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August 6, 2013

Baseball Therapy

Prioritizing the Pitcher's Health

by Russell A. Carleton

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Over the past few weeks, I've been taking an in-depth look at a single decision made by a manager: Tim Lincecum's 148-pitch no-hitter from a few weeks ago. Bruce Bochy left Lincecum in well past the usual 100-pitch limit to give him a chance at baseball immortality. But at what cost? We've seen that if a pitcher makes his next start on regular rest, there is a small carry-over effect of throwing a lot of pitches, but it's not all that big and it might even just be a methodological quirk anyway. We've seen some evidence that taking a pitcher out of a shutout (not necessarily a no-hitter) doesn't seem to affect him for good or for ill. But what about the obvious question. Are marathon pitching sessions penny-wise and pound-foolish?

There are plenty of people who would blame the demise of Johan Santana's career on his throwing 130 pitches in pursuit of a no-hitter in 2012 (despite the fact that he did miss all of 2011, so it's not like he was structurally sound to begin with.) There are still plenty of snide remarks about Dusty Baker's handling of Mark Prior and Kerry Wood during the Cubs' stretch run in 2003. Then again, Nolan Ryan has famously said that he does not believe that teams should be so beholden to the pitch count as they have been. Others have mumbled about how this is a problem of pitchers being soft and that they should "man up and shut up."

Does the evidence support the claim that pitchers who have especially long outings are more prone to injury? In the past here at BP, Rany Jazayerli popularized the idea of Pitcher Abuse Points, "awarded" to managers who allowed their pitchers to throw gobs of pitches. In 2000, Keith Woolner pulled pitch count and injury data from 1988-1998 and looked at career levels of pitcher abuse and the likelihood of injury. He found that "abused" pitchers (those who had games in which they threw a significantly large number of pitches) were more likely to be injured over the course of their careers. Let's take another look at the data, 13 years later and see whether the basic finding, that abusive pitch counts really are hazardous to a pitcher's health, is still supported.

Warning! Gory Mathematical Details Ahead!
I started with all games from 2003-2012, for the reasons that it's a nice 10-year stretch and we have pitch count data from all of those years. Here at Baseball Prospectus, we also have a database of all (reported) injuries since 2002, although for this study, I used only injuries that involved a pitcher being sent to the disabled list, since they were serious enough that a team realized that they needed to shelve a pitcher for at least two weeks to give him time to recover. I merged the two.

One problem with modeling injury risk is that one side effect of being injured is that you spend a good amount of time not pitching afterward. It might be two weeks or two months, but injured pitchers stop providing data (at least for a while). In research methodology terms, this is a clear bias in the data set. We need to find a way around that.

Fortunately, we can turn to the world of public health (and actuarial science) for some methodological help. One problem with modeling factors that can lead to death is that dead people don't provide much more data in the "after" phase of the research. Thankfully, there are techniques that take this very problem into account.

I'll be using a Cox regression analysis to model trips to the disabled list within a season. I structured my data set to look at each pitcher's starts sequentially from his first to his last start of the season, if he managed to avoid the disabled list all year, or from his first start to the last start he had before the first time he went on the DL. I realize that a pitcher might go on the DL, serve his two weeks, and come back and pitch, but previous research has shown that the greatest risk factor for being on the DL is whether a pitcher has previously been there. Once he's been on, his risk for subsequent trips (and subsequent lost productivity) goes up almost by a factor of 10 in the following year.

Cox regression assumes that at as time goes on, some percentage of the cases within a sample will "drop out." Not everyone who is exposed to a risk factor will be on the DL, but we will see that over time, those who are exposed to a risk factor will be more represented among those who drop out. And some pitchers who are not abused may simply land on the DL through dumb luck. Things happen.

I coded all starts for each pitcher for whether he crossed certain thresholds. I started at 75 pitches and worked my way forward in increments of five until I hit 130. For example, a pitcher who threw a standard 100 pitches crossed the threshold for 75, 80, 85, 90, 95, and 100 pitches. Since the theory of pitcher abuse suggests that not all pitches are created equal and that pitch 125 is marginally more damaging than pitch 85, for each line in the data set, I entered how many times a pitcher had crossed each threshold up to that point within that season. I controlled for the total number of pitches that he had thrown in total (yes, this will conflate a bit with the "threshold crossing" variables... we'll get to that) and for whether he had spent time on the disabled list in the previous year or two years prior.

I considered only starters who pitched their first game in April (or earlier) because those who came up later may have been in the minors, and who knows what happened there. This sampling method probably does have some noise in it, since some guys who make the team out of spring camp are found wanting and are sent back to Triple-A (and thus disappear from our radar), and there are swingmen who start sometimes and relieve sometimes. I'm willing to accept that noise.

The results of a Cox regression are similar in form to those of a binary logistic regression in that we are building a term that is a natural log of the odds ratio that an event will happen. Here, we are specifically modeling whether the pitcher will make his next start or will succumb to an injury severe enough to put him on the disabled list. This makes eyeball interpretations a little harder, but let's start with a pitcher in his first start who has no previous disabled list history.

First, here are the coefficients from the Cox regression:

Factor

B

Standard Error

Significant?

Crossed 75 pitches

.260

.095

Yes

Crossed 80 pitches

.238

.089

Yes

Crossed 85 pitches

.140

.071

Yes

Crossed 90 pitches

.238 [sic]

.060

Yes

Crossed 95 pitches

.167

.049

Yes

Crossed 100 pitches

.166

.049

Yes

Crossed 105 pitches

.165

.055

Yes

Crossed 110 pitches

.171

.065

Yes

Crossed 115 pitches

.253

.097

Yes

Crossed 120 pitches

.004

.167

No

Crossed 125 pitches

.333

.311

No

Crossed 130 pitches

.678

.478

Yes

Total number of pitches to date

(.038)

.002

Yes

DL stint last year (yes/no)

.560

.105

Yes

DL stint 2 years ago (yes/no)

.573

.107

Yes

Once a pitcher hits 75 pitches, we create the function that he will "die" (i.e., end up on the disabled list afterward) by taking the coefficient from crossing 75 pitches (.260) and adding the contribution of the number of pitches (-.038) * 75. We get -2.59. This is equal to 6.59 percent. That may seem like a lot, and it is. There's an unseen adjustment for the number of starts that a pitcher has made. In theory, his arm is not as tired (and injury-prone?) in his Opening Day start as it is in his 14th start. It isn't that he has a six and half percent chance of landing on the DL after throwing just 75 pitches on Opening Day. (It's actually much lower.) It's more instructive to look at how each step along the way adds to the overall injury risk.

Let's look at the predicted contribution toward injury risk that each step on the ladder makes and (more importantly) the change in that contribution over time.

Threshold crossed

Predicted contribution to injury risk

Delta from above

75 pitches

6.59%

--

80 pitches

6.91%

0.32%

85 pitches

6.59% [sic]

(0.32%)

90 pitches

6.89%

0.30%

95 pitches

6.75%

(0.14%)

100 pitches

6.59% [sic]

(0.16%)

105 pitches

6.43%

(0.14%)

110 pitches

6.32%

(0.11%)

115 pitches

6.71%

0.39%

120 pitches

5.62%

(1.09%)

125 pitches

5.85%

0.23%

130 pitches

10.19%

4.34%

This is a rather interesting table. Injury likelihood actually stays relatively flat up to 110 pitches. At 115 pitches, there's an upswing, then a downswing at 120. The finding that, of course, stands out is that pushing a pitcher to 130 pitches has an enormous effect, bumping up the chances that the pitcher will suffer an injury that will put him on the disabled list after this start by more than four percent, and in all of his subsequent starts for the year.

It's worth pointing out that if you look at the standard errors for those regression coefficients, they get bigger (that is, more unreliable) as the pitch counts get bigger. This is, in part, because there aren't a lot of games in which a pitcher clocks 130 (or 120) over the last 10 years. Small sample sizes make for unreliable regression coefficients. However, it seems that 130 pitches in one outing is the inflection point where small increases in injury risk (which will always be there) turn into downright hazardous working conditions for a pitcher.

Additionally, it's a biased sample that gets to go well above 110. Somewhat by definition, it's guys whom managers and pitching coaches believe are able to handle such a workload on one night and not suffer too great an effect. Assuming that they have some idea of what they are doing (i.e., they are smart enough to introduce bias into the sample—and I do worry about how much bias that is and don't know how to fully control for it), we need to be careful about saying that everything would be just peachy for all pitchers who get to 115. In that group, we're getting data only from those who are certified workhorses. Despite that, the effect at 130 shines through, and the effect size is larger than having a previous DL stint. It looks like even workhorses have a point where they break down and are sent to the glue factory.

I ran some supplemental analyses in which I looked to see whether these effects varied by age (on April 1st) by including all of the variables in the original regression, as well as an interaction term for each of those variables with age. None of the interaction terms reached significance. I did the same for body-mass index (perhaps bigger pitchers can handle the workload?) Nothing there. I also used body-mass index squared, to allow for a quadratic function. Perhaps there was a body-mass index that was a happy medium for handling workloads? There was not.

The Society for the Prevention of Cruelty to Pitchers
Let's sum up some take-home messages:

1) There will always be injury risk to starting pitchers. It happens.

2) Going a little bit beyond the usual 100-pitch limit does not appear to appreciably increase the risk of an injury later in the year. Whether or not a pitcher is effective after 100 pitches or whether the team would be better off with a fresh reliever is another issue. Frankly, if your bullpen is so bad that you don't have someone out there who is better than a starter with 110 pitches logged, you have a bigger problem.

3) Letting a pitch count climb up around 120 is entering a danger zone, and is probably understated somewhat by these findings due to the sample bias inherent in who gets to throw 120 pitches in a night. Letting any pitcher exceed 130 pitches has the same effect as going back in time and giving him a significant injury (one big enough to land him on the DL), and a previous DL trip is a very powerful predictor of a future DL visit.

4) Once a pitcher has thrown an extended outing, he will carry the "scar" of that event until the end of the season. He might not go on the disabled list the next day, but he's now a bigger injury risk every time he takes the mound.

5) We are dealing with probability here, not certainty. There will be pitchers who have a marathon outing and never get hurt. There will be those who are handled with kid gloves and get hurt after three starts. Sometimes, you do everything right and it doesn't work. Maybe the obsession with 100 pitches as a hard limit for a start isn't the right cutoff point for preventing injuries, but there is clearly a point where high pitch counts do become abusive to pitchers.

Russell A. Carleton is an author of Baseball Prospectus. 
Click here to see Russell's other articles. You can contact Russell by clicking here

Related Content:  Pitcher Abuse,  Pitchers,  Injuries,  Pitcher Usage

13 comments have been left for this article. (Click to hide comments)

BP Comment Quick Links

Shawn

What about a further look into "pitching load" of a game...or even just a straight look at speed of pitches in a game? From an intuitive standpoint, not all 100+ pitches games are the same from an effort point of view. Since we should have pitch f/x data for good time frame, it should be straight forward to come up with an "effort" metric and then see if there is a particular profile of a type of 100+ pitch effort that brings more danger than another...

Aug 06, 2013 05:44 AM
rating: 1
 
BP staff member Russell A. Carleton
BP staff

A thought that has crossed my mind as well. One problematic issue is that Pf/x doesn't capture mechanics. But, the motion for curvy stuff is probably harder on the arm than a fastball (which is why curves are often banned in little league). Maybe there's something to it.

Aug 06, 2013 06:45 AM
 
jroegele

When I did the Tommy John studies last year, I found a pretty clear indication of harder throwers being more susceptible (after controlling for age and pitching role). This was present across all pitch types.

In looking at pitch type frequencies, I found pitchers who went for TJS threw slightly more fastballs and sliders than the average pitcher, not curveballs. There seems to be academic literature that points in this same direction.

Really interesting article Russell!

Aug 06, 2013 08:38 AM
rating: 3
 
tannerg

The other "pitching load" factor I'd consider would be pitches per inning.

Back in the day, 30-pitch innings would just wipe me out. A 30-pitch inning was much more difficult on me than two 15-pitch innings. I'd likewise expect that a 110-pitch complete game is less dangerous than a 110-pitch six inning stint.

Aug 06, 2013 09:37 AM
rating: 6
 
Behemoth

Could the over 130 effect be partially caused by a considerable portion of over 130s being no hitters or attempts, which would mean that those pitchers are not necessarily the most able to get through a large number of pitchers?

It seems odd that there's no real difference up to 125 and then a huge difference at the 130 mark. Also, historically, pitchers frequently used to pitch what would be seen as ridiculous workloads to modern eyes without breaking down. While I get that this isn't necessarily comparable, in that pitchers are throwing harder than ever and so on, I have a feeling the story is more complex than the numbers initially suggest.

Aug 06, 2013 06:02 AM
rating: 1
 
BP staff member Russell A. Carleton
BP staff

It's always more complex than the numbers suggest. Teams have constructed the role of pitcher differently in the past 10 years than they did in the 70s. They also train differently, etc. The game is constantly evolving. I'd happily concede that my findings only apply to recent years, but thankfully, that recent era is still going on!

Aug 06, 2013 06:48 AM
 
StarkFist

So would that mean that a team could revive old timey training methods and get more starts and longer outings from their starters? Seems like an advantage to whichever team can make such an idea work.

Aug 06, 2013 14:56 PM
rating: 0
 
BP staff member Russell A. Carleton
BP staff

I wonder if it's olde timey training methods or olde timey understandings of risk management.

Aug 07, 2013 07:20 AM
 
StarkFist

Well you told Behemoth that differing training methods are a part of why starters, as recently as the 70s & 80s, handled workloads we now would consider abusive. Now I know that nobody's going to revive those methods so as to get 40 starts or 300 innings out of a starting pitcher - there's too much money to be lost by risking him that way over a 162 game season.

But a team that's in a tight pennant race might be tempted to do it over the closing weeks of the season, if it means their ace is going every 4th day and throwing 140 pitches, whereas their rivals are only able to run their ace out there every 5th day, for 100-110 pitches.

Aug 07, 2013 10:48 AM
rating: 0
 
m12981

Russell, really enjoyed the work as always. Do you think there might be any information to be mined from organizing the data based on pitching mechanics? For example, doug thorburn writes detailed reports about pitching mechanics of various pitchers in MLB, and I'm wondering if some of the mechanical indicators he writes about (trunk rotation, scapular loading etc) would provide an addition variable for use in isolating players with higher or lower probabilities of getting hurt under different work loads?

Aug 06, 2013 06:44 AM
rating: 0
 
BP staff member Russell A. Carleton
BP staff

One of my new year's resolutions is to kidnap Doug Thorburn and just pick his brain for an hour on the subject.

Aug 06, 2013 06:46 AM
 
jfranco77

Does PFx give you a breakdown of pitches by inning? I'd love to see a similar table with peak pitches per inning.

If someone has an inning where they throw 30+ pitches, their injury likelihood goes up by X. If they have an inning where they throw 40 pitches, it goes up by Y. Etc.

Or even a combo with this data... so you'd see

80 pitches/max no more than 20
80 pitches/max no more than 25
80 pitches/max no more than 30

Aug 06, 2013 12:35 PM
rating: 1
 
Duranimal

This is the kind of stuff that makes me wonder why Kershaw hasn't signed his mega deal yet. Why risk $200 million when every pitch you make could be your last.

Aug 06, 2013 15:20 PM
rating: 1
 
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