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

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.

Condition Similar Event Last Year No Similar Event Last Year Had an elbow injury 27.4% 2.0% Had a shoulder injury 32.4% 2.8% Had any injury 73.4% 5.1% Spent time on DL 43.7% 4.9%

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.

Condition Similar Event Two Years Ago No Similar Event Two Years Ago Had an elbow injury 15.2% 1.8% Had a shoulder injury 23.2% 2.3% Had any injury 55.6% 2.7% Spent time on DL 34.2% 3.5%

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.