Pitching a fit

Gobo's fun thinkpiece on falling in love with Randy Johnson and his related fears of what high pitch counts will do to Jason Schmidt's arm got me to thinking about the relationship between pitch counts and injuries. Higher pitch counts would seem to suggest a higher rate of arm fatigue, and therefore a higher potential for serious arm (elbow, rotator cuff, etc) injuries. I still think there's some sense in this; the problem becomes how to divine the magic number of pitch counts and get a sense of where pitchers traditionally run into trouble if you assume equal access to conditioning methods, etc.

Bobby Cox usually gets pegged as a guy who protects his pitchers. Here's where the Braves rotation falls in P/GS (pitches per game started) with their ERAs following in parentheses.

Mike Hampton: 95.4 (6.36 era)
John Thompson: 96.0 (5.01 era)
Russ Ortiz: 95.4 (5.18 era)
Jaret Wright: 94.4 (3.55 era)
Horacio Ramirez: 103.3 (2.25 era)

Dusty Baker usually gets pegged as a guy who abuses his pitchers. Here's where the Cubs rotation falls in P/GS with their ERAs following in parentheses:

Greg Maddux: 84.0 (4.44 era)
Matt Clement: 103.9 (2.53 era)
Carlos Zambrano: 105.1 (2.08 era)
Kerry Wood: 100.9 (2.82 era)
Sergio Mitre: 86.1 (4.93 era)

Let's leave Greg Maddux out of this for now, because he's an anomaly. And Jaret Wright isn't so interesting from a statistical perspective. Looking at everyone else, the guys with the highest pitch counts (Ramirez, Clement, Zambrano, Wood) are also averaging the highest number of innings per start. Ramirez, for example, has tossed more innings than Hampton in less starts. The other half (Hampton, Thompson, Ortiz, Mitre) have lower P/GS averages because they aren't going as deep into games because they simply haven't been as effective. Verdict: inconclusive evidence. One might suggest that both Cox and Baker are within the bounds of fair use on their rotation's arms.

Historical data on pitch counts is notoriously hard to come by, though we know that the 100-pitch benchmark is an invention of the candy-ass modern era because it held no place in the era of the 4-man rotation. So the difference between John Thompson's 96.0 P/GS and Carlos Zambrano's 105.1 isn't of much concern -- it's reflective right now of how successfully they've pitched. And that only amounts to a +/- differential of 5%. It's more about extremes. What excites and scares us is what happens when Kerry Wood throws, say, 120 pitches in a game. And then what happens when he throws, say, another 120 pitches in the following start. And what effect a certain amount of stress might have on his arm when he's averaging only about 100 pitches per start.

Rany Jazayerli of Baseball Prospectus used the 100-pitch benchmark as the basis for his Pitcher Abuse Points (PAP) study in the late 1990s. Rob Neyer (a frequent collaborator) hyped PAP considerably upon arrival and maintains his virulent distaste for high pitch counts; Jazayerli issued a retraction in 2001 and Baseball Prospectus has since removed the initial study from their website. No knocks against the brilliant Jazayerli, but he definitely bit off more than he could chew. You may recall this point-by-point evisceration of PAP done by Don Malcolm; if not, it's definitely worth following the link and reading up on the historical problems associated with developing a formula for weighing pitch counts.

One of the more interesting ideas that came out of Malcolm's response was the notion that multi-start windows were a better way of divining the injury risk that comes with high pitch counts. Malcolm and company settle upon 350 pitches / 3 starts (or an average of 115 pitches per start) as the cut-off, citing Jim Leyland's use of Alex Fernandez (397 pitches / 3 starts = career-ending injury) as an example of the effects of high pitch counts. Watch the magic number creep from "100" to "115" just like that!

Those guys at Baseball Prospectus sure are tenacious, though. Keith Woolner picked up where Jazayerli left off with using pitch counts to predict stress and issued his own revision called PAP^3. Woolner assumes that "all pitchers have the same physical reaction to a given number of pitches" and comes up with a lovely polynomial curve to illustrate his findings. It does not, however, draw a distinction between the types of pitches thrown or make any provisions for delivery/mechanics. Which is problematic.

What's interesting about the study is his consideration of "high endurance" pitchers -- a class which might currently include folks like Kerry Wood, Randy Johnson, Curt Schilling and Jason Schmidt. Here's the shocker: the difference between a 90 pitch start and a 129 pitch start with a well-traveled arm is imperceptible. As the fine folks at Baseball Reference point out in their analysis of Woolner's work, this class of pitcher actually sees a slight improvement from pitch 120-129, pushing the "danger zone" to 130 pitches and above. So under that logic, Jason Schmidt's 144 pitch outing of a couple nights back could be dangerous in a broader context.

PAP^3 earns higher marks than PAP, but even Woolner is quick to point out that his theories are begging for refinement. There's enough to like from all of the work done so far on pitch counts:

* Nothing has disproved the long-held supposition that high pitch counts ruin young arms. What would be intriguing is a specific study on exactly how high pitch counts affect young pitchers, perhaps by pulling a nice sample of rookies and comparing their progress/degradation by comparing what transpires, say, before the first 150 career innings pitched and after. Step two might be to get a sense of when to keep young pitchers to a strict pitch count and when to relax the restrictions.

* "100" is a nice, clean number -- but a misleading choice for a benchmark. Research done thusfar supports a higher total, perhaps with a +/- differential to account for some/all other mitigating factors.

* And the move from considering a pitcher's workload on a start-by-start basis to weighing workload in larger clusters or over a 30 start period is sensible.

It's telling that the saaviest sabermetric theories from the Baseball Prospectus camp over the course of the past decade have centered on offensive production/ defensive range/ how individual contributions relate to team contributions. Pitching is not so easy to consider. Then again, pitch counts have only been recorded on the books for about 15 years, less than the lifespan of some of this generation's finest arms. More accrued data can only help, though I also get the sense that this is one problem that even the great Bill James couldn't crack.