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A couple of weeks ago, I took on the "Verducci Effect". Tom Verducci of Sports Illustrated has hypothesized that a pitcher who is under 25 years old and who had an increase in his workload of 30 innings or more in the previous season is at greater risk for injury or for a steep decline in performance. This is a great hypothesis, but for the fact that it is not actually true.

It's nice that people can stop worrying about their favorite pitcher on the Verducci list (for now), but if all I do is play mythbuster, then I'm not really adding anything to the conversation. At that point, I'm the guy walking around with amazing hindsight talking about how amazing his hindsight is. In other words, I'm every caller on every sports talk radio show ever. So, let's get constructive: What actually does predict pitcher injuries?

Warning! Gory Mathematical Details Ahead!
To write the Verducci article, I had created a dataset which predicted injury risk based on factors from the previous year. Since I was already importing last year's stats, it wasn't that hard to add a few more in. I used only data that would have been available in the off-season prior to the season in question, so in looking at what predicted injuries in 2012, I used only data that would have been available at the end of the 2011 season. Pitchers of all ages were considered.

To that end, I constructed a few binary logit regressions modeling what variables were associated with a pitcher suffering an elbow injury. Then, a shoulder injury. Then, any injury whatsoever. Then, any injury that landed him on the disabled list. Similar to my Verducci analyses, I looked only at pitchers for whom 80 percent or more of their appearances came as starters.

I used a forward stepwise model to enter the following variables:

  • Whether or not the pitcher sustained any injury of any sort the year before, or the year before that
  • Whether or not the pitcher had been on the disabled list the year before, or the year before that
  • For the body part-specific injuries, whether he had an injury to that body part the year before or the year before that
  • The previous season’s K/BF, BB/BF, HR/BF, and ERA (MLB level only)
  • The previous year's flyball, groundball, and line drive rates (MLB level only)
  • How many batters the pitcher faced in the previous year (majors, including postseason, and minors) and how much of a change that was from the year before
  • How many innings the pitcher logged (majors, including postseason, and minors) in the previous season, and how much of a change this was from the year before
  • How many pitches he threw (MLB only) and how many pitches he averaged per batter faced (MLB only… and yes, I know this is a problem)
  • What percentage of time hitters made contact on his pitches (fair or foul)
  • The number of foul balls that a pitcher gave up in two-strike counts, per batter faced that got to a two-strike count (this is a proxy for "put him away” stuff)
  • His age (based on April 1st of the current year) and body-mass index

For those unfamiliar with how a stepwise method works, it considers all the predictors, finds the strongest one (assuming that at least one of them is a significant predictor), and runs a regression using that predictor. Then, it looks for the next-strongest unique predictor once the first variable has been controlled. In this way, we can look at which variables are strongest in predicting injuries.

First, shoulder injuries. In order of strength of prediction, the best predictors of whether or not you will have a shoulder injury in the coming year are whether you had a shoulder injury last year, how many pitches you threw last year, whether you had a shoulder injury two years ago, how many extra batters you faced last year from the year before (with a greater increase meaning that you were less likely to be injured), and the two-strike foul rate (just barely). It's clear that guys with pre-existing conditions are a risk. This shouldn't be too big a surprise. But if you were entrusted to face more batters last year, it might be a sign that the team thinks your shoulder is okay. It’s hard to tell whether the two-strike fouls issue is cause or effect. If you're not able to blow that fastball by hitters, it might be because there is some shoulder damage that's really the beginnings of an injury.

For elbows (in order): Home run rate (lower HR rate guys have elbow injuries more often), whether you had an elbow injury last year, the number of batters you faced last year, the change in the number of innings you pitched last year (again, a bigger increase leads to a lower rate of injury), and ERA (the higher the ERA, the more likely you are to get hurt).

For any injury at all, there were two factors: You are more likely to get injured if you threw more pitches last year, and if you had an injury last year.

For spending time on the disabled list, we see a similar pattern: the number of pitches thrown in the last year, spending time on the DL last year, and the change in the number of batters faced (once again, a big increase meant a drop in injury chances.)

How big is the risk?
It's clear that the biggest risk factor for injury is previous injury. How big? Turns out the answer is "very."

I compared players who had an elbow injury last year to those who did not, and the frequency at which they suffered an elbow injury in the present year. Then, I did the same thing for whether a pitcher had a shoulder injury last year and the chances of a shoulder injury. The results were rather startling.


Similar Event Last Year

No Similar Event Last Year

Had an elbow injury



Had a shoulder injury



Had any injury



Spent time on DL



Are you looking to avoid injury risk this year? Look for the guy who had a clean bill of health last year.

And no, just because you made it through last year without getting hurt, it doesn't reset the clock (although it does seem to ameliorate the problem). I eliminated all players who had a relevant injury in the previous year, and instead looked whether injury history two years earlier predicted current-year boo-boo chances.


Similar Event Two Years Ago

No Similar Event Two Years Ago

Had an elbow injury



Had a shoulder injury



Had any injury



Spent time on DL



As to extra pitches, it's harder to show the effects of what an extra pitch does to the chances of injury next year, owing primarily to the way that logistic regression works and that there are other factors involved. (For the initiated, the exponentiated B on the final model for DL stint was 1.000989073323). To give you some estimate of the effect that might have, imagine that a pitcher went from 3000 pitches in a season to 3300 (the equivalent of going from 30 starts with 100 pitches per start to 110 pitches per start). The increased chance of a DL visit is on the order of a couple of percentage points. Given that the baseline rate for a pitcher who is not previously injured is 4.9 percent, that's not trivial. Managers, please see to it that your pitchers never throw another pitch.

For what it's worth, I ran similar logistic regressions with several interaction terms (most of the above factors by age, and by injury history last year). The message remained the same. Injury history was still the top predictor, along with raw number of pitches thrown, and as you might expect, having a previous injury or being older made things somewhat worse.

What to make of it
Let's talk a little bit about risk vs. certainty. In this article, I'm presenting risk factors for future injury. Focusing for a moment on the data presented on disabled list time, a previous DL trip makes a pitcher about eight times more likely to land on the DL this season. But even at that, the rate at which previous disabled list visitors go back on is lower than 50 percent. A pitcher with an injury history is not a certainty to get injured, just a much higher risk. Let me also point out that my model is rather unsophisticated, but a better model would require medical training (which I don't have) and medical knowledge (which is not public).

The take-home message is one that is probably not very shocking to anyone. An injured body part is more likely to get hurt again. A pitcher who has thrown a lot of pitches is more likely to have a lot of wear and tear on that arm. It's not rocket science, although I do wonder if people understand the magnitude of the effect size. For those of you preparing for fantasy drafts by combing through the BP player cards, take a look at each pitcher’s injury history and pay attention to how many pitches he's thrown. Also, pay attention to whether he's a high or low pitch efficiency guy. There's a difference.

I'd love to say that there was some sort of magic formulation that predicts injuries. If nothing else, the Verducci Effect was a little more interesting than "things wear out." It "explained" really highly emotionally charged injuries (catastrophic ones to young pitchers) with a formulation that could be easily controlled. According to the Verducci Effect, teams needed only to avoid extending their young pitchers to maximize their odds of staying healthy. My model doesn't offer as much comfort. Once a pitcher is damaged, he's damaged goods. And it's not like you can tell a pitcher not to throw another pitch; that's what pitchers do. And sometimes they get hurt. That's life.

Thank you for reading

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This is awesome. It's such an important area of research, and it's great to see that we now have some tools to even begin to tackle it.

I'm trying to reconcile how throwing more pitches increases risk of injury, but a large increase in innings pitched corresponds to a reduced risk of injury. Did I understand that correctly? Wouldn't more pitches and more innings seem to go hand-in-hand?

Also, is there any way to consider single-game factors? (e.g. "having a game with 130+ pitches thrown corresponds to X% increase in likelihood to go on the DL next season [same season?])
It's all regression-based, so you have to interpret that as "holding everything else constant, another inning actually predicts a lessened chance of injury."

A lot of it comes down to pitch efficiency. The big message is that it's the number of pitches, not the number of innings that you rack up.
I also think players recover at different rates. A younger guy might be able to rehab faster than an older one(no data to support this). I'd be interested to see if you broke the model down more to include age, if possible. And also are some teams better at being able to notice injuries before they get worse?! To me there are many factors that can affect a players ability to get injured or stay healthy. I think some players are better conditioned, some are better at knowing their limits, some pitch hurt(to help the team) but it makes the injury worse and recovery time as well as future injury all the more likely. I think each case has to be looked at individually because there is so much noise or underlying factors involved with injuries. Some other factors to maybe look at: what type of pitcher(power, finesse, groundball, flyball, etc). Does a particular group get hurt more? And if so why? Is the power pitcher overthrowing rather than locating a fastball? Is there a hitch in the mechanics? Is the pitcher throwing over his body which could lead to injury as opposed to a smooth motion? Great informative article as always.
I did look at many of those issues, but didn't report due to space. I entered interaction variables (e.g., number of pitches x age) into the regression. Being older added injury risk, as might be expected. As to whether power/finesse pitchers are more likely to be injured, those were mostly secondary predictors when they were significant. But then, my model was a first pass at this sort of thing. Must. Improve. Regression. Equation.
Check out James Andrews' recently released book, Any Given Monday. It's a great read on sports injuries and the prevention of them.
I'm struck by how many of the predictors of injury might, themselves, be indicators of an already present, undiagnosed injury. All of the negative outcome predictors seem to have equifinality issues, in that they may be a predictor for future injury or simply an indication of a current injury that has yet to be diagnosed.
I think you're right on. I don't know if we can pull apart the chicken from the egg on that one.
Thanks, Russell. This is the sort of thing us BP readers have been hungry for.

Did you look into height? It has long been a rule of thumb that shorter pitchers burn out faster than taller guys, who might take longer to develop. Of course, burning out and getting injured are slightly different things. I'm not sure how telling plugging in height to this study would prove anything about career length, but it might be another variable worth testing for injury.

What would also be really interesting would be to compare pitchers who throw various types of pitches. With pitchers all throwing various percentage of pitches and various sources claiming different pitch type data, I realize that could get very messy. You'd be the man to sort it out, though, I do trust.
Oddly enough, I put in BMI, but not height... And I have height right there ready to go

Bad researcher. No Hot Pocket for you.
Nice work, Russell. If I am interpreting your findings correctly, the marginal risk to injury is greater when going from, say, 3000 to 3300 pitches in a season, than from going from 2000 to 2300. If the marginal risk doesn't increase, then it's, well, every pitch is dangerous so you might as well just work pitchers hard when they're at the peak of their abilities.
The marginal risk of pitch #2000 is different than the risk of pitch #3000, if ever so slightly. It then becomes a risk-tolerance question. You can push Smith for another inning and he may be better suited to handle it than anyone and you might need this inning, and maybe you don't blow out his arm. But maybe that's the sinker that breaks Smith's elbow.
Thank you, I was really looking forward to reading this article in light of conversations I had this weekend regarding Felix Hernandez. He's lost about 4 mph in the last 5 years, which is a significantly greater loss than an average pitcher over the same period. Did you consider using loss of velocity? Any other info you can share that's Felix-specific would be very welcome.
The reason that I didn't do velocity measures was that i didn't have time to merge in the Pf/x database. It's worth a look.
I actually thought the converse may be true. Perhaps a recent spike in velo could lead to ligament damage in the elbow. While everything else is strengthened, the ligament isn't and gives out. Danny Duffy comes to mind.
Duffy had had a tear in his UCL since 2009; it just finally gave out to the point of needing surgery. But you could still have a point...perhaps it wouldn't have given out if he hadn't had the velo increase.
The elephant in the room here is mechanics. I propose the following long-term study: Get two groups of people together to predict pitcher injuries based on what they see of pitchers' mechanics from the videos that are abundantly available today, one group comprised of so-called "experts" on pitching mechanics, one of random fans like most of us are. Conduct a modified Delphi experiment to get predictions on say 100 pitchers or so, then simply seal them away, unread, for the rest of the season. Haul them out after the season is over and see what happened, whether there is a correlation between predicted breakdowns and actual days lost. (And also, how much better the "experts" do at predictions than the hoi polloi; that too would be interesting to check out, and is the reason why I suggest two groups. Is there such a thing as "wisdom of the crowd" when it comes to pitching injuries? I really wonder.)

BP is one of the few sites out there that could actually bring this off, between access to some of those experts on the one hand, and continuity in your own staff, to be custodians of the predictions without spilling the beans, on the other. How about it?
It would be really interesting to examine the effect of multiple DL trips, and to include the length of the DL stay as a factor in the regression.
For elbow injuries you have home run rate listed as more predictive than a previous year's elbow injury. Is that right? Given how predictive previous injuries are, that would be scary for every groundballer out there.
Your reading is correct. And it is scary.
Thanks. Now I have to start worrying about Felix all over again.
Might be interesting to see if certain injuries affect certain aspects of pitching performance. For example, do certain types of shoulder injuries lead to worse BB/9 rates, etc.
So Brett Anderson, with a previous elbow injury and massive GB rate, is due for an elbow implosion that might destroy the entire Bay Area?
Great article!

a couple of things..

1. Does this ever so slighty confirm the old adage "Injury Prone"?

2. A friend of my just texted me: "You know what would be helpful though? I list of the at risk players for 2013 so I don't have to do it!"