In 2014 it seems like every young promising pitcher is going under the knife for Tommy John surgery. Baseball fans, teams, staff, writers, and analysts have written a lot of digital ink about what the causes of this seeming epidemic may be.

One writer, Joe Sheehan, piqued my interest in the May 28th edition of his newsletter. In it he explores the odds that velocity is a strong predictor of whether a pitcher has had or will have Tommy John surgery. He wonders in particular whether starting pitchers whose fastballs average 95+ MPH are at an increased risk vs. their counterparts. Hence his use of the word “demon” to describe the phenomenon:

I’m thinking of “The Right Stuff” here. The movie — it’s one of the few Tom Wolfe books I haven’t read — opens with a narration about “the demon” that lives at Mach 1, the speed of sound. Maybe, and I am spitballing here, 95 mph is where the demon lives when it comes to elbows.

(p.s. Joe, I’ll happily lend you the book if you like. It’s great.)

In reading his post and looking at his research and conclusions I immediately thought of the problem in Bayesian terms. We can ask ourselves the following questions:

- Given that a pitcher throws 95 MPH+, what is the probability that pitcher has experienced (or will experience) Tommy John surgery?
- Given that a pitcher throws 93-94.9 MPH, what is the probability that pitcher has experienced (or will experience) Tommy John surgery?

The goal here is to say, if all you know about a pitcher is that he throws 95+ MPH regularly, how likely is it that this nameless, faceless, team-less pitcher has had (or will ever have) Tommy John surgery? And how much more likely is he to experience this surgery than if he throws 93-94.9 MPH?

Here are the important numbers that Joe found with his research:

Velo Pitchers TJ post % TJ any %

95+ 22 5 23% 10 45%

93-94.9 98 13 13% 22 22%

Where:

- Velo is the average four-seam fastball velocity
- Pitchers is the number of pitchers who throw this hard. Note that Joe researched only starting pitchers here.
- TJ Post is the number of pitchers who had Tommy John surgery soon after recording the velocity
- % is TJ Post / Pitchers
- TJ any is the number of pitchers who had Tommy John surgery either
*before*or after recording the velocity. Joe’s reasoning here is that post-surgery pitchers generally return to throwing as hard as they did before the surgery. So if a pitcher throws 95+ MPH after the surgery, it’s safe to say he threw that hard before it. - % (the second one) is TJ any / Pitchers.

Regarding the % columns, you can see how he would conclude that it appears throwing 95+ MPH roughly doubles a pitcher’s chances of undergoing Tommy John surgery.

In my analysis I only concerned myself with the **TJ any** column. Let’s define our Bayesian variables for the first question:

*x*is the base probability of any pitcher having Tommy John surgery. This, according to another data point in Joe’s newsletter, is .20.*y*is the probability of experiencing Tommy John surgery, given a pitcher throws 95+ MPH. In this dataset that is .45 (as Joe found).*z*is the probability of experiencing Tommy John surgery, given a pitcher throws 93 – 94.9 MPH. In this dataset that is .22 (again, as Joe found).

Put it all together with (*xy*) / ((*xy*) + *z*(1-*x*)) and you have .34. That’s the answer to our first question. For the second question, you run the same math but swap *y* and *z* as defined above. You get .11. In each case the probability is slightly lower than what Joe found. But the questions we’re asking differ slightly.

.34/.11 is 3.05. This analysis shows that pitchers who throw 95+ MPH are not twice as likely, but **more than three times as likely** to experience (or to have experienced) Tommy John surgery as pitchers who average between 93 and 94.9 MPH. Put another way, if all you know about a pitcher is that he throws 95+ MPH and you guess that he’s had (or will have) Tommy John surgery, you will be right three times more often as you would be in making the same guess about a pitcher who throrws 93-94.9 MPH.

Further research is needed, but the numbers above seem like more evidence for a hypothesis that in general, the harder you throw your fastball as a starting pitcher, the higher the probability you’ll have Tommy John surgery. Indeed, the American Sports Medicine Institute recently released a position paper with their findings on the rash of surgeries. Their last reminder was that “Pitchers with high ball velocity are at increased risk of injury.” We’re starting to get an idea of just how much the risk increases.

Thanks again to Joe for inspiring this research!

Very interesting. Double odds is a big time #. Good work. It is amazing what 1 MPH will do