition on the ballot than did Andre Dawson and Bert Blyleven, but his career will be just as thoroughly vetted as those two's were.</span><p>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"></span><span class="Apple-style-span" style="border-collapse: collapse; font-family: Georgia, 'Times New Roman', serif;">According to Wikipedia, there are 203 former players currently in the Hall of Fame. These represent the achievements in Major League Baseball of the last 100 years, as well as a few achievements from the 19th century. That's somewhere between 1.7 to 2.0 players per year of Major League Baseball, depending on who's counting. By my count, we will have 1.4 players per year in the future, based on conservative projections of today's stars. Even accounting for the Veterans Committee's past indiscretions inflating the 2.0 number, I don't see a tightening of standards that will exclude Johnny Damon, Bobby Abreu, Jorge Posada, Lance Berkman or Todd Helton from being considered as legitimate candidates. According to my estimates, two of those five guys will get in, and I think that's about right.</span></p>Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com0tag:blogger.com,1999:blog-8942811343129148530.post-52021321032267904822010-06-23T14:13:00.000-07:002010-06-23T14:13:55.526-07:00Status Update!I've been off the blog for a month. I wrote a couple of followup articles for my pitcher type series, but never got around to editing and publishing them (yes, I actually edit my work).<br />
<br />
As per Dave Allen's suggestion, I created a category for two-seam fastball (sinking fastball) throwing pitchers. Also I did some analysis trying to figure out whether throwing lots of these pitches (ie qualifying for my new category over all the others) is an effective strategy. I had some game-theory ideas about giving up strikeouts for ground balls, etc. Then I just got busy with several other things. So what was going to be a week long delay turned into a month.<br />
<br />
I've been in Vegas, playing a few WSOP events. Also, I've been working on a software project, and doing a lot of drawing.<br />
<br />
Moreover, I've found that I'm less nuts about baseball that I was a few months ago. Baseball games are undeniably boring to watch in their entirety, and the season is too long for anyone to truly care about the result of any particular game. I still love baseball, but:<br />
<ol>
<li>None of my good friends do. Although they are all big sports fans.</li>
<li>I never go out of my way to watch a game on TV.</li>
<li>I don't get excited about seeing an MLB game in a new city when I am travelling.</li>
</ol>
The third point is hard to admit. I was in Chicago a month ago, and I had a free afternoon. I had never been to Wrigley, and the Cubbies were scheduled for a day game on a Friday. I'd have thought I'd jump on the chance to go to the game. But I didn't. I went to the Art Museum instead, and I didn't remotely regret it. If I can't get excited about going to a day game in Wrigley by myself, then I guess I'm not as big a baseball fan as I had thought. Or I'm just more interested in art at the moment.<br />
<br />
Maybe I'll get back to baseball soon, maybe I won't. But for now, I would rather spend the afternoon drawing, than spend it writing and revising a baseball article. I'll probably go back and revisit my preseason pitcher projections around the All-Star break. But that would be more for vanity than from an impartial sense of interest.<br />
<br />
In other news, I got an invitation to interview for the Diamondbacks statistical analyst job, but I turned it down (despite the fact that I respect their organization, and love the American Southwest). However this has more to do with my software projects than it has to do with my attitude toward baseball. It's a great job, and I hope the DBacks make a great hire. I'm sure they will!Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com0tag:blogger.com,1999:blog-8942811343129148530.post-36564637982223158342010-05-05T17:38:00.000-07:002010-05-06T01:30:52.888-07:00Does Dave Duncan hate change-ups?In the comments for my "eight types of pitchers" article, John noted:<br />
<blockquote>
<span class="Apple-style-span" style="font-family: 'Trebuchet MS', verdana, sans-serif; font-size: 13.1944px;">Type 3 pitchers seem to be Cardinals even though they're just 4% of pitcher seasons they made up 12.5% of the Cardinals' 16-man staff last season. Also, while Type 2 pitchers make up just 18% of the MLB population, they made up 31.25% of St. Louis' staff last season. They seem to be doing that by avoiding Type 0, 4 and 7 pitchers. I wonder if this could be a personal preference by pitching coach Dave Duncan. Do you have data that suggests some MLB teams look for certain types of pitchers and/or convince pitchers to use a certain percentage of their stuff?</span></blockquote>
In other words, does Cardinals pitching coach Dave Duncan encourage his pitchers to become certain types of pitchers, and not other types? Duncan has been lauded on many blogs and baseball news sites over the past couple of years due to his staffs' repeated successes. He seems to have revitalized multiple pitching careers over the past few years, including <a href="http://www.fangraphs.com/statss.aspx?playerid=1094&position=P">Joel Piniero</a> in 2009. Pitch F/X expert Dave Allen pointed out that <a href="http://www.fangraphs.com/blogs/index.php/the-dave-duncan-effect/">Duncan's pitchers get more ground balls</a> under his tutelage than they had before.<br />
<br />
Is there a secret to Duncan's (perceived) success in reclamation pitchers? Does he turn pitchers into specific types that are more successful, on average, than other pitcher types?<br />
<br />
John suggests above that Duncan's pitchers tend to be type 2 and type 3, but not types 0, 4, or 7, as compared to the league average last year. For those confused about the pitcher types, please read my article <a href="http://bezdomnybaseball.blogspot.com/2010/05/pitchers-eight-different-kinds.html">explaining the pitcher types</a>. The types are derived from what I determine to be a pitcher's <b>core</b> and <b>secondary</b> pitches. All pitchers are assumed to throw the fastball as core pitch (I do not <i>yet </i>distinguish between two-seam and four-seam fastballs; coming soon, Dave). As a quick reference:<br />
<br />
<ul>
<li>type 0: change-up core; slider secondary</li>
<li>type 1: cutter core</li>
<li>type 2: slider core; change-up secondary</li>
<li>type 3: slider <b>and</b> curve core</li>
<li>type 4: curve core; change-up secondary</li>
<li>type 5: change-up core; curve secondary</li>
<li>type 6: slider core; no secondary</li>
<li>type 7: splitter core; slider secondary</li>
</ul>
<div>
It turns out that John's observation is (mostly) correct.</div>
<div>
<br /></div>
<div>
I looked at 2005-2009, rather than just 2009. I counted all pitchers for each team that threw at least 20IP. This is plenty of playing time to establish a repertoire. Here is a list of <a href="http://spreadsheets.google.com/pub?key=t0XcP1TT7Q9kvYinW35dRwg&single=true&gid=1&output=html">all teams' pitcher types</a>, by count of 20IP+ pitchers. First are the percentages, then the raw counts. I included averages and standard deviations for reference. The data is missing all pitchers who were traded midseason. Sorry.</div>
<div>
<br /></div>
<div>
Indeed, the Cardinals' pitchers are more likely to be type 3 (and also type 1) than an average team. The differences lie outside of one standard deviation from the norm. Likewise, the Cardinals' pitchers over one standard deviation below the norm for type 0, type 5, and type 6. The staff is within one standard deviation from the norm for type 2, type 4 and type 7.</div>
<div>
<br /></div>
<div>
Here is an excerpt of my full team type chart:</div>
<div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-insideh-themecolor: text1; mso-border-insideh: .5pt solid black; mso-border-insidev-themecolor: text1; mso-border-insidev: .5pt solid black; mso-border-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 191;">
<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 59.35pt;" valign="top" width="59"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.75pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
T_0%<o:p></o:p></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.75pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
T_1%<o:p></o:p></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.75pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
T_2%<o:p></o:p></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.8pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
T_3%<o:p></o:p></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.8pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
T_4%<o:p></o:p></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.8pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
T_5%<o:p></o:p></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.8pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
T_6%<o:p></o:p></div>
</td>
</tr>
<tr style="mso-yfti-irow: 1;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 59.35pt;" valign="top" width="59"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
Average<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
(1 STD)<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.75pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
7-19<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.75pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
2-10<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.75pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
12-24<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.8pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
1-8<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.8pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
8-20<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.8pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
4-13<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.8pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
39-26<o:p></o:p></div>
</td>
</tr>
<tr style="mso-yfti-irow: 2;">
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Giants<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.75pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
10<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.75pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
6<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.75pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
17<o:p></o:p></div>
</td>
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6<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.8pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
11<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.8pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
7<o:p></o:p></div>
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41<o:p></o:p></div>
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Yankees<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.75pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
8<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.75pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
14<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.75pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
13<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.8pt;" valign="top" width="55"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
6<o:p></o:p></div>
</td>
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15<o:p></o:p></div>
</td>
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7<o:p></o:p></div>
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35<o:p></o:p></div>
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Cardinals<o:p></o:p></div>
</td>
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6<o:p></o:p></div>
</td>
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13<o:p></o:p></div>
</td>
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22<o:p></o:p></div>
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16<o:p></o:p></div>
</td>
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12<o:p></o:p></div>
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1<o:p></o:p></div>
</td>
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24<o:p></o:p></div>
</td>
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</div>
<div>
<br /></div>
<div>
The sample size (71 pitcher seasons) is too small to conclude anything, but here are some possible explanations of what is happening:</div>
<div>
<ol>
<li>Dave Duncan hates change-ups! Type 0 and type 5 are primarily change-up pitchers. Lots of really good pitchers have been type 5 (Greg Maddux & Tom Glavine, for example). However, very few of Duncan's pitchers fit this profile.</li>
<li>Dave Duncan doesn't care for young flame-throwers (or he reforms them quickly). Type 6 pitchers are the most common type of major league pitcher, by far. Many, if not most pitchers come up to the majors as hard-throwing type 6 guys, featuring a fastball, a slider, and not much else. There is a dearth of type 6 pitchers on Duncan's staff, although the number is not ridiculously low. They still make up 24% of his staffs (league average is 33%, and the Cubs form the high-watermark at 48%).</li>
</ol>
<div>
It actually doesn't take much analysis to see that Dave Duncan's pitchers throw fewer change-ups than any team in the baseball. FanGraphs has the <a href="http://www.fangraphs.com/teams.aspx?pos=all&stats=pit&lg=all&type=4&season=2009&month=0">aggregate pitch percentages by team year</a>. Cardinals pitchers threw fewer change-ups that any other team in 2009, although they are somewhat higher in 2010 (but still solidly near the bottom).</div>
</div>
<div>
<br /></div>
<div>
This may just be confirmation bias, but it is entirely plausible that John is right, and Dave Duncan teaches his pitchers to throw curveballs, and not change-ups. As I mentioned in my <a href="http://bezdomnybaseball.blogspot.com/2010/05/performance-by-type-intro.html">previous piece</a>, so far in 2010, Cardinals closer <a href="http://www.fangraphs.com/statss.aspx?playerid=1076&position=P">Ryan Franklin</a> is throwing more curve-balls then even before, and would currently be classified clearly as a type 4 pitcher. Earlier in his career, Franklin used to be a slider/change-up kind of guy.</div>
<div>
<br /></div>
<div>
If Duncan tells his pitchers to throw curves as their off-speed offerings instead of change-ups, then that would explain why his staff has an unusually high number of type 3 pitchers. I assume that conventional wisdom would dictate that a pitcher should throw a slider <b>or</b> a curve. Maybe Duncan is teaching his pitchers to throw both a slider <b>and</b> a curve. If so, that would explain Cardinals' pitchers' improved ground ball rates.</div>
<div>
<br /></div>
<div>
Change-ups, when put in play, tend to result in fly balls (sorry I don't immediately know of a study proving it, but this makes logical sense). Thus it seems plausible that throwing fewer change-ups will result in fewer fly balls. Recent advances in DIPS (defense independent pitching statistics) seems to suggest that <a href="http://www.hardballtimes.com/main/article/groundballs-and-homerun-rates/">pitchers with high ground ball rates also give up fewer home runs per fly ball</a> (as well as 0% home runs per ground ball).</div>
<div>
<br /></div>
<div>
In other words, in today's game, with short outfields walls and middle infielders who can hit one out, it may not make much sense to throw change-ups for any pitcher who does not have a swing-and-miss change-up.</div>
<div>
<br /></div>
<div>
Then again, this is just a theory. If you are interested in more data or have other ideas, drop me a line!</div>
<div>
<br /></div>
<div>
<b>Looking Ahead</b></div>
<div>
<br /></div>
<div>
I trained a basic model to adjust projected FIP using a pitcher's type. For the same 2005-2009 span, pitchers tended to underperform my projections (ie post higher FIP), if they had types 0, 2, 5 and 6. The worst-performing type was type 5. The best-performing type was type 1 (cutter-throwers). There were also trends from previous years' types, again suggesting that type 0 and type 5 pitchers under-perform their expectations. However these are just weak trends. I will write something if/when I get something more definitive.</div>
<div>
<br /></div>
<div>
<b>Strange Brew</b></div>
<div>
<b><br /></b></div>
<div>
I also ran a basic function, to figure out which teams had the most typical staffs and which had the strangest staffs, by pitcher type composition. The Cardinals have had the most unusual staff in the majors during 2005-2009. Closely followed by... the Brewers. So John was right in another respect. The Cardinals have the most unusual composition of pitchers in the majors during the past five years.</div>
<div>
<br /></div>
<div>
The most typical staff was that of the Giants, followed by the Florida Marlins.</div>
<div>
<br /></div>
<div>
Expect an article on this topic, as well.</div>Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com0tag:blogger.com,1999:blog-8942811343129148530.post-57111643684815303352010-05-03T01:26:00.000-07:002010-05-03T01:26:25.040-07:00Starter vs RelieverI was looking at ways to show (in a chart or map) how pitcher performance changes when pitcher change their type (ie learn or forget different pitches). I soon realized that I needed a single rate stat to measure how a group of pitchers' performance changes. Of course, this stat has to be FIP. However, there are starter/reliever issues that need to be considered first.<br />
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This problem has been considered before, and I not aim to shed much new light on it, except to show a couple of graphs based on recent data.</div>
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To establish the difference between starter and reliever performance, there is a long, <a href="http://www.hardballtimes.com/main/article/examining-the-relief-of-relieving">comprehensive article from Steve Treder</a> on THT that often gets cited. It looks at starter/reliever differences throughout baseball history, and concludes that the difference between starter and reliever performance is consistently about 8% of ERA (about 0.3-0.4 on the ERA scale). However that is not the question I need to answer. Instead, I want to compare a group of pitchers' collective performances, and adjust for the groups' tendencies to be throw innings as starters or as relievers. Since starters are, collectively, better pitchers than relievers, the adjustment has to be larger than 8%.</div>
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A more useful study is <a href="http://www.insidethebook.com/ee/index.php/site/comments/starter_v_relief_1953_2008/"><span class="Apple-style-span" style="color: black;">Tom Tango's work</span></a> on his blog. He looks at the same pitchers as starters and relievers, making several important adjustments. His conclusion is that pitchers have 17% more strikeouts, and 17% fewer home runs as relievers, as they do as starters. They also have a 17% better BABIP. He concludes that the same pitchers are "about a 1 run per 9IP" RA better as relievers. I did something simpler (although less thorough), and came up with much of the same conclusions.</div>
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Consider the graph below. I mapped IP to FIP by bucketing real pitcher seasons by IP (2005-2009 data). The graph plots the <i>median</i> FIP for each bucket, along with the <i>median</i> start percentage (% of innings thrown by individual pitchers in starting roles) for each bucket.</div>
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<a href="http://picasaweb.google.com/lh/photo/uqUSY5EbanCldnRj9VX6dhMXdkPFxccfzJHjXrBvTfE?feat=embedwebsite"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXWKCDd0cutVDJQNUSditFkq_E63ynX-kihSQrwJf68EDYR4fC77o0heOy4RoIUn2O-CjvBVS1rlUeQ3ZBdsUZbm6wInAn48yI3rMn4ajfNFIvb8fNgEqQASUtnCR5m6-aBO__7-zq6U0/s400/FIP_by_IP-buckets.gif" /></a></div>
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<a href="http://picasaweb.google.com/lh/photo/uqUSY5EbanCldnRj9VX6dhMXdkPFxccfzJHjXrBvTfE?feat=embedwebsite"></a>By looking at the median, rather than the average, it is easy to see where the transition from starters to relievers really takes place (as measured by IP). This is like chemistry class. As we move up the IP scale, the average pitcher has higher energy. However he needs to overcome a state change to move from full time reliever to full time starter. The 60-120 IP buckets find him in a state of transition. Supposing that these pitchers are all of roughly the same ability, and their FIP is different only due to role changes, I use the data to fit the following function (where start % is on a 0-1 scale):</div>
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trFIP = a + (start %) * b</div>
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Here "trFIP" represents a "translated FIP," which I assume to be constant, on average, throughout the transition. The best fit is for a = 3.92 and b = 0.81. Therefore for any pitcher:</div>
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trFIP = FIP + 0.81 (1 - start %)</div>
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Now FIP is meant to reflect the pitcher's skills at striking out hitters and at (not) giving up walks, but it also predicts ERA very well (at least for FIPs near the league average). The translated trFIP does not have this property. As Tom Tango showed, BABIP changes along with SO9 and HR9, so ERA increases more than FIP increases as relievers become starters. A similar exercise for ERA led me to this formula:</div>
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trERA = ERA + 1.19 (1 - start %)</div>
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However, trERA is not very useful in comparing talent levels between groups of pitchers. I can explain why, but let's get back to comparing groups of pitchers...</div>
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Back to trFIP, here is the same graph as before, but also with trFIP buckets by IP:</div>
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<a href="http://picasaweb.google.com/lh/photo/oJP1XRqYP50QzZUjbZNuzxMXdkPFxccfzJHjXrBvTfE?feat=embedwebsite"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjto_ahZwz-BON1Wqwt0W8lpNakdOWTqAc-0ivqzRpf-prT-As3sJn9Cdoau-KJ937au4iFS9Mhx92QcsaUhMlO_RnDrGbv_V14_JSVN2Z9_E03E5a7l95hGXmu3Q6Ga3rNUBh4TF3WncM/s400/FIP_and_trFIP_by_IP-buckets.gif" /></a></div>
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The graph between 60IP and 120IP is not <i>quite</i> flat. This is not surprising, as I am taking the <i>median</i> of individual trFIP values within the buckets. Some pitchers get the full 0.81 penalty, but not all do. I am taking the median of a combined distribution.</div>
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My study is not as thorough as Tom Tango's, but I like my results. My median trFIP buckets imply that your typical 60-80 IP pitcher from 2005-2009 is a <i>little bit better</i> than a typical 100-120 IP pitcher from the same time period. I think this is actually true. A 60-80 IP pitcher is very likely to be a high-IP reliever, such as a closer or setup man. He could also be a swing man/long man, but bear with me. A 100-120 IP pitcher is likely a back-end starter or also a swing man/long man who ended up filling in for an injured regular. Although the former is likely a failed starter, he must have found success in the bullpen to get such heavy use. At the very least, it is plausible to suggest that the top-end relievers are better overall pitchers than low-end starters, if only slightly.</div>
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The again, I might be reading too much into a small matter. Going forward, I will use trFIP as a simple measure of overall performance, which is not biased by changes in starter/reliever usage. It creates a useful benchmark, but is not meat to as an absolute definition of differences between starters and relievers.</div>
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Here is the same graph of average performance by pitcher type, but using trFIP instead of FIP:</div>
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<a href="http://picasaweb.google.com/lh/photo/YJr0AhzEUWdIdQ8AqSwtdxMXdkPFxccfzJHjXrBvTfE?feat=embedwebsite"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtDv570Lgc6OIMf7rjeFgEmKOrz6T8QQXIhmPb2XVcAx-MGflIPUu6UodVU_wKZ8KZerQjD9_zZ_6TMzwKJNBQEX68aI9uHjx6-a-eq7GvKlQNuo3jKZRFs2hJUfVt1ZZKdYIHoec-7f4/s400/types-for-web-w-trFIP.gif" /></a></div>
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The type 1 (cutter throwers) pitchers are still collectively the best of the groups, but the difference between type 2 (slider throwers with secondary pitches) and type 6 (slider throwers without secondary pitches) is eliminated by the differences in the trFIP adjustment.</div>
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Also trFIP shows type 0 pitchers and type 3 pitchers to be largely ineffective. Type 0 pitchers are those whose core pitch is a change-up, but who also throw other pitches, often sliders (as opposed to type 5 pitchers who throw change-ups, but with curveballs as secondary offerings). Type 3 pitchers throw both a slider and a curve, or possibly a slurve. </div>
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Type 3 pitchers are similar to both the type 2 slider-throwers and the type 4 curveball-throwers, but are more likely to become type 2 pitchers. Average trFIP seems to suggest that moving from type 3 to type 2 is not a bad move. This may just be confirmation bias, but the trFIP graph seems to suggest that throwing a slurve is, indeed, not an effective way to pitch. The fact that only 4% of pitchers feature both a slider and a curveball (but 70% featured one or the other) might also suggest the same. To be fair, successful type 3 pitchers Chris Carpenter and Adam Wainwright throw both a hard slider, and a slow curve. They are not throwing slurves. But most pitchers find more success with one pitch or the other, it seems.</div>
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Now that I have a way of comparing pitchers without concern for starter/reliever issues, I will look into what happens when pitchers switch types. Expect more charts, and maybe a confusion matrix.</div>Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com0tag:blogger.com,1999:blog-8942811343129148530.post-11159047313302638202010-05-02T16:28:00.000-07:002010-05-02T16:28:51.988-07:00Performance by Type (Intro)<a href="http://picasaweb.google.com/lh/photo/u8MIJnauBKqL-EzzTKZwtxMXdkPFxccfzJHjXrBvTfE?feat=embedwebsite"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7xmJP7CteH-JWl5Zu-AMW5Rd9PmpRhFC-wiI_KuLE_eWQKNjBYtxwL2bRP_hu-hdf8_I_RIai0V_63HoKUZCz_DPrcU6DR5LZD4FpZOXNDitz3Cye965x6Ee4w55Mtst2EjxR2O_NTBA/s400/performance-by-type.gif" /></a>
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Here is a graph of average pitcher performance by pitcher type, weighed by IP (over all pitchers with 20IP+ seasons).<br />
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There are non-trivial differences in strikeout rates, walk rates, and resulting FIP (HR9 rates are pretty constant, with a slight decrease for high-strikeout pitchers). However, there is not enough information in this one chart to jump to conclusions about what pitches to teach your 15-year old future major leaguer. Most clearly, pitchers can be successful by employing the methods of any of the eight pitcher types that I identified.<br />
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With selection bias playing a role, it is hard to conclude much from the raw differences between the performance of the pitcher types. However, the strikeout rates for type 6 and type 7 pitchers stand out, as compared to type 2 pitchers. Type 6 and type 2 are both fastball/slider pitchers, and yet type 6 pitchers have significantly higher strikeout rates. Type 6 pitchers surrender more walks, but still have lower FIPs than type 2 pitchers. However this difference can be explained by the facts that: type 6 pitchers throw harder fastballs on average (91.1 mph vs 90.1 mph), and they are much more likely to throw in relief (32% of innings vs 89% of innings).<br />
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Therefore, while it would be wrong to claim that type 6 pitchers are more effective then type 2 pitchers, it is fair to suggest that hard throwing fastball/slider pitchers (ie type 6) can be effective major leaguers by recording high strikeout rates, even if they can not control their walks very well. However, they are more likely to find success in relief roles with that repertoire.<br />
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I've often read that pitchers who are wild, inconsistent, or have limited repertoires should be relievers. I've also read that pitchers have the most value as starters, regardless of what they throw, as long as they guys out. <a href="http://www.fangraphs.com/statss.aspx?playerid=2692&position=P">Joba Chamberlain</a> has become somewhat of a contentious issue in this regard. I have read some respected writers claim emphatically that he should be a reliever (because of his stuff, and his temperament), and others just as strongly claim that he has the most value as a starter (even if his performance per inning suffer from the move).<br />
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In earlier posts, I wrote that Chamberlain's dramatic drop in strikeout rates (from 10.6 SO9 in 2008 to 7.6 SO9 in 2009) <a href="http://bezdomnybaseball.blogspot.com/2010/02/how-do-you-know-hes-unhittable.html">can be explained largely by his drop in average fastball speed</a> (from 95.0 mph to 92.5 mph). I argued that he never over-performed his expected SO9, relative to his fastball speed. Pitchers who throw 95 mph on average are <i>supposed</i> to have really high strikeout rates!<br />
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Now Joba Chamberlain is a typical type 6 pitcher, thinking about becoming a type 2 pitcher. He was a strong type 6 in 2008 (as well as in his magical 2007 debut). He became strongly type 2 in 2009 by throwing more curves, and adding a change-up. I guess he needed to expand his repertoire to make it as a starter.<br />
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In 2010, he is back to being a typical type 6 pitcher. Joba is throwing 65% fastballs, 32% sliders, 3% curves, and no change-ups. As a full time reliever, he has been pretty good so far (3.28 FIP and 8.7 SO9, albeit in only 10.1 innings). His fastball velocity isn't what it used to be, but it's up at tick at 93.1. The jury's still out on Chamberlain, but if I had to guess, I think he's a type 6 pitcher to stay. He can still be effective as reliever without a 95 mph average fastball, but he may unfortunately have peaked. That is strange to suggest for a guy who is only 24 years old, but he has lost some valuable velocity, and has not added much to his skill set.<br />
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Going forward, I will use my classifications to look at other pitchers' careers. This should illuminate some trends that simple averages of different pitcher types can not tell us.<br />
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Thankfully, pitchers change types quite often. In the last post, I mentioned some pitchers who have kept a consistent type for a long time. However, some pitchers re-invent themselves several times over a career. <a href="http://www.fangraphs.com/statss.aspx?playerid=1772&position=P">Rich Harden</a> started out as as a type 2 (slider with secondary), then was a type 7 (splitter with slider) for several years. More recently, he is a type 5 (change-up with curve) pitcher. All Star closer <a href="http://www.fangraphs.com/statss.aspx?playerid=1076&position=P">Ryan Franklin</a> has been a type 6 (fastball/slider only), type 2 (slider with other pitches), type 7 (splitter) and type 1 (cutter) in full seasons since 2002. This year, he is throwing lots of curve balls, and might end up as a type 4 (curveball with change-up backup)!<br />
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I look forward to analyzing this data more systematically. If you are interested in pitcher classifications for 2002-2009 (20IP+ seasons), they are <a href="http://spreadsheets.google.com/pub?key=tL9CP9AJ8Qv8zDBs_PHZXzg&single=true&gid=0&output=html">alphabetically listed here</a>. I have a notion of "weak membership" and "strong membership" for the categories, but I have not finalized it yet, so it's not included.Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com0tag:blogger.com,1999:blog-8942811343129148530.post-49134341351963953712010-05-02T14:58:00.000-07:002010-05-02T14:58:54.443-07:00Pitchers: Eight Different Kinds<br />
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I often read that: "pitcher X is similar to pitcher Y, so he should a) have similar performance b) age at the same rate c) experience a similar injury history." Sometimes the comparisons are based on height, weight, handedness, or otherwise, but usually we think of pitchers as being similar, if they deliver similar performance. Without advanced stats, we might consider pitchers similar if they had similar won-loss records or had similar strikeout rates. Now, some of us might think of pitchers as being similar if they are fly ball pitchers or ground ball pitchers, or if their fastball moves inside or outside to right-handed hitters. However, these categories all seem to reflect performance, to varying degrees.</div>
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My goal is to classify pitchers, in a performance-neutral way, based on the pitches that they throw. I will present eight categories that comprehensively classify pitchers into types, based almost exclusively on the percentages that they throw their pitches (collected for 2002-2009 by BIS and for 2007-20010 by PitchF/X, all viewable on <a href="http://www.fangraphs.com/">FanGraphs</a>).</div>
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<b>Why Classify by Pitches?</b></div>
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This is not to say that classification by factors other than pitch selection isn't interesting. We already classify pitchers by role (starter/closer/setup man) and by performance, in casual baseball conversations. However, I think it would be useful to classify pitchers by <i>how they pitch</i>, rather than by their results. In order to ask questions like "how do curveball pitchers age relative to other pitchers?" and "do fastball/slider pitchers make good starters?" it is necessary to have a way to classify pitchers based on what they throw, in a comprehensive and non-arbitrary way. (Declaring that a pitcher is a curveball pitcher if and only if he throws 25% curveballs seems too arbitrary, and unnecessarily restrictive.)</div>
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<b>Why Eight Categories?</b></div>
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Baseball Info Solutions (BIS) tracked & classified a large number of pitches for 2002-2009, giving us insight into how each pitcher's repertoire broke down over those years. This is the data that I use to derive my classifications. Since 2007, MLB has contracted Pitch F/X (same guys who do the virtual first-down line for NFL games) to track pitches in all major league stadiums. Their data is more comprehensive (Pitch F/X also tracks two-seam (sinking) fastballs), but it is available on a much smaller sample. (All of this data is hosted on FanGraphs and can be viewed for free.)</div>
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BIS recognizes seven pitches: fastball, slider, cutter, curve, change-up, splitter and knuckleball. A few months ago, <a href="http://bezdomnybaseball.blogspot.com/2009/12/pitcher-repertoire-depth-measure-of-how.html">I developed a system</a> to determine which of these were a pitcher's "core pitches," which were "secondary pitches," and which were pitches that he did not really throw (even if they had pitch counts over 0% according to BIS. Consider a pitcher who throws 70% fastballs, 25% sliders, and 3% change-ups and 2% curveballs. His core pitches are fastball and slider, while the others are not relevant. Now if he threw 70% fastballs, 20% sliders, 9% change-ups and 1% curveballs, we might says that fastball and slider are still his "core pitches," but "change-up" is now a "secondary offering." I classify pitchers based on these distinctions.</div>
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Over the course of a season, almost all pitchers' repertoires can be described as:</div>
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<li>core offerings: Fastball + 0-2 other pitches</li>
<li>secondary offerings: 0-3 other pitches </li>
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Actually, most pitcher seasons fall into an even tighter rule:</div>
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<ul>
<li>core offerings: Fastball + 1 other pitch</li>
<li>secondary offerings: 0-2 other pitches</li>
</ul>
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Therefore, the simplest way to describe a pitcher's repertoire is to name his core offering (ie the pitch he throws most often, not including his fastball). There is a strong correlation between the core offering and his likely secondary pitches. Pitchers who throw lots of curveballs tend to throw some change-ups, as well. Pitchers who throw splitters usually also throw sliders.</div>
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Since there are six possible pitches available as core offerings (not including the fastball, which everyone throws), there are six obvious categories. However, the knuckleball is so rare in today's game that I do not create a category based on it. Instead, there are five obvious categories (slider, cutter, curve, change-up, and splitter). In practice, more categories are needed, since not all pitchers who throw fastballs and sliders are truely similar, etc.</div>
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Using a simple clustering algorithm (SimpleKMeans using manhattan distance for the "core" and "secondary" pitches), I came up with seven categories. This was enough to get a category focused on cutters. I still needed a category for splitters, so I created one manually (by computing a centroid for all pitchers who throw a splitter). Then I tuned the weights and added other small considerations, so that the selection criteria for the categories were more intuitive.</div>
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<b>Eight Pitchers</b></div>
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Here are the eight pitcher categories that I came up with, along with explanations, examples, and obvious tendencies.</div>
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<b>Type 0: Changeup (Slider & Curve backup)</b></div>
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(14% of pitcher seasons)</div>
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The types start with 0, since nerds number their days 0-6.</div>
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A typical <i>type 0</i> pitcher throws 61% fastballs, 18% change-ups, 11% sliders, and 6% curves. They are most similar to <i>type 5</i> pitchers, although they are more likely to throw the slider, less likely to throw the curve, and less likely to be starting pitchers.</div>
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Sucessful <i>type 0</i> pitchers include:</div>
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<ul>
<li>Pedro Martinez (until 2006, when he became a <i>type 5</i>)</li>
<li>Felix Hernandez</li>
<li>Johan Santana (until 2007, when he became a <i>type 5</i>)</li>
</ul>
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<b>Type 1: Cutter (no common backup)</b></div>
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(4% of pitcher seasons)</div>
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A typical <i>type 1</i> pitcher throws 56% fastballs, 20% cutters, and various other pitches depending on the pitcher. <i>Type 1</i> pitchers are not similar to any other pitchers, but they are more likely to throw curveballs that sliders, which makes them somewhat similar to type 4 and type 5 pitchers. <i>Type 1</i> pitchers are likely to be starters, but some very successful closers are <i>type 1</i> pitchers.</div>
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Successful <i>type 1</i> pitchers include:</div>
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<ul>
<li>Mariano Rivera</li>
<li>Jon Lester</li>
<li>Andrew Bailey</li>
<li>Roy Halladay since 2007 (previously a type 4 pitcher)</li>
</ul>
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<b>Type 2: Slider (Change-up and Curve backup)</b></div>
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(18% of pitcher seasons)</div>
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<i>Type 2</i> pitchers are fastball/slider pitchers, who also throw other pitches at non-negligible rates. A typical <i>type 2</i> throws 62% fastballs, 18% sliders, 10% change-ups and 7% curves. <i>Type 2</i> pitchers are similar to <i>type 6</i> pitchers, but <i>type 2</i> pitchers are those that also have secondary offerings. <i>Type 2</i> pitchers are more likely to be starters than <i>type 6</i> pitchers, and also don't throw as hard.</div>
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Successful <i>type 2</i> pitchers include:</div>
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<ul>
<li>CC Sabathia</li>
<li>Zack Greinke</li>
<li>Jake Peavy</li>
</ul>
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<b>Type 3: Curve & Slider (no common backups)</b></div>
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(4% of pitcher seasons)</div>
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<i>Type 3</i> pitchers throw both a curve <b>and</b> a slider frequently enough for them to both be considered "core pitches." A typical <i>type 3</i> pitcher throws 57% fastballs, 18% curves and 16% sliders.</div>
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<div>
When I first saw this category, I thought these might be pitchers who throw a "slurve," or those pitchers who switched breaking pitches within a season. Those would end up in this category, to be sure, but successful <i>type 3</i> pitchers recently included some very good pitchers:</div>
<div>
<ul>
<li>Chris Carpenter (2005 and 2009)</li>
<li>Adam Wainwright (2005 and 2009, type 2 in between)</li>
<li>Matt Morris</li>
</ul>
<div>
<b>Type 4: Curve (with Change-up backup)</b></div>
</div>
<div>
(16% of pitcher seasons)</div>
<div>
<br /></div>
<div>
A <i>Type 4</i> pitcher throws 64% fastballs, 21% curves, and 9% change-ups. These pitchers typically throw very few sliders. They are most similar to <i>type 5</i> pitchers (who throw more change-ups), although a <i>type 4</i> pitcher can become a <i>type 3</i> pitcher if he starts to throw more sliders. </div>
<div>
<br /></div>
<div>
Successful <i>type 4</i> pitchers include:</div>
<div>
<ul>
<li>Roy Halladay before 2006 (now he's a type 1 pitcher)</li>
<li>Roy Oswalt</li>
<li>Ben Sheets</li>
<li>Justin Verlander </li>
</ul>
</div>
<br />
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<b>Type 5: Change-up (Curve backup)</b></div>
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(8% of pitcher seasons)</div>
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A typical <i>type 5</i> pitcher throws 62% fastballs, 23% change-ups, and 12% curves. <i>Type 5</i> pitchers are similar to <i>type 0</i> pitchers in that both rely heavily on the change-up. However <i>type 5</i> pitchers throw more curveballs, while <i>type 0</i> pitchers throw silders. Also <i>type 5</i> pitchers are the softest-tossing category that I considered, with a typical average fastball of only 89.1 mph.</div>
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Successful <i>type 5</i> pitchers include:</div>
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</div>
<ul>
<li>Cliff Lee (except 2007)</li>
<li>Tim Lincecum</li>
<li>Trevor Hoffman from 2002-2007 (currently type 0)</li>
<li>Tom Glavine</li>
<li>Greg Maddux</li>
</ul>
<div>
<b>Type 6: Slider (no backup)</b></div>
<div>
(32% of pitcher seasons)</div>
<div>
<br /></div>
<div>
<i>Type 6</i> pitchers are your prototypical fastball-slider flame throwers. A typical <i>type 6</i> pitcher throws 66% fastballs and 24% sliders, with 5% change-ups and no curveballs. <i>Type 6</i> pitchers are similar to <i>type 2</i> pitchers, but they throw fewer secondary pitches. When a slider-throwing <i>type 6</i> pitcher starts throwing a secondary pitch, be becomes a <i>type 2</i> and vice versa.</div>
<div>
<br /></div>
<div>
<i>Type 6</i> pitchers are the most common pitcher in MLB today, representing 32% of pitcher seasons from 2002-2009. They are the most common relief pitchers in baseball, but some successful starting pitchers were also <i>type 6</i> pitchers. <i>Type 6</i> pitchers often become <i>type 2</i> pitchers, but here are some successful <i>type 6</i> pitchers who have remained so throughout their careers:</div>
<div>
<ul>
<li>Randy Johnson</li>
<li>BJ Ryan</li>
<li>Joe Nathan</li>
<li>Brad Lidge</li>
<li>Josh Johnson </li>
</ul>
<div>
<b>Type 7: Splitter (Slider backup)</b></div>
</div>
<div>
(4% of pitcher seasons)</div>
<div>
<br /></div>
<div>
<i>Type 7</i> pitchers have become a rare breed, still I felt compelled to force a category for them. Splitter throwers have been some of the most successful pitchers of the last 20 years, so even if there are very few left in 2010, they are still worth separating them from the <i>type 6</i> pitchers that they most resemble. A typical <i>type 7</i> pitcher throws 60% fastballs, 15% splitters, and 10% sliders. </div>
<div>
<br /></div>
<div>
Successful <i>type 7</i> pitchers include:</div>
<div>
(4% of pitcher seasons)</div>
<div>
<ul>
<li>Roger Clemens</li>
<li>Curt Schilling</li>
<li>Hideo Nomo</li>
<li>Armando Benitez</li>
</ul>
<div>
Of course, Bruce Sutter is most famous for "inventing" the splitter. His version was thrown very hard, as a fastball with movement. Pitchers before him threw a split-finger pitch called a forkball, but that was more of a change-up. For some reason, the splitter has lost its popularity in the last few years, despite some of the best pitchers in recent history being avid proponents.</div>
</div>
<div>
<br /></div>
<div>
Typical <i>type 7</i> pitchers throw even harder (91.5 mph average fastball) than typical <i>type 6</i> slider-throwers (91.1 mph average fastball). This suggests that only hard-throwing slider-type pitcher ever become splitter-throwers. For some reason, recently very few <i>type 6</i> pitchers have attempted this transition. There are probably good baseball reasons why this is has been the case, but I don't know what those might be. I'm an expert on machine-learning classification, not pitcher mechanics!</div>
<div>
<br /></div>
<div>
Hopefully the classifications and examples sound intuitive & intriguing. FWIW, here is a <a href="http://spreadsheets.google.com/pub?key=tL9CP9AJ8Qv8zDBs_PHZXzg&single=true&gid=1&output=html">list of all 2009 pitcher seasons (over 20IP)</a> with type classification (seasons ranked by pitcher VORP).</div>
<div>
<br /></div>
<div>
Despite the fact that these classifications are made without any consideration for performance, there are definitely differences in average performance between the eight categories of pitchers. I will follow up to discuss some of those differences. However, I think the most useful aspect of my categories is their descriptive quality. Although they rely (almost exclusively) on comparing % breakdowns of pitches thrown, the categoires can be described simply and intuitively. Not all pitchers fit neatly into a category, but very few pitchers don't belong in any category at all. I have made simplifications by ignoring knuckleballs and different fastball types, but without these simplifications, the list of categories might be even longer. My aim is to be insightful, but simple. </div>
<div>
<br /></div>
<div>
I'm working on a site to host some of my data, including profiles for all pitchers, and their classifications by pitcher type. However, this will take some time. If you are interested in the type breakdown for a specific pitcher, <a href="http://spreadsheets.google.com/pub?key=tL9CP9AJ8Qv8zDBs_PHZXzg&single=true&gid=0&output=html">take a look at this list</a>, or contact me! </div>
<br />Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com5tag:blogger.com,1999:blog-8942811343129148530.post-69147803708382011352010-04-23T19:06:00.000-07:002010-04-23T19:06:45.108-07:00Pitcher injury effects on projected value (Part I: Overview)<br />
I often read about pitchers having high "injury risk," but what exactly does that mean? When projecting pitcher performance (for fantasy or otherwise), should I be concerned that a pitcher will miss time with injury, or that he will be ineffective when he pitches? I will try answer this question.<br />
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Of course, injuries are different, and even the same injury may have different effects on different pitchers. Just bear with me on this one. If modeling the effects of injuries on pitcher performance was easy, it would be less interesting.</div>
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<b>Measuring Pitcher Value</b></div>
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If a pitcher's value is defined as <i>runs saved</i>, then his value can can be expressed as:</div>
<blockquote>
Runs saved = Innings pitched (IP) * Runs saved per inning (ERA - replacement ERA)</blockquote>
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When we look at past performance, we may want to consider the pitcher's defense, park factor and run context. However if we are projecting future value, these issues can easily be ignored. I am projecting ERA before park and defense adjustments. Other factors effecting ERA are so small compared to variance in projections that these factors can easily be ignored.</div>
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<br /></div>
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A commonly used statistic to measure pitcher runs saved is <a href="http://en.wikipedia.org/wiki/Value_over_replacement_player">VORP</a>. Therefore in this study, I project VORP from my IP and ERA projections. A lot of very smart people (such as Tom Tango) have argued very convincingly that VORP sets the replacement ERA level way too low. They are right, but for this study, setting the replacement level for ERA is not very important, as long as it is consistent. FWIW, VORP sets the replacement level ERA to around 5.4 (although it does so via RA). If we set the replacement ERA level to something like 4.9 for relievers and 5.3 for starters (where I think it belongs), there would not be much of a difference to this study.</div>
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<br /></div>
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In any case, I am trying to see how injury data can help me predict VORP, both by changing IP projections, and by changing ERA projections.</div>
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<br /></div>
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<b>Data Sources & Results</b></div>
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<br /></div>
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I am using rich injury data from <a href="http://www.baseballinjurytool.com/">Corey Dawkins's injury tool</a>. Using this data, I generate features like "did he have surgery in year X," "did he hit the DL in camp," and "how many days did he spend on the DL."</div>
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<br /></div>
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I have written about <a href="http://bezdomnybaseball.blogspot.com/2010/03/elbows-shoulders-surgeries-seven-mini.html">using this data to improve IP projection</a>. Executive summary: there are several (7) categories of injuries that have large predictive effects on IP. </div>
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<br /></div>
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More recently, I looked at how injury data can improve my FIP projections. Some features were useful, but not nearly as many features as for IP projections, nor by as much. I will write more about the details of this work later. I project ERA by translating my FIP projections, so I will write about the two interchangeably. </div>
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<br /></div>
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Now that I have IP and ERA projections, both with and without injury features, I can compute four different versions of the VORP (runs saved) projection, and see which one is best at predicting actual VORP. Since pitchers without an injury history in Corey's database will not have their IP or ERA projection affected at all, I only include the pitchers affected by injury history. (These are all pitcher seasons 2005-2009 for which the pitcher either pitched or pitched the previous season & didn't retire. I'm trying to avoid selection bias by not ignoring projections for 0 IP seasons, or for little-used pitchers.)</div>
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</div>
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<br /></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
Correlation
to (real) VORP<o:p></o:p></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
STDEV from
baseline projection<o:p></o:p></div>
</td>
</tr>
<tr style="mso-yfti-irow: 1;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
Basic (no
injuries)<o:p></o:p></div>
</td>
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0.587<o:p></o:p></div>
</td>
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0.0<o:p></o:p></div>
</td>
</tr>
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ERA with
injuries<o:p></o:p></div>
</td>
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0.599<o:p></o:p></div>
</td>
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1.2 VORP<o:p></o:p></div>
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IP with
injuries<o:p></o:p></div>
</td>
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0.619<o:p></o:p></div>
</td>
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2.8 VORP<o:p></o:p></div>
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ERA &
IP with injuries<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
0.624<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
3.2 VORP<o:p></o:p></div>
</td>
</tr>
</tbody></table>
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<br /></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
Using injury data improves my ability to project both IP and ERA. However, IP changes are both more useful in predicting VORP, and they are also larger in the average effect on VORP.</div>
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<br /></div>
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None of this is surprising. If we know that a pitcher had Tommy John surgery last year, we should expect his IP to drop (usually to 0 IP) the next season. Also, we can project his IP to recover the season afterward to a higher than he would be otherwise projected. However, how should we expect his ERA to change when he comes back? It's hard to say.</div>
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<br /></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<b>Why injuries don't affect ERA/FIP projections much</b></div>
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<br /></div>
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Even for injuries that do not typically lead to a missed season, the effects on ERA are harder to predict than the effects on IP. Whereas there were 35 individual injury features that affect the IP projections, only 5 injury features had any effect on FIP projection (that my model was able to pick up). Here are those features:</div>
<blockquote>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
-0.4223 *
inj_elbow_surg_not_tj_2008 </div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
+ 0.0671 *
inj_anyDL_2008 </div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
+ 0.1826 *
inj_dl_camp_2008 </div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
+ 0.1641 *
inj_anyDL_average </div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
+ 0.2736 *
inj_surgery_ip_average</div>
</blockquote>
Without completely explaining my notation, FIP projections increase if a pitcher was DL'ed last year, DL'ed in camp before the current season, or DL'ed in the previous three years. Recent non-Tommy John elbow surgery lowers the FIP projection, although any recent surgery increases the FIP projection.<br />
<br />
The features are pretty non-specific, and the changes are not large (very few pitchers have their FIP projections affected by more than +- 0.3 FIP). Mostly, the injury features allow my model to reward pitchers who <b>did not</b> hit the DL or undergo surgeries in recent years. Contrast this to the <a href="http://bezdomnybaseball.blogspot.com/2010/03/elbows-shoulders-surgeries-seven-mini.html">extensive injury-based adjustments</a> that I found for my IP model.<br />
<br />
<b>Selection bias?</b><br />
<br />
I was surprised not to find stronger effects on FIP from injury features. Maybe there is a selection bias in the way I look for effects on FIP? After all, if a pitcher can't pitch well, maybe he will throw fewer innings and thus not be included in the data set?<br />
<br />
For my FIP training, I include <b>all</b> pitcher seasons. However, I weigh instances by the inverse of expected FIP variance, estimated from real IP. I wrote about this in my <a href="http://bezdomnybaseball.blogspot.com/2010/04/how-to-weight-fipera-instances-by-ip.html">previous post</a>. The lower the pitcher's actual IP, the less weight I put on projecting his FIP correctly. However the effect for IP > 30 is small, and no pitcher seasons are completely excluded.<br />
<br />
Still, to check for bias, I trained an FIP model on pitchers with 40+ IP, giving all of them equal training weight. Then I looked at the effects of injuries on this model. Nothing much changed.<br />
<br />
Another possible manifestation of the selection bias might be that pitchers who are below-average to begin with can't handle an injury-based performance drop, and so pitchers who over-perform after injuries are over-represented? To test this possibility, I excluded all pitchers with a projected FIP > 4.2 (without considering injuries). Now I trained an injury model. Again, no noticeable changes.<br />
<br />
<b>Conclusions? Effects on Fantasy?</b><br />
<br />
I am not going to claim that injury history can not help predict FIP/ERA. However, while it was fairly easy to find many injury features that have a significantly positive effect on predicting IP, that was not true for predicting FIP/ERA. Moreover, the features that do effect FIP/ERA projection tend to be fairly general, while some very specific features affect IP projection. I'd love to see someone else research this issue and come up with better results, but this is what I got.<br />
<br />
If my observations prove to be true, what does this mean for projecting "injury risk" for fantasy pitchers?<br />
<br />
Beyond the "he had Tommy John surgery, don't draft him," there are many cases where a pitcher has significant risk of missing time due to injury. The clearest example of this is for major shoulder injuries. Pitchers with shoulder-related DL stints are always at risk for another stint on the DL, whether or not they had surgery on the shoulder, and whether or not they were injured recently.<br />
<br />
However, there is no noticeable effect on FIP/ERA from past shoulder injuries when projecting future performance based on past results. Therefore, <b>if he plays</b>, there is no statistical reason to expect a dip or to expect a rise in ERA based on a history of shoulder injuries. If you want an high injury-risk sleeper for your fantasy team, take a pitcher with a dodgy injury history, but strong recent performance when healthy.<br />
<br />
However if a pitcher's recent performance wasn't good, don't think it will improve after surgery. Surgery is meant to get a player back on the field. Those effects are consistent enough to measure. However surgery does not typically improve pitcher performance. I am trying to find examples where is does, but I have yet to find any.<br />
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<br /></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
I will follow up with some specific examples, and with updated projections for 2010. I know the season has already started, but I think it's still early enough to make some of those projections interesting. </div>Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com0tag:blogger.com,1999:blog-8942811343129148530.post-88728911889037888682010-04-11T17:54:00.000-07:002010-04-11T17:54:19.875-07:00How to weight FIP/ERA instances by IPI like training on all of the available data, rather than only on data from "necessarily high IP sample size". However if I am trying to establish a relationship (between fastball speed and strikeout rate, between FIP and ERA, or between past and future ERA, for example), I can not simply use samples based on 5 IP and 200 IP in the same way. When fitting a function to my data, I will invariably generate larger errors for those data points based on smaller sample sizes. Thankfully, I have a 60's era statistics book to help me out. According to M.G. Bulmer in <i>Principles of Statisics</i>:<br />
<blockquote>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
If the form of the relationship between the variance of <i><b>Y</b> </i>[dependent variable] and <i><b>x</b> </i>[independent variable] is known, for example if the variance is known to be proportional to<b> </b><i><b>x</b></i>, more efficient estimators can be obtained by weighting the observations with weights inversely proportional to their variances. In general, however, small departures from normality or homoscedasticity will have little effect on inference about the regression line and may be ignored.</div>
</blockquote>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
In other words, if we can approximate the variance of our dependent variable by some function, then we can weight all data points in reverse proportion to that variance. But if the function does not suggest large differences in variance, we need not bother with the weighting.</div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<br /></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
Therefore, while many baseball studies are based on data points pruned by IP cutoffs, my studies use all available data, but with points weighted by the inverse of those points' variance (variance in whatever I am predicting), estimated based on the IP for the data point. This necessarily means that I have to compute a variance function every time I want to predict something new. Strikeout rates, ERA, FIP, etc all have different variance based on IP of the sample size. For every new dependent variable, I have to compute observed variance data points, plot them on a graph, and find a fit for this curve. However, this is no worse than picking (often arbitrarily, or worse, deliberately) an IP cutoff for one's baseball studies.</div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<br /></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
If you wanted to do a study predicting ERA or FIP from something (your independent variables are unimportant), you can take a shortcut by using my ERA and FIP variance estimates, based on single-season IP.</div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<br /></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
To approximate variance at each plotted data point (ie group of 320 pitcher seasons), I computed the RMS (root mean squared) error between real ERA (or FIP) and my basic projection system for ERA (or FIP). I could just use RMS deviation from the mean of each sample, but that would use incorrect baselines for the individual pitchers. My projection system is simple a statement of previous ERA/FIP, regressed toward the league average. Therefore, deviation from my simple estimate is a better measure of variance than is deviation from the mean of each sample.</div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<br /></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
Here are the data points for the observed ERA and FIP variance, along with my fits for that variance. The ERA and FIP variance is plotted on a logarithmic scale.</div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<br /></div>
<a href="http://picasaweb.google.com/lh/photo/pmpNpkNNLeJxPJbqHbff4hMXdkPFxccfzJHjXrBvTfE?feat=embedwebsite"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimJznaUDIIRofIJ4KFKaxddkWboOFA08zqdDVqZyT4g9SS9399BJKARouNT_Un9k9Gzyt74t3VmcNTChD2GcIBAaU9FCEZm71ZRxlaIx5OQbEixkkrgubhdfkJ3JIvn_8CMxp3o9vnZiQ/s400/ERA-FIP-error-by-IP_log_scale.gif" /></a>
<br />
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<br /></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
I fit both ERA and FIP variance to functions of the following type: (Also I minimize <i>relative</i> (rather than absolute) error at the data points, so as not to over-fit my function to the very low IP points.)</div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<br /></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
RA_VAR = A * (IP)^(B) + C</div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<br /></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
Here, <b>C</b>-term represents the ERA/FIP variance that one might expect from a very high IP sample, while the first term represents the variance differences between different IP sample sizes.</div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<br /></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
The variance functions for ERA/FIP are:</div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<br /></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
FIP_VAR = 296 * IP^(-1.63) + 0.32</div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
ERA_VAR = 994 * (IP)^(-1.66) + 0.58</div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<br /></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
Since both functions have the same <b>B</b> term, it looks like variance for FIP and ERA converges at the same rate. Variance for ERA is always higher, which should surprise no one, but it's interesting that FIP does not converge faster than ERA, since it eliminates luck based on BABIP and other defense-related factors.</div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<br /></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
In any case, since the variance estimates converge at similar rates, M.G. Bulmer's book tells us that they can be used interchangeably without any effect on inference.</div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<br /></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
Therefore, if you are doing a study that looks at the effects of *something* on pitcher season ERA or FIP, you can use the FIP_VAR formula above to properly weight your data points, in order to compensate for variance caused by differences in IP sample size.</div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<br /></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
To get a feel for this function, here is a chart of suggested weights for various IP samples:</div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<br /></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
</div>
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<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 112.6pt;" valign="top" width="113"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
IP<o:p></o:p></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 121.6pt;" valign="top" width="122"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
1.0 / FIP_VAR<o:p></o:p></div>
</td>
</tr>
<tr style="mso-yfti-irow: 1;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 112.6pt;" valign="top" width="113"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
5<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 121.6pt;" valign="top" width="122"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
0.05<o:p></o:p></div>
</td>
</tr>
<tr style="mso-yfti-irow: 2;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 112.6pt;" valign="top" width="113"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
10<o:p></o:p></div>
</td>
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0.14<o:p></o:p></div>
</td>
</tr>
<tr style="mso-yfti-irow: 3;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 112.6pt;" valign="top" width="113"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
20<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 121.6pt;" valign="top" width="122"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
0.39<o:p></o:p></div>
</td>
</tr>
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<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 112.6pt;" valign="top" width="113"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
40<o:p></o:p></div>
</td>
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0.96<o:p></o:p></div>
</td>
</tr>
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80<o:p></o:p></div>
</td>
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1.81<o:p></o:p></div>
</td>
</tr>
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160<o:p></o:p></div>
</td>
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2.53<o:p></o:p></div>
</td>
</tr>
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<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 112.6pt;" valign="top" width="113"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
240<o:p></o:p></div>
</td>
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2.79</div>
</td></tr>
</tbody></table>Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com0tag:blogger.com,1999:blog-8942811343129148530.post-22181548930477085252010-04-10T15:19:00.000-07:002010-04-10T15:19:09.533-07:00FIP & ERA baselines from projected IP (an alternative take on replacement level)In my <a href="http://bezdomnybaseball.blogspot.com/2010/04/predicting-era-trials-tribulations.html">last article</a>, I complained that my FIP/ERA projection system tends to regress all pitchers to the same baseline (around 4.6 FIP/ERA). This is an appropriate MLB average, but fringe pitchers (especially starters) should probably be regressed to a much lower baseline. So here, I show what such a baseline might look like. Incidentally, this can also be used to compute the "replacement level" FIP/ERA for starters and relievers.<br />
<br />
The question I set out to answer was: given an IP projection (split by starter IP and reliever IP), what FIP/ERA should I expect from a pitcher? If I map <b>actual</b> IP to ERA, then I get a very nice graph with the properties that one would expect. But this graph is biased by the survivor effect. Better pitchers throw more innings, even if they start out with lower expectations.<br />
<br />
Instead, what if we graph <b>expected</b> IP to actual FIP/ERA? Now we can answer a questions like: "what FIP/ERA should a team expect from a fringe starter (projected for 30.0 IP as a starter, or about five starts)?" My IP projection system is trained on <i>all</i> apitcher seasons from 2005-2009, including low-IP, high-IP and 0 IP seasons, so it projects realistic IP for all pitchers, not just the good ones. Also it gives separate estimates for starter IP and reliever IP.<br />
<br />
Using actual performance for all pitcher seasons, I separated the pitchers into two groups:<br />
<ol>
<li>IP >= 1 and (starter IP) >= 40% * (total IP)</li>
<li>IP >= 1 and (starter IP) < 40% * (total IP)</li>
</ol>
<div>
This is my categorization into "mostly starters" and "mostly relievers." The cutoff might seem arbitrary, but it separates the starter and relievers quite well. I could have left out a batch of pitchers around 50%, but I don't like excluding examples from my training sets, and there are not many such pitchers in any case.</div>
<div>
<br /></div>
<div>
Now I rank "mostly starters" by <i>projected starter IP</i>, and I rank "most relievers" by <i>projected reliever IP</i>. Within each group of 320+ pitcher seasons, I find the median FIP and raw ERA. Thus I create the series that are mapped below:<br />
<br /></div>
<a href="http://picasaweb.google.com/lh/photo/tNxTSfWal4kNXPYtIWxd-hMXdkPFxccfzJHjXrBvTfE?feat=embedwebsite"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYO7Se330KHvACllc-VHxwJXFHRhx_husCSndC25TdGUlVm5jSFV33A6udTNJB5ftNVn89eCLWPz5hCcT8Kw2jq7fyIEErJL3dUBeysFN1OrWmB2R3KhqLtmwN8S4SnxH3KVuPnhLh9WQ/s400/ERA-FIP-by-proj-IP-start-and-rel-smaller.gif" /></a>
<br />
<div>
<br />
If some of that is confusing, let me explain that again with an example. Take the "mostly starter" IP series. The highest IP datapoint occurs at IP = 165.4. That is the median projected IP_Start for the top 320 pitchers seasons, ranked by projected IP_Start, provided that those pitchers threw at least 1 IP, and that 40% of their IP came as starters. These pitcher seasons include:</div>
<div>
<ul>
<li>Johan Santana (2009), projected to throw 214 IP (threw 166.2 IP)</li>
<li>Brandon Webb (2009), projected to throw 206 IP (althrough he only threw 4.0 IP)</li>
<li>Does not include Ben Sheets (2009), since he threw 0 IP.</li>
</ul>
<div>
I hope that makes things more clear.</div>
</div>
<div>
<br /></div>
<div>
Within a group of 320+ pitcher seasons (I use larger samples at the lower IP data points), I computed the median FIP and ERA, regardless of the IP for each instance. So in the example above, Johan Santana's ERA based on 166.2 IP in 2009 would be used on the same scale as Brandon Webb's ERA based on 4.0 IP in 2009. I purposely don't weight the instances by IP, since that would introduce survivor bias. Without biasing myself toward how many innings the pitchers actually ended up throwing, I want to know: given a projection of "X IP_Start" and "Y IP_Relief", what is a baseline for that pitcher's ERA and FIP.</div>
<div>
<br /></div>
<div>
<b>Replacement Level</b></div>
<div>
<br /></div>
<div>
Incidentally, my graph also suggests possible replacement levels for starters and relievers. If we view replacement level as the level of performance that can be easily acquired from the waiver wire or from the minor leagues, then the low-end FIP/ERA projections from the graph should offer some guidance.</div>
<br />
For relief pitching, the median FIP for low-end projections is around 4.5 (ERA 4.6-4.7). For starting pitching, the median FIP on the low-end is around 4.8 FIP, but the median ERA is around 5.3.<br />
<br />
The low-end starter group might look like an outlier, but the median FIP/ERA are based on 400 pitcher seasons with the lowest IP_Start projections, but for those who actually pitched mostly as starters. This group had an average <i>actual</i> IP of 58.9 (52.0 IP as starters). The median <i>actual</i> IP was 42.7 (34.5 as starters). Therefore the group is a good representative of pitchers who one would not have expected to start many innings, but were pressed into starter roles and typically started multiple games. I believe they represent a good estimate of the kind of production a team might get from a spot starter pulled from the bullpen, or from a starter pulled up from AAA.<br />
<br />
Going forward, I will use assume the following FIP and ERA (league-neural and park-neutral) replacement levels to fill a team's "missing innings" in projecting overall team ERA and overall pitcher VORP:<br />
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-insideh-themecolor: text1; mso-border-insideh: .5pt solid black; mso-border-insidev-themecolor: text1; mso-border-insidev: .5pt solid black; mso-border-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 191;">
<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Times, 'Times New Roman', serif;">FIP<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Times, 'Times New Roman', serif;">raw ERA<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Times, 'Times New Roman', serif;">Starter<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Times, 'Times New Roman', serif;">4.9<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Times, 'Times New Roman', serif;">5.3<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Times, 'Times New Roman', serif;">Reliever<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Times, 'Times New Roman', serif;">4.5<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Times, 'Times New Roman', serif;">4.6<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<br />
This is not the only way to estimate replacement level for pitchers, but these are the values most consistent with my individual projections. If one were to use a different system to project IP, then one would get different results. However I don't know of another system that accurately projects IP_Start and IP_Relief for low-end pitchers. Compared to my system, <a href="http://bezdomnybaseball.blogspot.com/2010/03/2010-ip-projections.html">PECOTA and CHONE massively over-estimate the IP for low-end pitchers, especially rookies</a>.<br />
<br />
<b>FIP vs ERA disparity</b><br />
<br />
Since FIP is meant to predict ERA (after removing the differences due to defense and BABIP luck), it may seem strange that replacement starter ERA is 0.4 runs higher than replacement starter FIP. However students of DIPS will know that FIP tends to under-estimate ERA for bad pitchers, and over-estimate ERA for good pitchers.<br />
<br />
My graph seems to suggest that FIP trails ERA nicely in the range (4.1, 4.7), but the relationship starts to break down beyond that range. This is (in part) because FIP assumes that:<br />
<ul>
<li>pitcher skills are limited to strikeout rate, walk rate and home run rate</li>
<li>these skills are linearly related to ERA</li>
</ul>
<div>
Both of these relationships break down on the high end and the low end of pitcher performance. Elite pitchers tend to have lower BABIPs than do average pitchers (although luck and defense constitute most of the BABIP difference for individual cases). Also elite pitchers tend to be better than average at secondary skills like holding runners, situational pitching, and fielding their position. Conversely, low-end pitchers are worse than average at all of these skills. Also, <a href="http://www.tangotiger.net/rc2.html">since outs have a non-linear relationship with runs</a> (the more outs a pitcher produces, the less valuable each extra out is), pitchers who get very few easy outs (strikeouts, popups or soft ground balls) tend to have an even higher ERAs than can be linearly approximated from the factors of FIP. Think of <a href="http://www.fangraphs.com/statss.aspx?playerid=1029&position=P">Adam Eaton</a> of 2007-2009. His FIP and xFIP were bad, but his ERA was consistently even worse.</div>
<br />
<b>Effects on Team Pitching Projections</b><br />
<br />
Armed with new replacement levels for starters and relievers, I should have better team pitching projections soon. Since there is a large separation between replacement level for starter ERA and reliever ERA, teams will suffer disproportionately depending on whether their "missing innings" (ie those innings not filled by IP projections for pitchers on their opening day roster) will need to be starter of reliever innings. The Nationals, with holes in their rotation, will have to fill those missing innings at a higher ERA than the Royals, who have a set rotation, but will need to fill some of their bullpen at replacement level.<br />
<br />
Teams will get no credit for relievers projected to post an ERA above 4.9, but will get credit for any starters with projected ERA below 5.3 (before league and park adjustments). This will make my projections much more accurate, even if they are now being made a little too late to count as pre-season predictions.<br />
<br />
<b>Davis, Buehrle, Feliz and Mariano Rivera</b><br />
<br />
Also the baselines help me to resolve a couple of specific problems I noticed for individual pitchers. I projected <a href="http://www.fangraphs.com/statss.aspx?playerid=7441&position=P">Wade Davis</a> at a lower FIP and ERA than <a href="http://www.fangraphs.com/statss.aspx?playerid=225&position=P">Mark Buehrle</a>. Davis pitched well in 36 IP as a rookie in 2009, and his ERA, FIP and xFIP were all better than Buehrle. However there is no way that one should project him to be better than Mark Buehrle in 2010. The baseline FIP/ERA for starters by projected IP allow me to fix this problem. In the new FIP and ERA projections, I am regressing pitchers to their individual baselines, rather than to the MLB baseline of 4.6. This will help Mark Buehrle.<br />
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-insideh-themecolor: text1; mso-border-insideh: .5pt solid black; mso-border-insidev-themecolor: text1; mso-border-insidev: .5pt solid black; mso-border-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 191;">
<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
IP Start
(projected)<o:p></o:p></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
IP Relief
(projected)<o:p></o:p></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
FIP
baseline<o:p></o:p></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
ERA
baseline<o:p></o:p></div>
</td>
</tr>
<tr style="mso-yfti-irow: 1;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
Wade Davis<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
90.5<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
9.4<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
4.69<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
4.78<o:p></o:p></div>
</td>
</tr>
<tr style="mso-yfti-irow: 2; mso-yfti-lastrow: yes;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
Mark Buehrle<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
178.0<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
0.9<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
4.16<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
4.16<o:p></o:p></div>
</td>
</tr>
</tbody></table>
<br />
Similarly, I projected Neftali Feliz to post a lower FIP & ERA than Mariano Rivera in 2010. This is even more unreasonable, and new baselines should fix this:<br />
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-insideh-themecolor: text1; mso-border-insideh: .5pt solid black; mso-border-insidev-themecolor: text1; mso-border-insidev: .5pt solid black; mso-border-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 191;">
<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 99.9pt;" valign="top" width="100"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 77.2pt;" valign="top" width="77"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
IP Start
(projected)<o:p></o:p></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
IP Relief
(projected)<o:p></o:p></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
FIP
baseline<o:p></o:p></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
ERA
baseline<o:p></o:p></div>
</td>
</tr>
<tr style="mso-yfti-irow: 1;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 99.9pt;" valign="top" width="100"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
Neftali
Feliz<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 77.2pt;" valign="top" width="77"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
11.2<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
28.7<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
4.57<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
4.73<o:p></o:p></div>
</td>
</tr>
<tr style="mso-yfti-irow: 2; mso-yfti-lastrow: yes;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 99.9pt;" valign="top" width="100"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
Mariano
Rivera<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 77.2pt;" valign="top" width="77"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
8.9<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
55.5<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
4.13<o:p></o:p></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
3.93<o:p></o:p></div>
</td>
</tr>
</tbody></table>
<br />
Once I iron out a few more kinks, I should have new FIP, ERA and VORP projections for both individuals and teams. I have not yet done much with park adjustments, other than to adjust the individual and "missing innings" ERA projections to the team's park factor from 2009. It would be nice to consider a pitcher's park factor in terms of specific effects on HR rate, but everything that I've read on this issue seems to suggest that park <a href="http://www.hardballtimes.com/main/article/home-run-park-factor-a-new-approach/">HR factors vary too much year to year</a> to be of much use. With so many teams having changed stadiums in the past few years (or having changed major characteristics of the field, wind patterns or the ball itself), long-term park factors do not seem very useful for predicting future park factors. I'd rather use a cruder park factor that is more current.Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com0tag:blogger.com,1999:blog-8942811343129148530.post-45019500703584662010-04-07T15:53:00.000-07:002010-04-07T15:56:56.071-07:00Predicting ERA (the trials & tribulations thereof)<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Unlike my IP predictions, what I did for ERA/FIP was very simple. In fact, my 2009 analysis showed that my ERA predictions (retroactively, and in sample) were no better than CHONE's ERA predictions (made before the 2009 season, so obviously out of sample). My 2009 retroactive IP predictions were also in-sample, but they were </span><i><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">much</span></i><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> better than those of PECOTA or CHONE, and my methods were clear and logical (even if the actual formula was somewhat complicated).</span><br />
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span><br />
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">However, I think even my simple ERA projection system worth explaining, if only to organize my thoughts in regard to making future improvements.</span><br />
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span><br />
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Building an ERA prediction model involves two major choices:</span><br />
<ul>
<li><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">How do we select and weigh instances (ie pitcher seasons)?</span></li>
<li><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Do we want to predict ERA, RA, FIP, or something else?</span></li>
</ul>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">It isn't obvious at first why these choices might be important. Indeed, one could build a decent system (Tom Tango's MARCEL) by completely ignoring them. MARCEL predicts that future ERA should be a linear combination of previous years' ERAs. Then one might make adjustments by considering a pitcher's defense, park factor, age, and the natural regression toward the mean. However, if one is to build a regression model (which is what I'm doing here, mostly), then one must consider how to properly weigh his instances, and whether we should be predicting ERA directly, or whether we should predict something else that translates into ERA easily. Let me explain why.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<b><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Weighing instances by sample size</span></b></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">In 2009, </span><a href="http://www.fangraphs.com/statss.aspx?playerid=1692&position=P"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Brandon Webb</span></a><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> posted an ERA of 13.50. He wasn't terribly unlucky with defense or balls in play, since his FIP was 10.85. Ok, he was unlucky with home runs, so his xFIP was 6.05. How significant is all this? Were all the predictive systems wrong in predicting Webb for an ERA below 4.0? Of course not! Brandon Webb pitched only 4.0 IP in 2009.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">When we evaluate (or train) predictive models, there are two ways of handling cases like Webb's. We can either throw them out using an IP cutoff. Or we can reduce the significance of outliers. Or we can reduce the significance based on a non-constant instance weighting model (ie we don't treat errors for all pitchers on the same scale). Ok that's three methods, but the last two are versions of the same idea.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Most analysis comparing model or training models just throws out the low-IP cases. However, where do we draw the cutoff line? Perhaps we don't care about predicting ERA for guys who only throw 40+ IP, since the variances for those guys is so high anyway. But what makes a 41 IP guys significant, but a 39 IP guy insignificant? I like using all of the data!</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">In training predictive models, as in training in the gym, specificity of training applies. One gets better at rock climbing (or running, or pitching) by climbing rocks (or running, or throwing a baseball). Similarly, if we want to predict ERA for guys who throw less than 40 IP in a season, we must include 40 IP cases in our ERA training. </span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">I discussed all of this at length when I wrote about </span><a href="http://bezdomnybaseball.blogspot.com/2010/02/handling-small-sample-sizes-k9-variance.html"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">training strikeout rate (SO9) models</span></a><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">. Here is a graph of my basic SO9 prediction model's error, bucketed by IP:</span></div>
<a href="http://picasaweb.google.com/lh/photo/lfl-fICwsTbfpKvjNT75KA?authkey=Gv1sRgCLaNoIGW2MfxYw&feat=embedwebsite"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfkRnz1YDDde523pViW4oHr4do_Ow1jqN9k8naceKYPxmHxYyr4q2wmGsqAzPKpyITOMDmNlJOK6UeO5WRsADGBRvuKjB1xjwE_GeMILtdFwV2eAAuAYcBXMvOUdDJTrVUje8zUK-ZLKs/s400/K9-variance-by-IP.png" /></span></a><br />
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">In the graph above, I refer to SO9 error as "VAR" and "STDEV" since modeling error by IP allows us to estimate SO9 variance and standard deviation by IP. Assuming that my model is not biased in predicting SO9 for pitchers with different IP, the difference in SO9 error must reflect the variance in observed SO9.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">If we weight training instances by 1/(expected VAR), then it is possible to build a model that trains on </span><i><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">all of the data</span></i><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">, but assigns less meaning to prediction errors for cases that have a known high variance in the independent variable. Since we can set the baseline arbitrarily, and only relative differences in weights are meaningful, I set the baseline to 100 IP --> 1.0 training weight. Here are some training weights for the strikeout model, based on 2009 pitcher seasons:</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-insideh-themecolor: text1; mso-border-insideh: .5pt solid black; mso-border-insidev-themecolor: text1; mso-border-insidev: .5pt solid black; mso-border-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 191;">
<tbody>
<tr>
<td style="border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Pitcher
Season<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">IP<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Instance weight<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Zack
Greinke_09<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">229.3<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">1.72<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Mariano
Rivera_09<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">66.3<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">0.82<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Matt
Capps_09<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">54.3<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">0.73<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Brandon
Webb_09<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">4.0<o:p></o:p></span></div>
</td>
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<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">0.15<o:p></o:p></span></div>
</td>
</tr>
<tr>
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<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Ivan
Bezdomny_09<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.05in;" valign="top" width="148"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">0.0<o:p></o:p></span></div>
</td>
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<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">0.0<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
</div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">By using a system like this one, it's possible to include Brandon Webb's results in my training set, without giving them unfair weighting (and thus regressing too far toward the mean for guys with more meaningful sample sizes).</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">As my </span><a href="http://bezdomnybaseball.blogspot.com/2010/02/handling-small-sample-sizes-k9-variance.html"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">SO9 article showed</span></a><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">, this method (compared to simple IP cutoffs with equal weights assigned to all instances) had the same error on higher-IP pitchers, but had much lower error for low-IP guys. As the specificity of training principle would indicate, you can't predict instances well if you don't train on similar instances.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Since FIP suggests that ERA is linear in respect to SO9 rates, I simply used the SO9 formula to weight ERA training instances. This is lazy. I should compute a new formula for estimating ERA variance from IP, but I doubt the difference would make a noticeable difference. As long as the ERA variance follows a similar graph to SO9 variance, with a similar exponent, the difference would be negligible. </span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<b><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Should we predict ERA directly?</span></b></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Whether we weight pitcher seasons as described above, or exclude all low-IP pitcher seasons, it's very hard to predict ERA much better than assigning a league average to all pitchers. A simple model predicting ERA from previous years' ERA, FIP and QERA gave me no better than a 0.22 correlation (r) with the actual data. In part, this is due to park and league factors. While the vast majority of pitchers should be predicted to an ERA of between 4.0 and 5.0, league and park factors can affect ERA by +-0.3 runs or more. The average run context for the White Sox is about 0.7 R/G higher than for the Giants. About 93% of that difference is attributed to ERA. Run factor differences and the variance due to defense and BABIP luck dwarf the skill differences for most pitchers.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Of course, we could even out some of those differences by removing the BABIP luck, the defense, and the park factors from a pitcher's performance. Or we can predict FIP, which does most of those things already. Within the DIPS (Defense Independent Pitching Statistics) family of stats, FIP may not be the most accurate ERA approximate, but it's a simple stats, and more complex stats are not provably more effective predictors of park-neutral ERA. The FIP formula predicts ERA simply from strikeout rate, walk rate and HR rate:</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">FIP = (HR*13 + BB*3 - K*2)/IP + 3.2</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">While FIP is not quite park or league neutral, it is less biased by park factors than ERA. Also since FIP explicitly ignores the sequencing and interaction between home runs, walks and strikeouts, it is possible to adjust those rates independently for park and league context. Walk rates do not change much my league or park, but </span><a href="http://bezdomnybaseball.blogspot.com/2010/02/dear-mr-cashman-no-more-nl-starters.html"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">strikeout rates change significantly by league</span></a><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">, and HR rates are different for each major league park. Best of all, one can predict FIP in a straightforward manner (from previous FIP and QERA) at a 3.2 correlation (r) with the real FIP.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Here is another way of thinking about this:</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">I build an model to predict ERA that takes previous difference in past ERA/FIP between pitchers into account. It's trying to do the right thing, but variance due to park factors and BABIP luck is so high that the system freaks out and sets everyone to around a 4.6 ERA.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Alternatively, I build a model to predict FIP. The differences between pitchers are roughly the same as before. But by eliminating BABIP luck and by reducing the variance to to park factors, the model is more confident in assigning FIP predictions further away from the mean.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">I chose the blue pill, and I think it should be pretty clear why.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<b><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Conclusions & Ongoing Work</span></b></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Comparatively, a non-regression system like MARCEL takes past performance as an indicator of future performance, without giving consideration to deviation from the mean. It is more likely to predict exceptional cases well (since it's not afraid to stray from the baseline prediction), but it will more often be fooled by unsustainable outlier performance.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Not surprisingly, my models is still heavily regressed toward the mean, even when I predict FIP and translate that into team-specific ERA. Very few starting pitchers get assigned an ERA prediction of under 4.0 FIP. Tim Lincecum is by far the lowest FIP prediction for 2010 (among starters) with a projected for 3.29 FIP. Even with a favorable league and park, I project his ERA for 3.04. The second-best starter projection for 2010 is Zack Greinke with 3.47 FIP. His adjusted ERA projection comes out to 3.53. That means that Greinke is equally likely to post a 4.03 ERA and a 3.03 ERA.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">I'm ok with these projections, since even great pitchers often revert toward the mean, but have less room for further improvement. However, my system projects FIP of below 5.0 for some very marginal pitchers, and no 2010 pitcher is projected for an FIP of above 5.79. Natural selector (ie the MLB front offices) tend to make sure that high-FIP pitchers don't stay around for long in the majors, but my system is still making a mistake by regressing everyone aggressively toward the mean, simply for being on a major league roster. Distribution of talent is not symmetrical in MLB, so regression toward the mean should not be either. I'm not sure how to properly account for this.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">I am making major improvements to my FIP/ERA projection formula, so I will not discuss the formula I currently use in much more detail. Right now, my adjustments for park and league are not very good, and I'm not adjusting the HR% part of FIP by HR% for different parks. Worst of all, I am not adjusting previous years' FIP feature by sample size. So if a pitcher threw had an FIP of 2.48 in only 31.0 IP in 2009, I treat that the same for future predict as a 2.48 FIP in 200+ IP. As a result, </span><a href="http://www.fangraphs.com/statss.aspx?playerid=18&position=P"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Neftali Feliz</span></a><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> is my second-best FIP projection for 2010, behind only </span><a href="http://www.fangraphs.com/statss.aspx?playerid=4759&position=P"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Jonathan Broxton</span></a><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">. Actually 31.0 IP isn't bad for a 1-year projection and my system is used to handling those sample sizes. Unfortunately, that's also his 3-year total, any my system assigns more weight to 3-year averages than to last year's figures. I can only imagine the ridiculous projection it would have given to Joba Chamberlain going into 2008!</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">I will fix the most pressing issues, and soon I'll have a very good projection for FIP/ERA. Stay tuned.</span></div>Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com0tag:blogger.com,1999:blog-8942811343129148530.post-63755440976453425952010-04-05T19:20:00.000-07:002010-04-05T19:20:41.044-07:00Team Pitching Projections (V: Chicago White Sox)Last year, the White Sox quietly had the fourth-best pitching staff in baseball at 242.6 VORP. This year, that staff will be bolstered by a full season of Jake Peavy. The White Sox pitchers should be pretty good again this year (<a href="http://spreadsheets.google.com/pub?key=tqUzb0MyGjRkLnhfF1pWJKw&single=true&gid=7&output=html">individual projections here</a>), even if their team's 1.04 run factor makes their raw ERAs look less impressive than the Giants and the Dodgers.<br />
<br />
The CHONE system projects the White Sox for 216 VORP (worse than the Yankees and Red Sox, but still 40 runs above average). My system projects then for 195 VORP (worse than the Yankees, but on second best among the 12 teams I looked at). The difference in the two projections is the difference in projecting Mark Buehrle:<br />
<br />
<ul>
<li>CHONE: 192 IP, 4.12 ERA, 4.31 FIP (<a href="http://www.fangraphs.com/statss.aspx?playerid=225&position=P">all stats on FanGraphs</a>)</li>
<li>my system: 179 IP, 4.70 ERA, 4.48 FIP</li>
</ul>
<div>
My ERA estimates are computed from FIP and the team "run factor" only, so I could never project Buehrle to perform better than his FIP, given that The Cell is a hitter's park. However CHONE seems to pick up on the fact that Buehrle has exceeded his FIP consistently throughout his career, with career ERA of 3.80 and career FIP of 4.17. He has pitched his entire career in Chicago.</div>
<div>
<br /></div>
<div>
Buehrle is not a strikeout pitcher. His career 5.19 K/9 is below average, and is very low for a top pitcher. However he doesn't walk anyone, and he is an extreme ground ball pitcher. Also, he apparently has an Andy Pettitte-like <a href="http://rmlumley.com/2009/04/no-one-runs-on-mark-buehrle/">pickoff move</a>. This all adds up to a high runner strand rate, and an ERA that is consistently below his FIP in one of the toughest run environments in baseball. My projection system actually has his FIP close to what CHONE projects, but I have no way of accounting for his FIP to ERA magic. At least not yet!</div>Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com0tag:blogger.com,1999:blog-8942811343129148530.post-55803105421244827622010-04-05T18:37:00.000-07:002010-04-05T18:39:20.945-07:00Team Pitching Projections (IV: San Francisco Giants)Unlike the Rays, my system and CHONE disagree strongly on our expectations for the SF Giants. <a href="http://spreadsheets.google.com/pub?key=tqUzb0MyGjRkLnhfF1pWJKw&single=true&gid=6&output=html">Individual projects can be found here</a>.<br />
<br />
Last year the Giants compiled 264.4 pitcher VORP, good for 3rd in MLB. This propelled them to an unlikely Wild Card run, despite having no hitting beyond Pablo Sandoval.<br />
<br />
The one Giants game I attended last year must have been a typical win for last year's squad. Tim Lincecum <a href="http://sports.yahoo.com/mlb/boxscore;_ylt=AjfZvnm1Pi99nueKXJMpRIGFCLcF?gid=290801126">threw eight shutout innings</a>, striking out eight, walking one, and giving up only seven singles. The Giants' hitters looked just as hapless against Joe Blanton as the Phillies looked against Lincecum. They won 2-0 on two Juan Uribe sac flies. Brian Wilson pitched the ninth for his 27th save, and the Giants' secondary pitchers never even warmed up.<br />
<br />
Neither my system nor CHONE expects the Giants to repeat their amazing pitching performance this year. CHONE projects them to fall to 134 VORP. That would be the same value as last year's Royals staff (substitute Lincecum for Greinke, Brian Wilson for Soria, and Barry Zito for Gil Meche). My system, however, regresses the Giants' projection down to 189.7 VORP only, which would still make them about 20-30 runs better than the MLB average.<br />
<br />
The reason for this 55 run difference is that I'm more bullish on each of the Giants' top four starters:<br />
<br />
<ol>
<li>Tim Lincecum: 225 IP, 3.02 ERA (196 IP, 3.12 ERA for CHONE)</li>
<li>Matt Cain: 197 IP, 3.89 ERA (188 IP, 3.93 ERA for CHONE)</li>
<li>Barry Zito: 148 IP, 4.32 ERA (169 IP, 4.85 ERA for CHONE)</li>
<li>Jonathan Sanchez: 163 IP, 3.92 ERA (151 IP, 4.47 ERA for CHONE) </li>
</ol>
<br />
I was going to write about how Jonathan Sanchez has been much better than his raw ERA and losing win-loss records show, and that at 27, we should expect him to be at least as good as he was in 2008-2009, but probably much better. However, Peter Bendix of RotoGraphs <a href="http://www.fangraphs.com/fantasy/index.php/breakout-candidate-jonathan-sanchez">explains all of this much better</a>!<br />
<br />
I am similarly puzzled by CHONE's low projection for Barry Zito's ERA. Despite the really bad contract, he's still a useful starting pitcher, and has consistently had a ERA below 5.0, except for his poor 2008 season. At 31 he isn't that old yet, and has thrown 180IP+ each of the past 10 years. If anything, my 148 IP estimate looks low, while the 4.32 ERA looks about right.<br />
<br />
Enough has been written about how Matt Cain's 2.89 ERA last year was due to unsustainable good luck with BABIP and with stranded runner rates. Both me and CHONE agree that he should be good, but not elite, in 2010.<br />
<br />
Tim Lincecum was easily my highest VORP projection for 2010, and also one of my lowest ERA projections, even with relievers included. As Tom Tango pointed out in his <a href="http://www.insidethebook.com/ee/">blog</a>, projecting a 3.04 ERA means that there the same chance that he will post a 2.54 ERA as the chance that he will post a 3.54 ERA. If so, that would make today's Tim Lincecum a value similar to mid 1990's Greg Maddux! Does that seem plausible? My projection system seems to think so.Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com1tag:blogger.com,1999:blog-8942811343129148530.post-54575121234031116692010-04-05T17:36:00.000-07:002010-04-08T00:03:18.131-07:00Team Pitching Projections (III: Tampa Bay Rays)In projecting the Rays' staff, my VORP projections and those implied by CHONE's ERA and IP projections are mostly in agreement. The full set of <a href="http://spreadsheets.google.com/pub?key=tqUzb0MyGjRkLnhfF1pWJKw&single=true&gid=9&output=html">individual projections is here</a>.<br />
<br />
The Rays were 14th in pitcher VORP last year, and both systems expect them to stay a little above average this year. The Rays don't have an elite #1 starter, but their top two starters, James Shields and Matt Garza, project to be the 20th and 37th most valuable in MLB according to my system (or 14th and 34th most valuable according to CHONE).<br />
<br />
As I wrote in the <a href="http://bezdomnybaseball.blogspot.com/2010/04/team-pitching-projections-ii-totals.html">averages section</a>, the Rays have the most valuable 6th-15th pitchers of all the teams that I looked at. They have six legitimate starting pitchers (if you count Andy Sonnanstine), and a deep bullpen. To paraphrase what I wrote there, I project the Rays to get 66.6 VORP from the pitchers on their opening day roster, not including the five most valuable pitchers. That is 18 more runs than the Yankees, and 36 more runs than the Red Sox. The average projection for the teams I looked at is 39.8 VORP, so the Rays get 27 runs (about 3 wins) more from the secondary pitchers on their major league roster than does the average team. This is similar to me saying that the Rays' staff depth is worth 3 wins, without taking any account for their depth in AAA. The Rays' top five is average, but the depth of their pitching staff makes their pitchers collectively as valuable as the Red Sox' pitchers, and only a little less valuable than the Yankees' pitchers.<br />
<br />
The Rays' most intriguing projection is <a href="http://www.fangraphs.com/statss.aspx?playerid=7441&position=P">Wade Davis</a>. He came up last year after Scott Kazmir was traded and threw very well in a small number of innings (over six starts). His 3.72 ERA in 36 IP was impressive, but his 2.90 FIP was even more impressive than that (although the 3.54 xFIP makes you wonder about that low HR rate).<br />
<br />
In any case, my projection system is buying his performance, and projecting him for a 3.98 ERA, although it is cautiously predicting only 100IP in playing time. CHONE is buying his spot in the starting rotation, projecting 159IP (more than David Price and the same as Jeff Neimann), but projects a 4.58 ERA. Total value projected is about the same, but I'm curious to see how Davis actually performs. He wasn't exactly lights out in AAA (3.90 FIP over 200IP in 2008-2009), but his success at the major league level has got to mean something. The Rays seem to be willing to give him a chance. Let's see what he makes of it.Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com0tag:blogger.com,1999:blog-8942811343129148530.post-67349109016548424042010-04-05T16:57:00.000-07:002010-04-05T16:57:39.102-07:00Team Pitching Projections (II: Totals & Averages)I was going to break down my projections for several interesting teams, but first I wanted to look at some aggregate stats for the various projections (mine, CHONE & PECOTA). Next thing you know, I've gotten a dozen team projections, and more averages that I can fit in a spreadsheet. I thought the results were interesting, so I'll present them here.<br />
<br />
Here are the VORP projections for the dozen teams, from my system, PECOTA and CHONE (along with last year's values and MLB rankings):<br />
<br />
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-insideh-themecolor: text1; mso-border-insideh: .5pt solid black; mso-border-insidev-themecolor: text1; mso-border-insidev: .5pt solid black; mso-border-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 191;">
<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Team<o:p></o:p></span></span></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">2009 VORP<o:p></o:p></span></span></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">My System<o:p></o:p></span></span></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">PECOTA<o:p></o:p></span></span></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">CHONE<o:p></o:p></span></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Dodgers<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">265.3<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">(1</span></span><sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">st</span></span></sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> MLB)<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">181.2<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">224.5<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">168.9<o:p></o:p></span></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Giants<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">264.4<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">(3</span></span><sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">rd</span></span></sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> MLB)<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">189.7<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">241.2<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">134.0<o:p></o:p></span></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">White Sox<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">242.6<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">(4</span></span><sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">th</span></span></sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> MLB)<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">195.0<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">202.7<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">216.1<o:p></o:p></span></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Red Sox<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">237.7<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">(5</span></span><sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">th</span></span></sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> MLB)<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">189.3<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">259.8<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">264.2<o:p></o:p></span></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Yankees<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">209.4<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">(12</span></span><sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">th</span></span></sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> MLB)<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">217.6<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">193.7<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">258.6<o:p></o:p></span></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Rays<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">194.3<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">(14</span></span><sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">th</span></span></sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> MLB)<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">189.3<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">241.6<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">204.1<o:p></o:p></span></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Rockies<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">177.0<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">(17</span></span><sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">th</span></span></sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> MLB)<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">172.6<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">217.0<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">133.4<o:p></o:p></span></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Phillies<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">172.1<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">(18</span></span><sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">th</span></span></sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> MLB)<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">185.3<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">253.1<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">147.9<o:p></o:p></span></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Royals<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">120.2<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">(20</span></span><sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">th</span></span></sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> MLB)<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">167.9<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">191.7<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">208.5<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Indians<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">83.6<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">(26</span></span><sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">th</span></span></sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> MLB)<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">121.4<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">163.9<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">159.6<o:p></o:p></span></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Brewers<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">34.6<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">(29</span></span><sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">th</span></span></sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> MLB<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">155.1<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">162.8<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">72.3<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Nats<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">-10.0<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">(30</span></span><sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">th</span></span></sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> MLB)<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">112.9<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">212.0<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">81.3<o:p></o:p></span></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">--------<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">------<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">-----<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">----<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">----<o:p></o:p></span></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Average<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">165.9<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">(15</span></span><sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">th</span></span></sup><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> MLB)<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">173.1<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">213.7<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">170.7<o:p></o:p></span></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 15; mso-yfti-lastrow: yes;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.6pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">STDEV<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">90.6<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">30.3<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">32.2<o:p></o:p></span></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 88.55pt;" valign="top" width="89"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">61.9</span></span></div>
</td>
</tr>
</tbody></table>
<br />
I chose a rather extreme set of 12 teams (most of the best & worst pitching teams of 2009), so it's not surprising to see those teams' pitching VORP variance to fall precipitously.<br />
<br />
What is surprising, however, are the PECOTA projections. Not only is the average way too high, but PECOTA projects the Nationals' pitchers to be 10 runs better than the White Sox, and 20 runs better than the Yankees. I don't think that anyone at BP believes this. They have issued several updates to PECOTA recently. Although the data I'm using here is very recent, maybe it still has some flaws. Whatever it is, summing up the PECOTA VORP projections for individual pitchers doesn't work. I'm going to ignore the PECOTA forecasts.<br />
<br />
My system and CHONE seem to give more reasonable results. The averages look fine. While the two systems disagree strongly on some teams, they generally agree that the Yankees, Red Sox and White Sox should have the best staffs, while the Brewers and Nationals should have the worst staffs out of these dozen teams.<br />
<br />
However, CHONE's projections have twice the variance that mine do. A few disagreements aside, my projections resemble a regressed version of CHONE's. Is that really what's happening? Am I regressing too far toward the mean?<br />
<br />
As I wrote in the <a href="http://bezdomnybaseball.blogspot.com/2010/04/team-pitching-projections-i-intro.html">intro piece</a>, I assign "missing innings" for each team to an unknown pitcher with a 5.0 league-neutral and park-neutral ERA. This is the ultimate reversion to the mean (claiming each team's available minor league talent is the same). To break this down ever further, I break up each team's VORP into three components:<br />
<ol>
<li>VORP for the top 5 pitchers</li>
<li>VORP for all other pitcher projected (ie "secondary pitchers")</li>
<li>VORP for "missing innings"</li>
</ol>
<div>
To get the top five pitcher, I rank all pitchers by expected VORP, based on the average of the three systems. So CHONE's top 5 and my top 5 are looking at the same pitchers in all cases. Usually, picking the top 5 pitchers is easy. It's going to be a team's best 3-4 starters, and its best 1-2 relievers.</div>
<div>
<br /></div>
<div>
Here are the breakdowns for team VORP (from my system) by the three categories:</div>
<div>
<br /></div>
<div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-insideh-themecolor: text1; mso-border-insideh: .5pt solid black; mso-border-insidev-themecolor: text1; mso-border-insidev: .5pt solid black; mso-border-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 191;">
<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Team<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Top 5<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">(my VORP)<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Secondary<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">(my VORP)<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Missing Innings<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 1;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Dodgers<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">106.4<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">30.5<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">44.3<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 2;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Giants<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">131.0<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">28.1<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">30.6<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 3;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">White Sox<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">115.9<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">49.8<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">29.3<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 4;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Red Sox<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">143.9<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">30.5<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">14.9<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 5;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Yankees<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">145.8<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">48.5<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">23.4<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 6;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Rays<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">102.6<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .1pt; margin-left: 0in; margin-right: 0in; margin-top: .1pt;">
<span style="font-family: Georgia;">66.6<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">20.1<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 7;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Rockies<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">99.7<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .1pt; margin-left: 0in; margin-right: 0in; margin-top: .1pt;">
<span style="font-family: Georgia;">37.8<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">35.1<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 8;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Phillies<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">130.1<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .1pt; margin-left: 0in; margin-right: 0in; margin-top: .1pt;">
<span style="font-family: Georgia;">34.4<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">20.8<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 9;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Royals<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">95.4<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .1pt; margin-left: 0in; margin-right: 0in; margin-top: .1pt;">
<span style="font-family: Georgia;">31.5<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">40.9<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 10;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Indians<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">44.7<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">32.9<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">43.8<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 11;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Brewers<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">81.6<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">50.1<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">23.4<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 12;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Nats<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">44.9<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">36.4<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">31.6<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 13;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">--------<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">------<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">------<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">-----<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 14;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Average<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">103.5<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">39.8<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">29.9<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 15; mso-yfti-lastrow: yes;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">STDEV<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">33.7<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">11.6<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">9.7<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
</div>
<div>
<br /></div>
<div>
There is high variance among the teams' top pitchers, but teams' secondary and fringe players are projected to provide about the same total value for all teams. The Rays have a very deep pitching staff, with six legitimate starters and a bullpen with good pitchers for every role. According to my projections, their "secondary pitchers" (ie Rafael Soriano, Andy Sonnanstine, JP Howell, Grant Balfour and Dan Wheeler) are worth about 30-40 runs (3-4 wins) more than the weaker "secondary pitchers" on the Giants, Indians, Dodgers and Royals. That seems plausible.<br />
<br />
Let's compare this to what CHONE projects:<br />
<br />
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-bottom-style: none; border-collapse: collapse; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; width: 443px;">
<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Team<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Top 5<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">(CHONE)<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Secondary<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">(CHONE)<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Missing Innings<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 1;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Dodgers<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">101.2<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">43.0<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">24.7<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 2;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Giants<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">98.4<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">24.5<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">11.1<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 3;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">White Sox<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">136.0<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">47.6<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">32.5<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 4;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Red Sox<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">172.0<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">91.1<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">1.1<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 5;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Yankees<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">163.0<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">80.2<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">15.5<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 6;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Rays<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">111.0<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">83.4<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">9.7<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 7;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Rockies<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">74.7<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">51.3<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">7.4<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 8;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Phillies<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">123.1<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">24.8<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">0.0<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 9;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Royals<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">128.5<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">54.8<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">25.2<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 10;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Indians<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">68.8<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">90.8<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">9.0<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 11;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Brewers<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">58.3<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">13.9<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">0.1<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 12;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Nats<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">51.4<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">29.9<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">0.0<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 13;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">--------<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">------<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">------<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">-----<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 14;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">Average<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">107.2<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">52.9<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">11.4<o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 15; mso-yfti-lastrow: yes;">
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">STDEV<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">39.3<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">27.6<o:p></o:p></span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 110.7pt;" valign="top" width="111"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Georgia;">11.1<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<br />
<div class="MsoNormal">
The "top 5" projections are on the same scale as with my system, and with about the same variance. The "missing innings" projections are lower, but also with the same variance. However, the "secondary pitchers" projections are very different.<br />
<br />
The variance in the "secondary pitcher" projections from CHONE are <b>huge</b>. The chart is telling me that:<br />
<br />
<ol>
<li>The Indians' "secondary pitchers" are 8 runs better than the Rays'</li>
<li>The Phillies' "secondary pitchers" are almost 70 runs worse than the Red Sox'</li>
</ol>
<div>
I don't believer either of those projection, nor much else in what I see here. The Indians' staff is very young. I think they'd gladly sign a binding contract for 60% of the Rays' bullpen's value right now, never mind for 110%.</div>
<div>
<br /></div>
<div>
However the issue here is not that rankings for secondary pitcher values are off, but rather that these rankings are what's driving much of the disagreement between my system and CHONE's system. CHONE's team-wide projections have a 60IP standard deviation. Almost half of that is due to variation in the secondary pitchers. I don't think that makes sense.</div>
<div>
<br /></div>
<div>
Secondary pitchers do often end up providing a lot of value to a team, but we can almost never expect that before the fact. By definition, the secondary pitchers can only be the 4th-7th best starters or the 2nd-7th best relievers on a team going into the season. Unless the player is under team control (with minor league option years left), a team can not stick really good pitchers into such roles, or to hide them in the minor leagues. A top starting pitcher can project for 25-50 VORP, and a top reliever can project for 15-25 VORP. However, it's almost impossible for a team to get this kind of <i>projected</i> value from their 6th-15th best pitchers. I might be projecting the Nationals and Indians generously by giving them credit for filling their missing innings with 5.0 ERA pitchers. Perhaps they won't be able to to that. However, I can't give the Rays more credit that I am already giving them for having a deep staff.</div>
<div>
<br /></div>
<div>
Therefore, although I probably <i>am</i> regressing my projections to closely to the mean, I do not think that CHONE's approach to projecting non-top players is better.</div>
<div>
<br /></div>
<div>
<b>Has MLB become the NFL?</b></div>
<div>
<br /></div>
<div>
If you look back at my team projections, you will notice that the best team (the Yankees at 217.6 VORP) are only projected at 100 VORP higher than the worst team (the Nationals at 112.9 VORP). That almost seems to imply that, if the stars align, the Nationals might have a better staff in 2010 than the Yankees. That will almost certainly not happen. If the Yankees staff suffers a major injury, they will likely trade for a replacement, or find another solution. They will probably add a pitcher at the trade deadline. It's hard to imagine the Nats doing so, and easier to imagine them shedding talent at the deadline, possible to those same Yankees.</div>
<div>
<br /></div>
<div>
Still, the separation between the best teams (Yankees, White Sox, Red Sox and Rays) seems small, compared to the worst teams (Nats, Indians and Brewers). These groups of teams are less than 70 projected pitching VORP apart. Are the best and worst pitching teams really only 7-8 wins better than each other? Has MLB become the NFL, <a href="http://www.advancednflstats.com/2007/09/pre-season-predictions-are-worthless.html">where parity ensures that advanced preseason projections are worthless</a>?</div>
<div>
<br /></div>
<div>
Not necessarily. Seven wins is still significant, and my system does not simply regress last year's projections. Everyone expects the Nats and Brewers to improve, but my system also projects the Yankees to improve significantly. The Giants and Royals are intriguing teams, mainly because both are so top-heavy in terms of pitching value. Both me and CHONE project the Royals to improve while the Giants regress. However CHONE's projections are much more aggressive, projecting the Royals to have one of the best staffs in baseball, while the Giants become a below-average staff. Despite the high uncertainty in these projections, the differences are not small.</div>
<div>
<br /></div>
<div>
Still, why aren't projected differences in pitcher value larger than 7-10 wins at the extreme?</div>
<div>
<br /></div>
<div>
As I argued earlier, it's very difficult for a team (even the Yankees) to get great pitchers past their top five. However, no team's top five pitchers are projected to pitch more than 800 IP in 2010. Divide 800 by 5. That's 160 IP. In today's MLB, with injuries and pitcher usage being what they are, one's best pitchers do not project for more than 160 IP on average for a given season. This means that 45%-60% of a team's innings are projected to go to the <i>non </i>top-five guys. Good teams do not stand to gain much marginal value on those innings, and yet they make up half the expected IP total.</div>
<div>
<br /></div>
<div>
In earlier times, good starting pitchers might be reasonably projected to throw 200+IP, and top relievers threw over 100IP every season. Careers were shorter, so the three-year projections might have been the same, but the one-year projections for pitchers surely were higher. Now a team's top five pitchers could be expected to throw as much as 1000 IP from a teams' expected 1450. So in a sense, MLB is becoming more like the NFL. At least in respect to pitching value. Since hitter projections are less variable than pitcher projections, and most good hitters still play every day, I doubt that this argument translates for projecting hitter value.</div>
</div>
</div>Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com0tag:blogger.com,1999:blog-8942811343129148530.post-4828668306259145292010-04-04T22:02:00.000-07:002010-04-04T22:02:49.823-07:00Team Pitching Projections (I: Intro & Adjustments)It's opening day! I didn't get to produce reasonable projections for everything I set out to do before the season started, but I still got a lot done. Now that I published my VORP and ERA, I thought I'd break down a few teams' pitching staffs for 2010, and see how my projections compare to those of PECOTA (Baseball Prospectus's famous projection system) and CHONE (another famous projection system).<br />
<br />
I didn't have the current updated teams for every player, so instead I chose a few teams, took their opening day rosters and DL'ed pitchers, and based my team projections based only on those 11-14 guys. The opening day rosters I used are from an article on BP for April 1st (<a href="http://www.baseballprospectus.com/article.php?articleid=10353">AL rosters</a>, <a href="http://baseballprospectus.com/article.php?articleid=10371">NL rosters</a>).<br />
<br />
In the next few posts, I will present and discuss my team projection for the Yankees, Rays, White Sox, Rockies and Giants. Since these are all good pitching teams, I will also break down my projections for the Indians.<br />
<br />
Most of the stats I show are pretty straightforward: take some projections & add 'em up. However, there are a few caveats. I explain those below. If you don't care, just skip forward to the team breakdowns, and maybe come back here if something doesn't make sense.<br />
<br />
<b>Missing Innings</b><br />
<br />
In a 162-game season, each team's pitchers should throw 1450 innings, give or take a few. However, as I noted for my <a href="http://bezdomnybaseball.blogspot.com/2010/03/yankees-25-man-pitchers-everyone-loves.html">Yanks</a> and <a href="http://bezdomnybaseball.blogspot.com/2010/03/rays-pitchers-ip-projections.html">Rays</a> IP breakdowns, a system should not project 1450 total innings to any team's top 11 pitchers. Teams end up using guys not on the opening day roster to pitch anywhere from 100-600 innings every season. Not infrequently, some of those innings go to pitchers who are not even projected by PECOTA or CHONE, systems that project thousands of minor league players. Therefore, no matter how many pitchers we project, the team numbers should add up to less than 1450.<br />
<br />
In order to have projections for team ERA and team VORP that do add up, I credit the "missing innings" to an unknown player. It would be nice to give that player a "replacement level" ERA and a VORP of 0.0, but that doesn't quite work out. PECOTA uses a replacement level of around 5.4 ERA (equivalent to 5.8 RA), league-neutral and park neutral. However both my system and the CHONE system project an average ERA of 5.0 for the bottom 1/6 of projected pitchers. In other words, both my system and CHONE starts a pitcher off at 5.0 ERA, if we know nothing about him, other than the fact that he's not on an MLB opening day roster, but ends up pitching in the majors.<br />
<br />
Therefore, I credit the "missing innings" to a pitcher with league-neutral and park-neutral 5.0 ERA in all cases. I do the same thing for the "missing innings" for PECOTA and CHONE's projections, if there are any.<br />
<br />
Without this adjustment, projected VORP totals would end up being low, compared to previous years' averages.<br />
<br />
FWIW, I'm not claiming that the replacement level should be set to 5.0 ERA. I'm just saying that my system would project an unknown pitcher to a 5.0 ERA, so I wanted the VORP projection to reflect that. I don't know how PECOTA or CHONE would project such a player, so I fill out their team projections at the same level, for consistency.<br />
<br />
<b>Team Run Factors</b><br />
<br />
My FIP/ERA projections are based off of previous years' QERA and FIP. Since these are not affected much by the league or park of the pitcher, I can use my VORP projections directly without team-based adjustment. I also use PECOTA's VORP projections directly. However, CHONE does not project VORP. It projects WAR, but I'm not project that as of yet. So I compute VORP projections from CHONE based on its ERA and IP projections. I'm assuming that CHONE's ERA figures take park and league into account. If so, I need a different "replacement level" RA for each team in order to compute VORP properly. For this, I use the 2009 VORP and RA/G season totals for each team from Baseball Prospectus's "Team Audit" pages.<br />
<br />
As an added bonus, I can compute the team's "run factor," compared to the MLB average. My ERA projections are league-neutral and park-neutral, but using this factor, I can project ERA for each player adjusted to his current team's "run factor."<br />
<br />
My adjusted ERA projections (based on that team's run factor) are listed for each pitcher. Also I included each team's 2009 run factor and team VORP, as well as implied replacement-level RA.<br />
<br />
Hopefully you'll find my projections interesting. Can't wait to see they turn out...Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com0tag:blogger.com,1999:blog-8942811343129148530.post-19781124896293960742010-04-03T03:25:00.000-07:002010-04-05T20:09:28.755-07:00VORP, ERA and FIP projections (keeping it simple)In honor of Bill Simmons (one of my favorite sportswriters) <a href="http://sports.espn.go.com/espn/page2/story?page=simmons/100402">getting on board with sabermetrics</a>, I'm gonna keep this one simple. As Bill put it, VORP is a great stat because "it's not easy to figure out, but it's easy understand!" So I'll try to keep the intro quick, and maybe even interesting. If you prefer, just skip forward to the <a href="http://spreadsheets.google.com/pub?key=t5bbK1PY29qKUrqPc3_jVjg&output=html">2010 projection</a>, or you can read a (abridged) explanation of what I did.<br />
<br />
<b>Estimating ERA via FIP and VORP via ERA</b><br />
<br />
For my IP projections, I looked at many factors in the player's past performance. Then I looked at his i<a href="http://bezdomnybaseball.blogspot.com/2010/03/2010-ip-projections-with-injury-data.html">njury data to tweak those IP projections</a>. Doing so, I got a somewhat complicated system that <a href="http://bezdomnybaseball.blogspot.com/2010/03/2010-ip-projections.html">performs considerably better than PECOTA or CHONE</a>.<br />
<br />
However to estimate value, I took a simpler approach. I projected FIP (Fielding Independent Pitching [ERA approximator]), then used that value to calculate ERA.<br />
<br />
Given a projection for ERA, I take my injury-based IP projection, and get a projection for VORP (Baseball Prospectus's runs above replacement level stat). I do not make any adjustments for league, park factors, quality of opposition, or whether innings where pitched in start or relief.<br />
<br />
Now, to make sure all of this works, I compare my ERA and VORP projections to PECOTA's and CHONE's preseason projections for 2009. I compute VORP (with no park or league adjustments) from PECOTA's and CHONE's projections for IP and ERA, thus making them comparable to my VORP projections.<br />
<br />
<b>Comparisons to PECOTA and CHONE</b><br />
<br />
The ERA comparison results are simple:<br />
<ul>
<li>My 2009 ERA projections (all weighted by <i>actual</i> IP) are better than PECOTA and equal (50%-50%) to CHONE.</li>
<li>CHONE is better that my system (56%-44% with smaller average error) if we only look at 60IP+ pitchers.</li>
</ul>
<div>
Therefore, my simple ERA projection system is better than PECOTA, and slightly better than CHONE for fringe guys, but slightly worse for true major leaguers (who managed not to get hurt too much). And this is with my system treating all players equally, without park or league adjustment, and without using minor league stats of any kind.</div>
<div>
<br /></div>
<div>
When I combine my superior IP projection system with an ERA-projection system that's a little worse than CHONE, I have a superior system for projecting VORP (or any other runs over replacement stat). Whether we look at all projected pitchers, those pitchers projected for 60IP+ (by either system), or those projected for 120IP+, my VORP approximations are better then CHONE or PECOTA by a significant margin.</div>
<div>
<br /></div>
<div>
I also do significantly better (60%-40% with 10% lower average error) compared to PECOTA when using the final VORP figures that BP itself published (rather than the ones that I approximate with a static 5.8 replacement-level RA and static 0.93 RA/ERA ratio).</div>
<div>
<br /></div>
<div>
I'll probably have the details for all these tests up in the future, but just take my word for it for now.</div>
<div>
<br /></div>
<div>
<b>The Point</b></div>
<div>
<br /></div>
<div>
I'm not arguing that my ERA approximations are amazing. They don't look at anything other than the last three years' FIP, QERA (BP's fielding independent stat that ignores HR%), start/relief ratio and rookie status. My ERA approximations ignore league and park effects on ERA entirely. Rather, I admit that CHONE probably has better ERA approximations that I do at this point.</div>
<div>
<br /></div>
<div>
However, if you want to know what value a player will have to his team (in runs saved, or otherwise), it's important to have a good projection of playing time. CHONE and PECOTA over-estimate IP across the board, but they do so especially for young players. The chance of injury or collapse in performance is always there, and needs to be a part of the projection process.</div>
<div>
<br /></div>
<div>
For every Mariano Rivera and CC Sabathia (consistently good), there is an occasional Brandon Webb (unexpected injury) or Brad Lidge (collapsed value) or Cole Hamels (very bad luck with BABIP). These cases seem rare when they happen, but we have cases like these every season. Therefore, a projection system has to either catch these cases more often than not, or it has to temper high expectations across the board. My IP system does a little of both. Even combined with simple ERA projections, I've still got a very good projector of overall pitcher value.</div>
<div>
<br /></div>
<div>
<b>2010 projections</b></div>
<div>
<br /></div>
<div>
Follow this link to see <a href="http://spreadsheets.google.com/pub?key=t5bbK1PY29qKUrqPc3_jVjg&output=html">IP, ERA, FIP and VORP projections</a> for all pitchers who either pitched in 2009, or threw 120IP in 2008 and don't seem to be officially retired yet (ie Ben Sheets).</div>
<div>
<br /></div>
<div>
For those not familiar with some of the stats above, here is a quick reference below. I think they are pretty intuitive, even if you don't know how they are computed. As Bill Simmons wrote, "I don' care how you killed the cow; just give me a great steak!" These projections is what's for dinner, in time for the season opener.</div>
<div>
<br />
<b>Stats I'm projecting</b><br />
<br /></div>
<a href="http://www.rotosavants.com/2008/06/fantasy-baseball-sabermetric-review-fip.html">FIP</a> (Fielding Independent Pitching):<br />
<ul>
<li>Approximates ERA by using only the strikeout rate (SO9), walk rate (BB9) and home run rate (HR9)</li>
<li>FIP = (13*HR9 + 3*BB9 - 2*SO9)/9 + 3.2</li>
</ul>
<a href="http://sports.espn.go.com/mlb/hotstove06/columns/story?columnist=neyer_rob&id=2751842">VORP</a> (Runs (saved) Over Replacement):<br />
<ul>
<li>How many runs was the pitcher worth, compared with those same innings going to a replacement-level (AAA) player?</li>
<li>Replacement level varies by league and is different for starter and relievers.</li>
<li>I just set it at ERA_replacement = 5.4; RA_replacement = 5.8 (post 2005 data) when I'm lazy.</li>
<li>Since 10 runs ≈ 1 win, a 35.0 VORP player is worth about 35.0/10 = 3.5 wins to his team. A replacement-level player is worth nothing, independent of playing time.</li>
</ul>
Using the fact that VORP translates directly into runs and wins, it's a nice stat for approximating how well a team's pitching staff will do as a whole. Since we assume that guys not on the season-opening 25-man roster or the DL are probably "replacement level," we can approximate the value of the rotation as a whole. We add the VORP projections for the top guys, and don't worry about who the excess innings will go to.<br />
<br />
Since my IP projections take account of injury histories, and VORP is proportional IP, my VORP projections take injury histories on the staff into account. Individual projection can often look strange, but since those projections average out, staff projections should be more accurate that projections for individual pitchers.<br />
<br />
I intend to have the staff projections for a couple of teams tomorrow.<br />
<br />
<b>Odds & Ends</b><br />
<br />
There is a better stat than VORP for approximating wins added called <a href="http://www.fangraphs.com/blogs/index.php/pitcher-win-values-explained-part-two/">WAR</a> (Wins Above Replacement). It's similar to VORP, but takes into account a few important factors that VORP does not. However I didn't have time to generate WAR projections. I'll try to get to that later today or tomorrow before the season starts.Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com0tag:blogger.com,1999:blog-8942811343129148530.post-8178819921031539612010-03-31T18:12:00.000-07:002010-03-31T18:12:46.362-07:00Final(!) 2010 IP projections (with injury data)Unhappy with my incomplete updates for guys starting the year on DL, I got a much more thorough list. From Baseball Prospectus, I got a list of (probable) opening day rosters with DL. I checked all injuries on MLB.com & put in approximate surgery dates where appropriate:<br />
<a href="http://baseballprospectus.com/article.php?articleid=10371">http://baseballprospectus.com/article.php?articleid=10371</a><br />
<a href="http://baseballprospectus.com/article.php?articleid=10353">http://baseballprospectus.com/article.php?articleid=10353</a><br />
<br />
New projections are down by 1.1 IP per pitcher, which is good! Here is the complete list, sorted by projected 2010 IP. These should be my final projections. Mostly improved, with obvious DL guys updated, but no major pitchers affected. The exception is Cliff Lee, who's down to a 150 IP projection, since he will likely start the season on the DL. The number sounds low, but starting the year on the DL is never a good thing. Here is the full list:<br />
<a href="http://spreadsheets.google.com/pub?key=t4Db7PGjjU7lY4JJNP212Dg&output=html">http://spreadsheets.google.com/pub?key=t4Db7PGjjU7lY4JJNP212Dg&output=html</a><br />
<br />
Hoping to have ERA/FIP/VORP projections here soon. Maybe not of the same detail as my IP stuff, but at least something decent before the season starts...<br />
<br />
Can't wait for opening day!Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com0tag:blogger.com,1999:blog-8942811343129148530.post-11143409494804326272010-03-30T17:43:00.000-07:002010-03-30T17:43:48.577-07:002010 IP projections (with injury data)I'm not very patient, so instead of making sure that I had this year's spring training DL listings up to date, I updated information for some prominent cases (ie Joe Nathan), and made sure I covered all the guys listed in these FanGraphs articles. Thank god that fantasy baseball fans care so about DL possibilities for lot and lots of pitchers :-)<br />
<a href="http://www.fangraphs.com/fantasy/index.php/the-dl-on-the-dl-march-28th-more-pitchers-headed-for-the-dl/">http://www.fangraphs.com/fantasy/index.php/the-dl-on-the-dl-march-28th-more-pitchers-headed-for-the-dl/</a><br />
<a href="http://www.fangraphs.com/fantasy/index.php/dl-roster-spot-all-stars/">http://www.fangraphs.com/fantasy/index.php/dl-roster-spot-all-stars/</a><br />
<a href="http://www.fangraphs.com/fantasy/index.php/the-dl-on-the-dl-march-25th/">http://www.fangraphs.com/fantasy/index.php/the-dl-on-the-dl-march-25th/</a><br />
<br />
My <a href="http://spreadsheets.google.com/pub?key=t3bkdwzEX-f_-GUPErUOpDg&output=html">updated 2010 IP projections are here</a>, sorted by +- from my previous projections when I take injury histories into account. I call this adjustment "inj_gain" in the spreadsheet.<br />
<br />
As the name indicates, more pitchers gain IP than lose IP through these adjustments. In fact, the average pitcher has his IP rise from 59.8 innings to 65.1 innings. This is not actually gonna happen, but is rather a reflection of the unusually high number of players coming off of injuries in 2009. The <i>average</i> pitcher who was on a major league roster in 2009 spent 21.9 days on the DL. The 2005-2009 average was just over 15 days, so the trend of more pitcher injuries is going strong. Since I trained my projections on 2005-2009 data, it's not surprising that 2010 projected gains are too high. Also I'm missing some guys who will open the season on the DL, as I mentioned already. I probably got all the big names right, but pitchers who are not on the fantasy radar might be missing camp-related DL deductions.<br />
<br />
Looking at the top of my list, here are the pitchers who stand to gain the most from my injury-based adjustments:<br />
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<br /></div>
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<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">2009 IP</span></div>
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<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">2010 proj</span></div>
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<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">w/
injuries</span></div>
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<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">DL days
2009</span></div>
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<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Carl
Pavano</span></div>
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<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; height: 13.4pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 1.0in;" valign="top" width="72">
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<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">199.3</span></div>
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<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">116.6</span></div>
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<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">189.8</span></div>
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<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">0</span></div>
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<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Tim Hudson</span></div>
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<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">42.3</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; height: 12.6pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 71.0pt;" valign="top" width="71">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">92.5</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; height: 12.6pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 73.0pt;" valign="top" width="73">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">155.4</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; height: 12.6pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 85.5pt;" valign="top" width="86">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">167</span></div>
</td>
</tr>
<tr style="height: 13.4pt; mso-yfti-irow: 3;">
<td style="border-top: none; border: 1.0pt; border: solid black; height: 13.4pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 108.9pt;" valign="top" width="109">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Chris
Carpenter</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; height: 13.4pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 1.0in;" valign="top" width="72">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">192.7</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; height: 13.4pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 71.0pt;" valign="top" width="71">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">162.7</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; height: 13.4pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 73.0pt;" valign="top" width="73">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">225.3</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; height: 13.4pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 85.5pt;" valign="top" width="86">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">35</span></div>
</td>
</tr>
<tr style="height: 12.6pt; mso-yfti-irow: 4;">
<td style="border-top: none; border: 1.0pt; border: solid black; height: 12.6pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 108.9pt;" valign="top" width="109">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Francisco
Liriano</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; height: 12.6pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 1.0in;" valign="top" width="72">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">136.7</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; height: 12.6pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 71.0pt;" valign="top" width="71">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">97.6</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; height: 12.6pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 73.0pt;" valign="top" width="73">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">159.6</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; height: 12.6pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 85.5pt;" valign="top" width="86">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">22</span></div>
</td>
</tr>
<tr style="height: 12.6pt; mso-yfti-irow: 5;">
<td style="border-top: none; border: 1.0pt; border: solid black; height: 12.6pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 108.9pt;" valign="top" width="109">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">John
Lackey</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; height: 12.6pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 1.0in;" valign="top" width="72">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">176.3</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; height: 12.6pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 71.0pt;" valign="top" width="71">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">169.5</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; height: 12.6pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 73.0pt;" valign="top" width="73">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">225.9</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; height: 12.6pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 85.5pt;" valign="top" width="86">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">50</span></div>
</td>
</tr>
<tr style="height: 26.05pt; mso-yfti-irow: 6; mso-yfti-lastrow: yes;">
<td style="border-top: none; border: 1.0pt; border: solid black; height: 26.05pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 108.9pt;" valign="top" width="109">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Brandon
McCarthy</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; height: 26.05pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 1.0in;" valign="top" width="72">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">97.3</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; height: 26.05pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 71.0pt;" valign="top" width="71">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">88.1</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; height: 26.05pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 73.0pt;" valign="top" width="73">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">143.1</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; height: 26.05pt; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 85.5pt;" valign="top" width="86">
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">0</span></div>
</td>
</tr>
</tbody></table>
<br />
<div class="MsoNormal">
<o:p><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">The projected returns of Carl Pavano, Tim Hudson and Francisco Liriano are all hard to argue with. However the adjustments for Chris Carpenter and John Lackey seem a bit excessive. Increasing their IP projections makes sense, but their non-injury projection were already pretty high, and thus did not need to go up by 60 IP. Then again, my system does not have many other examples of pitcher who missed a month of the season, and still threw many innings and were every effective. As I wrote before, my system does not take account of value (ERA, VORP, etc) when computing the injury adjustments, so it has no way of knowing that these guys are already projected to be pretty good in 2010. My hunch is that those two should project around 200 IP each.</span></o:p></div>
<div class="MsoNormal">
<o:p><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></o:p></div>
<div class="MsoNormal">
<o:p><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">I hadn't heard of Brandon McCarthy until I ran these numbers, but there is a <a href="http://www.fangraphs.com/fantasy/index.php/under-the-radar-brandon-mccarthy/">nice article about him on FanGraphs</a>. He's a young starting pitcher with a history of injuries and of giving up home runs, but is now finally healthy (and still pretty young). He's not listed on the <a href="http://texas.rangers.mlb.com/team/depth_chart/?c_id=tex">Rangers' official depth chart</a>, so he might start the season in AAA, but there is a good chance that he's end up in the Rangers' rotation sometime this season. Given the context, his new 143.1 IP projection is too high, but it would have been a reasonable projection if the Rangers had a hole in their starting staff.</span></o:p></div>
<div class="MsoNormal">
<o:p><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></o:p></div>
<div class="MsoNormal">
<o:p><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Most of the large decreases in IP projection are for the pitcher mentioned in those FanGraphs articles above. Most of the pitchers mentioned will start their seasons on the DL, which leads to large reductions in projected IP. Unfortunately, Joe Nathan's projection goes down only to 33.7 IP, rather than to the 0 IP that will actually happen. On the other hand, the 0 IP projection for Chien-Ming Wang, the 28.3 IP projection for Brandon Webb, and the 7.9 IP projection for Brad Lidge are all too low, even though the algorithm has every reason to be bearish on these pitchers.</span></o:p></div>
<div class="MsoNormal">
<o:p><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></o:p></div>
<div class="MsoNormal">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">His injury history takes Roy Halladay down to 203.2 IP, a full 20 IP below John Lackey's new projection. That's a bit of over-compensation, but the algorithm is right to put those two in the same ballpark in expected IP. Other than that, there are no top-line pitchers taking large projected IP losses, except those who experienced recent injuries.</span></div>
<div class="MsoNormal">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div class="MsoNormal">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">As you can see, the injury-based adjustments are rather crude and they often lead to estimates that over-shoot or under-shoot the mark. However I think that most of the estimates shoot in the right direction, and sometimes they are able to fix obvious problems with projections that don't use injury data. </span></div>Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com0tag:blogger.com,1999:blog-8942811343129148530.post-72103807842599677792010-03-30T03:42:00.000-07:002010-03-30T03:44:49.962-07:00Elbows, Shoulders & Surgeries (seven mini-models by injury type)<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">As I mentioned in my </span><a href="http://bezdomnybaseball.blogspot.com/2010/03/ip-projection-adjustments-with-injury.html"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">last post</span></a><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">, I created seven mini-models to look at how different types of injuries affect IP predictions. I thought the individual mini-models were interesting, and also very readable. Let me show what I'm doing with an example.</span><br />
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span><br />
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">(A </span><a href="http://docs.google.com/View?id=dff86hng_19w54j2qhh"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">full text of the seven mini-models</span></a><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> is here.)</span><br />
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span><br />
<b><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="font-size: x-large;">Elbow Problems</span></span></b><br />
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span><br />
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Suppose I want to see how elbow-related injuries should affect my IP projection. I train an M5Rules linear model in WEKA with my non-injury IP projection, and all elbow-related features. I won't go over the M5Rules model again. However it's important to note that it will not use all of the features that I provide. Instead, there is some feature selection that takes place, so features that do not provide information gain for the model are excluded. Here's what's left:</span><br />
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span><br />
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">IP_2009 = </span><br />
<span class="Apple-tab-span" style="white-space: pre;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> </span></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">-22.0378 * inj_tj_surgery_2008 </span><br />
<span class="Apple-tab-span" style="white-space: pre;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> </span></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">- 34.7761 * inj_tj_recovery_camp_2008 </span><br />
<span class="Apple-tab-span" style="white-space: pre;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> </span></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 39.0062 * inj_tj_surgery_average </span><br />
<span class="Apple-tab-span" style="white-space: pre;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> </span></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 31.5039 * inj_elbow_surg_not_tj_average </span><br />
<span class="Apple-tab-span" style="white-space: pre;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> </span></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 50.288 * inj_elbow_strain_average </span><br />
<span class="Apple-tab-span" style="white-space: pre;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> </span></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 0.9455 * proj_IP_v27_w_value </span><br />
<span class="Apple-tab-span" style="white-space: pre;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> </span></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 6.794</span><br />
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span><br />
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">The projection consists of:</span><br />
<ul>
<li><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">a linear constant</span></li>
<li><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">0.9x * simple IP model</span></li>
<li><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">weighted sum of several elbow-related features</span></li>
</ul>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Hopefully most of the feature names are self-explanatory, though I will explain the interesting ones. A feature that ends in "_2008" relates to the year previous to the one we want to predict (so it would actually be 2007 stats for 2008 predictions, etc). A feature that ends in "_average" is a linear average of the three years prior to "_2008." So "_2008" features represent the near past, whereas the "_average" features represent the older background for the player.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">To compute the "elbow related factor" used as part of the IP predictions, I just use the weighted sums of the elbow features above, ignoring the constant term and the "0.9x * proj_IP" term.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Therefore, the pitcher will increase or decrease his IP projection due to past elbow injuries depending on the sign and magnitude of this term:</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<br />
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">- 22.0378 * inj_tj_surgery_2008</span></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">- 34.7761 * inj_tj_recovery_camp_2008</span></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 39.0062 * inj_tj_surgery_average </span></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 31.5039 * inj_elbow_surg_not_tj_average </span></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 50.288 * inj_elbow_strain_average</span></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">In words, the player gets negative IP for:</span></div>
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
</div>
<ul>
<li><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Tommy John surgery in the past year</span></li>
<li><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">"Tommy John recovery" DL listing in spring training of </span><i><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">this year</span></i></li>
</ul>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">However the player gets positive IP for:</span></div>
<div>
<ul>
<li><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Tommy John surgery in the past (but not last year)</span></li>
<li><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">non-Tommy John elbow surgery in the past</span></li>
<li><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">elbow strain DL stints in the past</span></li>
</ul>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">To any fan who knows a little bit about pitchers' recovery from elbow surgery, none of these features should be surprising. So at least the elbow model passes the sniff test.</span></div>
</div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">To those interested in the magnitude of the features weights, I should point out that all yearly feature weights are binary {0,1}, thus making all "_average" values {0, 1/3, 2/3, 1}. Since the incidence of a particular injury is rare, "_average" values can be thought of as binary values, but at 1/3 of the weight.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<b><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="font-size: x-large;">Creaking Shoulders</span></span></b></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">The features for shoulder injuries are a little different from the elbow features:</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<br />
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">- 43.2967 * inj_labrum_surgery_2008 </span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">- 8.357 * inj_shoulder_tendonitis_2008 </span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">- 9.3244 * inj_shoulder_inflam_2008 </span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">- 19.828 * inj_shoulder_strain_average </span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">- 25.3431 * inj_shoulder_inflam_average </span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 12.2862 * inj_shoulder_average </span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">- 54.3987 * inj_labrum_surgery_recovery_average </span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Histories of shoulder strains, shoulder inflammations and especially of shoulder labrum surgeries are predictors of downward IP projections well into the future. Whereas the model projects a strong rebound for Tommy John survivors, a history of shoulder trouble is not a good sign for a pitcher holding up long-term, even if he stays off the DL for a while. Once a pitcher has major shoulder problems, they tend to bother him for the rest of his career.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<b><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="font-size: x-large;">Stiff Forearms</span></span></b></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">I trained a separate model for arm injuries not involving the elbow or the shoulder:</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<br />
<div style="direction: inherit; margin-bottom: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">- 16.8042 * inj_forearm_2008 </span></div>
<div style="direction: inherit; margin-bottom: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 25.4747 * inj_forearm_average </span></div>
<div style="direction: inherit; margin-bottom: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 27.0505 * inj_upper_arm_average </span></div>
<div style="direction: inherit; margin-bottom: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div style="direction: inherit; margin-bottom: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Although I remember reading somewhere that forearm soreness is often a precursor to elbow problems, this injury seems to follow a simple pattern: recent injury is bad, but a history with no re-injury means projections can be raised.</span></div>
<div style="direction: inherit; margin-bottom: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div style="direction: inherit; margin-bottom: 0px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="font-size: x-large;">General Surgery</span></span></b></div>
<div style="direction: inherit; margin-bottom: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div style="direction: inherit; margin-bottom: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Here is a look at surgeries, but from a more general sense:</span></div>
<div style="direction: inherit; margin-bottom: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div style="direction: inherit; margin-bottom: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+30.7839 * inj_recovery_2008 </span></div>
<br />
<div style="direction: inherit; margin-bottom: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">- 14.106 * inj_shoulder_surgery_2008 </span></div>
<div style="direction: inherit; margin-bottom: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">- 72.0142 * inj_surgery_camp_2008 </span></div>
<div style="direction: inherit; margin-bottom: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">- 49.5069 * inj_recovery_camp_2008 </span></div>
</div>
</div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">If the player was DL'ed last year with "recovery from surgery," then he should expect to play more in the upcoming year. Also it's not surprising that having surgery in spring training is not a precursor of playing a lot. Nor is going on the DL in spring training as "recovery from surgery" a good sign, either.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Somewhat surprisingly, recent shoulder surgery garners only 1/3 of the penalty for "shoulder labrum surgery". I guess there are simpler shoulder procedures that pitchers undergo, from which the recovery time is much faster than for SLAP, or any of the other labrum surgeries. This is not to say that all non-labrum shoulder surgeries are no big deal, but there is a huge difference between Mariano Rivera's 2008 surgery to remove "calcification" in the shoulder, and Brandon Webb's surgery last year to repair a "fraying labrum."</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Having said that, neither me nor WEKA knows much about the anatomy of shoulder injuries. I don't really understand where the rotator cuff ends and where the labrum begins. I know what a labrum is and I've known several friends to tear their labrums playing football & rugby, but I don't really know how those gets repaired for pitchers. If you are reading this and know more about labrums than I do, please let me know!</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<b><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="font-size: x-large;">Missed Seasons</span></span></b></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">I'm not sure why I combined "offseason surgery," "missed season due to injury [over 149 days on the DL]," and "season ending DL [30+ days through October]" together, but here it is:</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<br />
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">- 16.5312 * inj_season_ending_2008 </span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">- 18.7897 * inj_offseason_2008 </span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 31.5928 * inj_offseason_average </span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 18.9852 * inj_missed_season_average </span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Ending a season on the DL or having offseason surgery are not good signs, but these are not as strongly negative as one might have expected. Past offseason surgery corresponds to gains in IP (I won't speculate why). Spending entire seasons on the DL in the past is positive for IP projection for obvious reasons.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<b><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="font-size: x-large;">Spring Cheating</span></span></b></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">As I wrote in my last post, my system takes account of DL transactions from spring training. This is the time of year when teams often tip their hand on a pitcher's health. Getting placed on the DL to start the season is never a good thing:</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 8.2829 * inj_camp_2008 </span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">- 48.6768 * inj_dl_camp_2008 </span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 21.7274 * inj_camp_average </span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 42.948 * inj_surgery_camp_average </span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 54.6509 * inj_recovery_camp_average</span></div>
</div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">According to the model, showing up on the injury report in camp, but not on the DL, is not a bad thing. However opening the season on the DL is very bad for that year's playing time. Being at least a full season removed from surgery and/or subsequent recovery (but not currently back on the DL) is good.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<b><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="font-size: x-large;">Days and Weeks</span></span></b></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Finally, let's look at the features derived simply from the occurrence of DL stints (and days on the DL), irrespective of the injury description or timing:</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">- 7.5115 * inj_15DL_2008 </span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 0.3146 * inj_days_DL_average </span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">- 33.9261 * inj_anyDL_average </span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 24.378 * inj_something_average </span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">- 23.5081 * inj_long_DL_average</span></div>
</div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Being on the DL last year is not great, but not a large downward factor, either. The "_average" features are confusing, but they mainly cancel each other out.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Here "long_DL" means any DL stint of over 60 days. Most surprisingly, there is no negative feature for "long_DL" in the past year. The seven mini-models are trained independently, so this model does not take account of the downward adjustments that we make for specific major injuries, surgeries, recoveries, etc.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">If we know that a player missed lots of time in the past year due to injury, but we don't know what his injury was, whether he missed the whole season, or whether he had surgery, then we know very little about how to adjust his future IP projection.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">I started out trying to predict future performance by looking at past DL time, but now I see why this would never work well. To predict anything meaningful from injuries, the type of injury is important, and the timing is important. Compared to those factors, time missed is not very important.</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">I also tried to train mini-models on several other injury types, but didn't have useful results. Most injuries are too rare to be selected by features selection algorithms as being sufficiently meaningful (back surgery, for example, among pitchers, is not very common). Other injuries are somewhat common, but don't seem to have much predictive value (hamstring strains, oblique strains, and the flu).</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Hopefully you'll agree that my mini-model are readable, interesting, and pass the sniff test. I'll be happy to hear suggestions for further improvements. I'm glad this thing worked, but I'm sure it's possible to build a better model!</span></div>
</div>
</div>
<br />Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com0tag:blogger.com,1999:blog-8942811343129148530.post-19243939135995662832010-03-30T00:11:00.000-07:002010-03-30T00:12:47.206-07:00IP projection adjustments (with injury data)After several earlier failed efforts (over the past six months), I finally managed to substantially improve a prediction system by using rich injury data. With data from <a href="http://www.baseballinjurytool.com/">http://www.baseballinjurytool.com/</a>, I built an additional layer to my IP projection system (described in <a href="http://bezdomnybaseball.blogspot.com/2010/03/updated-2010-ip-projections.html">earlier posts</a>), that has substantially improved results based on retrospective analysis.<br />
<br />
To demonstrate what I'm doing, I'll show how the injuries data changes my system's projections for some 2009 pitchers' IP (based on 2004-2008 data). But first, let me quickly explain what I'm doing.<br />
<br />
The data from Corey Dawkins' DL tool includes information about all major league players' in-season DL stints, as well as "Camp" (ie spring training) injuries, "Offseason" injuries, and also descripitive information about all surgeries. Unfortunately, the data does not include this same information for minor league players, or for players without teams (ie Ben Sheets in 2009). However the data is otherwise very thorough, and complete in the vast majority of cases.<br />
<br />
In short, the data is very good. Having said that, getting predictive value from injury data is very difficult. A few months ago, I built models projecting a player's likely DL days during the next season, as well as his likelihood of suffering an elbow injury, a shoulder injury, a surgery, etc. These models gave me predictions with non-trivial correlation to reality, but they were not helpful for improving my predictive models for IP, VORP, or ERA. Therefore, I have re-defined my earlier goals for injury data.<br />
<br />
My goal is simply to <i>improve my existing IP projection system</i> using features derived from the DL information that I have available. Intuitively, we know that some injury histories should make us want to downgrade a pitcher's playing time projection. But if my ML system can't find an IP prediction improvement in using that feature, then that feature does not make its way into the model. I will get back to this idea when I talk about my Randy Johnson projection for 2009.<br />
<br />
<span class="Apple-style-span" style="font-size: x-large;"><b>My System</b></span><br />
<br />
Looking at the injuries listed, I came up with ~60 features that I thought might be useful in a predictive model. Features might be something like "did pitcher X have an elbow injury" or "did pitcher X have Tommy John surgery" or "did pitcher X spend over 60 days on the DL." Features are generated per pitcher per season, and they range from the general to the very specific.<br />
<br />
As with my <a href="http://bezdomnybaseball.blogspot.com/2010/03/2010-ip-projections.html">previous IP prediction system</a>, I build a model to predict a pitcher's stats using his last four years' data. So for 2009 predictions, I'm looking at 2005, 2006, 2007 and 2008 data, as well as some averages. To simplify injury-based IP projections, I only considered "2008" and "average" (ie 2005-2007 arithmetic average) features for injuries.<br />
<br />
If I'm looking at "shoulder surgeries," I will only at whether the pitcher had a shoulder surgery in the <i>year previous</i> to April 1 2009, and also at <i>how many years during 2005-2007</i> did he have at least one shoulder surgery. In other words, I am asking "did he just come off of shoulder surgery?" and "does he have a history of shoulder surgeries in the past?"<br />
<br />
The devil's in the details, but I think this approach makes logical sense, and it makes for models that are easy to understand.<br />
<br />
One interesting aspect of looking at an injury type in the short run and in the longer run is that having a history or a particular injury could <i>raise</i> a pitcher's IP projection. A good example is Tommy John surgery. If pitcher X has TJ surgery in 2007, he can expect to miss most of the 2008 season (which will usually be listed as "recovery from TJ surgery" in the 2008 DL listings). Such a history should make us want to increase his 2009 IP projections from what they otherwise would be. Maybe he didn't throw many innings in 2008, but he had a good excuse, and as long as he does not undergo more surgery in 2008, he should be good to go in 2009.<br />
<br />
Asked to evaluate the TJ-related features, my system gives a value for "how will an average pitcher's IP be affected by these injury features?" This is limiting, since the projected IP gain or loss should change depending whether we are talking about AJ Burnett, Billy Wagner, or Eddie Guardano. But for now model, I ignore this issue. I am simply trying to find which features have power to predict IP (on top of a good system that doesn't use injury data).<br />
<br />
I built separate mini-models for predicting IP changes due to:<br />
<br />
<ul>
<li>elbow injuries</li>
<li>shoulder injuries</li>
<li>forearm & upper arm injuries</li>
<li>offseason injuries & surgeries</li>
<li>injuries sustained in camp (spring training)</li>
<li>other surgeries (not including features already covered above)</li>
<li>DL listings and # of days on DL</li>
</ul>
<div>
These models are interesting in their own rights. I will list the features that they use and explain them in a future post.</div>
<div>
<br /></div>
<div>
Now I have seven possible causes to increase or decrease a pitcher's IP projection. I sum the values to get a single "injury adjustment feature."</div>
<div>
<br /></div>
<div>
Now I can train a final model with:</div>
<div>
<ul>
<li>my non-injury based IP projection</li>
<li>my "injury adjustment feature"</li>
<li>whether the pitcher still qualifies as a rookie</li>
</ul>
<div>
The later is necessary since I do not have injury data for pitchers while they were not on an MLB roster, nor do I use minor league stats in my projections. Therefore it is often useful to project rookies differently from veterans.</div>
</div>
<div>
<br /></div>
<div>
Using the three features above, I get the following simple model:</div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><span class="Apple-style-span" style="font-family: Times;"><br /></span></span></div>
<div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">IF</span></div>
<div>
<span class="Apple-tab-span" style="white-space: pre;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> </span></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">proj_IP <= 81.746</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">THEN</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">IP_2009 = </span></div>
<div>
<span class="Apple-tab-span" style="white-space: pre;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> </span></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">8.1498 * ROOKIE_2009 </span></div>
<div>
<span class="Apple-tab-span" style="white-space: pre;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> </span></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 0.2684 * injury_sum </span></div>
<div>
<span class="Apple-tab-span" style="white-space: pre;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> </span></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 0.9539 * proj_IP</span></div>
<div>
<span class="Apple-tab-span" style="white-space: pre;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> </span></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 5.989</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">ELSE</span></div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">IP_2009 = </span></div>
<div>
<span class="Apple-tab-span" style="white-space: pre;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> </span></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">0.783 *injury_sum </span></div>
<div>
<span class="Apple-tab-span" style="white-space: pre;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> </span></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 0.7377 * proj_IP </span></div>
<div>
<span class="Apple-tab-span" style="white-space: pre;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"> </span></span><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">+ 41.7999</span></div>
</div>
<br />
<br />
This method is imperfect, but at least my system is able to recognize that injury-based IP adjustments need to be much large for starters than for relievers. Naturally, I don't allow IP projections below 0.0. Also, the model above only applies to pitchers with an <i>injury history</i> (ie at least one injury listing in the past four years). Pitchers with no injury history simply get the "proj_IP" value with no changes.<br />
<br />
Ok, now that I've explained what I did, let me show the biggest hits and misses for 2009 IP predictions using injury data. The <a href="http://spreadsheets.google.com/pub?key=tr95VNgmJ-ShLCt8BGfC94g&single=true&gid=2&output=html">best and worst 20 changes can be seen here</a>, and I will break down a few cases below.<br />
<br />
<span class="Apple-style-span" style="font-size: x-large;"><b>I coulda told you that...</b></span><br />
<br />
The injury-using system makes major gains by predicting much lower IP in 2009 for:<br />
<br />
<ul>
<li>Jake Westbrook, Shaun Marcum, Dustin McGowan</li>
<li>Tim Hudson, Ben Sheets, Jeremy Bonderman, Jeff Francis</li>
</ul>
<div>
By the start of the 2009 season, all of these guys were coming off of major injuries and were DL'ed by their teams to open the season. My system was able to take that into account and dramatically slash their projected IP. Am I cheating? I'll discuss that in a second. Fact is, if you generate injury data saying that pitcher X is going to open the season on the DL with "recovery from Tommy John surgery," my system will take that into account. I'm not aware of other projection systems that take that into account automatically.</div>
<div>
<br /></div>
<div>
<b><span class="Apple-style-span" style="font-size: x-large;">Making an expected recovery</span></b></div>
<div>
<br /></div>
<div>
The injury-based system beats the simple system by significantly boosting IP projections for:</div>
<div>
<ul>
<li>Josh Johnson, Chad Gaudin, Jorge De La Rosa</li>
<li>Josh Beckett, Brandon Looper, Francisco Liriano</li>
</ul>
<div>
These guys had severe injuries in the past, but were relatively healthy heading into 2009. Therefore, the system substantially increased their IP projections. In these cases, the increased IP projections look good, but that doesn't always work out.</div>
</div>
<div>
<br /></div>
<div>
<b><span class="Apple-style-span" style="font-size: x-large;">Bad interaction</span></b></div>
<div>
<br /></div>
<div>
I've tried to keep the system simple, to make it (relatively) easy to understand, and also to reduce over-fitting (more on that below). However this means the system will occasionally output predictions that are clearly flawed. Here are a couple of cases.</div>
<div>
<br /></div>
<div>
My simple system projected Randy Johnson for 128.5 IP in 2009. However, the injury-based model boosted him up to a projected 208.0 IP, one of the highest projections in baseball for 2009. Johnson has a history of back injuries, including back surgeries in 2006 and 2007. However, he did not have any surgeries in 2008. My system does not use specific features for "back surgery" or "herniated disc surgery," but it does use general features for "surgeries." Therefore, Johnson's back surgery gets lumped in with all other surgeries, including stitches, appendix removals and scoped knees. Tommy John surgery and shoulder labrum surgery get their own specific features, but back surgeries do not. And yet, we <i>know</i> that back injuries tend to be chronic. Indeed, Randy Johnson only threw 96.0 IP in 2009, and spent 71 days on the DL with back problems. Should I have trained a mini-model for back injuries? Maybe I should have.</div>
<div>
<br /></div>
<div>
In a totally different kind of failure, my system used injury data to increase Sidney Ponson's IP projection for 2009 from 84.8 IP to 128.1 IP. He only threw 58.7 IP. He also happened to spend 49 days on the DL, but I doubt that 128.1 IP is a reasonable projection for a healthy Sidney Ponson. At 32, Sir Sidney is a journeyman pitcher. His projections should remain low, not only because of injury risk, but also because there is a good chance that he won't stick on a major league roster. My simple model looks at a pitcher's effectiveness (VORP, SNWP, etc) in making IP predictions, but the injury-based adjustments are made without looking at value. Sometimes, this causes unrealistic projections.</div>
<div>
<br /></div>
<div>
<b><span class="Apple-style-span" style="font-size: x-large;">Am I cheating?</span></b></div>
<div>
<br /></div>
<div>
With my methods, some over-fitting is unavoidable. There is not enough recent injury data to have large separate training and testing sets. All I can do is to keep over-fitting to a minimum. I create features that make logical sense and I avoid lumping unrelated categories together ("surgery" or "elbow surgery" or "Tommy John surgery," rather than "complicated surgery (including TJ, shoulder labrum and herniated disc in the lower back)." Also my methods exclude features from training that don't provide a significant amount of information gain. I'll write more about what actual features I include in a future post, but my entire injury-based adjustment only uses about 25 features total (out of a possible 120 or so candidates).</div>
<div>
<br /></div>
<div>
As I alluded to earlier, I use injury listings from spring training to predict <i>that year's</i> injury-based adjustments. I consider everything listed before April 1, 2009 as "2008 data." If a player is recovering from Tommy John surgery, the team will typically place him on the DL before the season starts. I use that information to predict that he will likely not pitch that year.</div>
<div>
<br /></div>
<div>
One can argue that my system will output inaccurate IP estimates before the last week of March, but that isn't quite so. The system will output good estimates in January, too, but they will change if more information is added. Also, if you are looking at the projection of a pitcher, and you <b>know</b> that he will be DL'ed to start the season, it's ok to just put that future expected DL listing into the input file. I think this is a better approach than manually editing projections for known major injury cases, or for outputting incorrect projections for pitcher that we know will likely miss the season.</div>
<div>
<br /></div>
<div>
<b><span class="Apple-style-span" style="font-size: x-large;"><span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Is it worth it?</span></span></b></div>
<div>
<br /></div>
<div>
My injury-based adjustments do not affect the 2/3 of pitcher who do not have an injury history (in the past four years) at the MLB level. However the remaining 1/3 of pitcher (including the vast majority of veterans) get significantly better IP projections if we take injury data into account.</div>
<div>
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-insideh-themecolor: text1; mso-border-insideh: .5pt solid black; mso-border-insidev-themecolor: text1; mso-border-insidev: .5pt solid black; mso-border-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 191;">
<tbody>
<tr>
<td style="border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 114.6pt;" valign="top" width="115"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 112.65pt;" valign="top" width="113"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">IP_proj</span></div>
</td>
<td style="border-left: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 1.6in;" valign="top" width="115"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">IP_proj
(with injuries)</span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 114.6pt;" valign="top" width="115"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">Average error</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 112.65pt;" valign="top" width="113"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">33.4</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 1.6in;" valign="top" width="115"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">30.1</span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 114.6pt;" valign="top" width="115"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">RMS error</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 112.65pt;" valign="top" width="113"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">46.0</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 1.6in;" valign="top" width="115"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">41.6</span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 114.6pt;" valign="top" width="115"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">r^2 (with
actual)</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 112.65pt;" valign="top" width="113"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">0.49</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 1.6in;" valign="top" width="115"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">0.58</span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1.0pt; border: solid black; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 114.6pt;" valign="top" width="115"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">% better</span></div>
</td>
<td style="border-bottom: 1.0pt; border-bottom: solid black; border-left: none; border-right: 1.0pt; border-right: solid black; border-top: none; mso-border-alt: .5pt; mso-border-alt: solid black; mso-border-bottom-themecolor: text1; mso-border-left-alt: .5pt; mso-border-left-alt: solid black; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: .5pt; mso-border-top-alt: solid black; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 112.65pt;" valign="top" width="113"><div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">50.1%</span></div>
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<span class="Apple-style-span" style="font-family: Georgia, 'Times New Roman', serif;">49.9%</span></div>
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Although only 50% of cases are improved, the average improvement is greater than the average mistake. I am improving r^2 by 10% for a system that already <a href="http://bezdomnybaseball.blogspot.com/2010/03/2010-ip-projections.html">compares very favorably</a> with PECOTA and CHONE for IP projection.<br />
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<b><span class="Apple-style-span" style="font-size: x-large;">2010 projections</span></b><br />
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I will have new 2010 IP projections up soon. Since these take account of the 2010 DL listings that take place during March, I want to make sure I have the most up to date DL listings first. But I will have something here very soon, in any case.<br />
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<br />Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com0tag:blogger.com,1999:blog-8942811343129148530.post-60292495866348497282010-03-24T22:20:00.000-07:002010-03-24T22:20:23.944-07:00Rays' pitchers' IP projectionsAfter breaking down the Yankees' pitchers' IP projections, I thought I'd look at another team, one the I do not know as well as I know the Bombers.<br />
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I do know that the Rays' staff is a young staff, with the Rays having a supposed glut of quality starting pitchers. After the 2008 season, they traded away Edwin Jackson, and last year they traded Scott Kazmir in mid-season. Both moves were made in part to make room for promising starters that they wanted to promote from the minors.<br />
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Here is a <a href="http://spreadsheets.google.com/ccc?key=0ApeOIUHA0khidFN5WUJWdTQyZFZIX0QwNUhTbDlRUnc&hl=en">list of my projections</a>, along with PECOTA and CHONE, for the Rays' top twelve pitchers, according to the <a href="http://tampabay.rays.mlb.com/team/depth_chart/index.jsp?c_id=tb">official depth chart</a> on the Rays website. Unlike the Yankees, the Rays project to have six guys primarily as starters, and six guys primarily as relievers:<br />
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<li>Starters: James Shields, Matt Garza, Jeff Neimann, David Price, Wade Davis and Andy Sonnanstine</li>
<li>Relievers: JP Howell, Rafael Soriano, Lance Cormier, Dan Wheeler, Grant Balfour and Randy Choate</li>
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Also unlike the Yankees, the Rays don't have four experienced starting pitchers. James Shields has four years of full-time starter experience, and gets projected at 190+ IP by all three projection systems. Matt Garza has two full seasons of MLB starter experience, both good but not amazing. He projects at 160 IP by my system, and somewhat higher by PECOTA and CHONE. The other four Rays' starters don't have much of an MLB track record, or at least not a record of consistent MLB success.</div>
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Jeff Neimann and David Price both have one full season of MLB starter experience, with decent but not amazing results. Andy Sonnanstine has 2.5 years of starter experience, but none of it was very good. Wade Davis was solid in a 36 inning debut last year.</div>
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I have all of these four pitchers projected to throw between 81.0 (Sonnanstine) and 142.3 (Neimann) innings this year. PECOTA has them all between 160 and 180 innings each. CHONE has them all between 155 and 171 innings (except for Price at 123 innings).</div>
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In this case, I must say that my estimates look low, when take together. I project the Rays' starting six to throw only 800 innings in 2010. A team typically has about 1000 innings thrown by starters (the Devil rays had 974 IP by starters in 2009). So my projections are about 200 IP short for starting innings. This suggests that the Rays are likely to use another starter (not in the 12 listed here) during the 2010 season, or multiple such starters. While that may happen, it's likely that the pitchers listed above will indeed pitch more than the 800 innings that I project for them.</div>
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Conversely, PECOTA projects the top six Rays' starters for 1082 IP, while CHONE projects them for 985 IP. The PECOTA figure is clearly high, while the CHONE figure looks about right. Then again, there is probably a chance that at least <i>some</i> starts will end up going to a Ray outside of the top six starters listed above, so the CHONE projection might be a little high, as well.</div>
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I think it's interesting to note that my system projects Wade Davis at a higher IP than Andy Sonnanstine. The later is more experienced, and threw a lot more innings last year than Davis. However, Sonnanstine's performance has not been great in 2009, nor has it been great in years prior. Davis was effective in 36 innings last year as a starter. My system projects him to throw 99.9 innings in 2010, which happens to be the highest projected increase from 2009 to 2010 among the MLB pitchers that I project.</div>
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Although my system does not use minor league stats, major league depth charts, scout projections or any other information besides MLB stats, it projects Davis as the #5 starter, and Sonnanstine as the #6. I thought that was interesting.</div>
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In summary, I think my system gives reasonable projections for the Rays' pitchers' IP, even if I would like to nudge them a bit higher collectively. CHONE also has reasonable projections (on average), although they assume that the Rays will not use any starters outside the six that they have on the MLB roster. PECOTA, as with the Yankees, significantly over-estimates the pitchers' playing time.</div>
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I'm curious to see how the season will unfold, and which of the set of predictions will come closest to what actually happens with the Rays' staff this year. The Rays have a young staff that many people think should be better in 2010 than it was in 2009. If so, my projections will probably end up being too low. The Rays are an exciting team, and I'd like to see them do well, so let's hope my models are wrong on this one.</div>Ivan Bezdomnyhttp://www.blogger.com/profile/07903311111105818224noreply@blogger.com0