Pitcher injury effects on projected value (Part I: Overview)

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.

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.

Measuring Pitcher Value

If a pitcher's value is defined as runs saved, then his value can can be expressed as:

Runs saved  = Innings pitched (IP) * Runs saved per inning (ERA - replacement ERA)

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.

A commonly used statistic to measure pitcher runs saved is VORP. 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.

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.

Data Sources & Results

I am using rich injury data from Corey Dawkins's injury tool. 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."

I have written about using this data to improve IP projection. Executive summary: there are several (7) categories of injuries that have large predictive effects on IP. 

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. 

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.)

	Correlation to (real) VORP	STDEV from baseline projection
Basic (no injuries)	0.587	0.0
ERA with injuries	0.599	1.2 VORP
IP with injuries	0.619	2.8 VORP
ERA & IP with injuries	0.624	3.2 VORP

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.

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.

Why injuries don't affect ERA/FIP projections much

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:

-0.4223 * inj_elbow_surg_not_tj_2008

+ 0.0671 * inj_anyDL_2008

+ 0.1826 * inj_dl_camp_2008

+ 0.1641 * inj_anyDL_average

+ 0.2736 * inj_surgery_ip_average

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.

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 did not hit the DL or undergo surgeries in recent years. Contrast this to the extensive injury-based adjustments that I found for my IP model.

Selection bias?

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?

For my FIP training, I include all pitcher seasons. However, I weigh instances by the inverse of expected FIP variance, estimated from real IP. I wrote about this in my previous post. 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.

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.

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.

Conclusions? Effects on Fantasy?

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.

If my observations prove to be true, what does this mean for projecting "injury risk" for fantasy pitchers?

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.

However, there is no noticeable effect on FIP/ERA from past shoulder injuries when projecting future performance based on past results. Therefore, if he plays, 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.

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.

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.