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Weekend Report: Pitcher Abuse Points
Geoff Jenkins will be out for the year with a fractured thumb, but his performance during this streak is unforgettable.

What we don't know about pitchers and injuries could fill an encyclopedia set, yet few can doubt the importance of producing healthy and productive pitchers. Whether you admire or despise Oakland's success with minimal resources or Atlanta's decade-plus of dominance, finding and keeping Cy Young caliber starters healthy has been key to both organizations. With this in mind, we'll examine Pitcher Abuse Points (PAP) as a statistic to see how it attempts to shed light on the subject. I'll analyze the evolution of the statistic from its beginning to its current incarnation.

It is rather surprising that PAP works, given its origin ( ). Rany Jazayerli more or less made it up out of thin air as an alternative to pitch counts. He started with two ideas. The first was earlier empirical work that suggested that pitch counts over 100 were associated with increases in the rate of pitcher injury. The second idea is that not all pitches over 100 were equal. It seemed logical that the chance of injury increased faster as more were pitches thrown. As an example, 101 pitches doesn't seem nearly as bad as 121 or 131. To represent this, he chose to assign points only for pitches thrown in excess of 100 (with zero points for 100 or less pitches). Each pitch after 100 would add 1 more abuse point up to 109, from 110-119 each pitch adds 2 points, for 120-129 each pitch adds 3 points and so on. That's all there was to it - no sophisticated analysis involving multi-variate statistics or anything.

Now we jump ahead four years to 2002. The analysis begins. In two articles ( ) BP author Keith Woolner looks at PAP as a measure of long term risk to pitchers and the intriguing notion that high pitch counts have an immediate short term impact on the pitcher's next few starts. The summary of both articles is this: high pitch counts have a significant negative impact in the short term and the longer the outing, the worse the performance. For long term injury risk, high PAP pitchers are much more likely to be injured compared to low PAP pitchers who have worked a similar number of innings.

If we delve into the details, more is important because the PAP used in Keith Woolner's work is actually PAP^3. In the work on short term performance issues, they developed a performance index (a conglomerate of K rate, BB rate, hit rate, and runs allowed individually - each one has the same shape when compared to workload so the particulars aren't very important) and then proceeded to find the best fit for PAP that they could. It worked out that the best fit was obtained by starting to count abuse points at 101 pitches and cubing the total. This captures the dramatic decrease in effectiveness that extremely high (130+) pitch counts lead to while retaining the modest decrease of higher work loads (110+). Here's a link to the graph . Keep in mind that this is only a short term effect of roughly three weeks. It is certainly within the realm of reason that a manager could decide it's in the club's best interests for a key game to ride his starter hard, knowing that he won't be quite the same later. It seems hard to justify frequent and early high pitch counts with the exception of Randy Johnson, who has consistently bucked these trends in a freakish manner.

The short term effects are certainly interesting and important, but PAP was all about long term health risks. How does it do at predicting them? First, PAP^3 was used for Keith's analysis but he analyzed other variations and reported that generally any method that gave increasing weight to higher and higher pitch counts was equally valid, so sticking with PAP^3 (from here on out I will just use PAP) made sense because it does two things at once. The first item of business is to define what exactly constitutes an injured pitcher. For the study in question, the pitchers to be considered were all starters, had accumulated less than 100 innings before 1988 (before pitch counts were available), and had been on the DL for 30 or more days with an arm injury. Comparable pitchers to the injured pitchers were found by looking at pitchers who had a similar pitch count total (within 10% either way) at the same age and who wasn't on the injured list even if the injury occurred later. There were 73 injured pitchers and 569 comparable seasons. The key to the analysis is that for PAP to be useful, it must not merely predict an increased injury risk. It needs to be significantly better than pitch counts, or it would be of little use. A simple plot of PAP vs. pitch count was done for both healthy and injured pitchers ( . Here's the key: 31% of the injured pitchers had career PAP totals above the average for their pitch counts, while only 9% of the healthy pitchers had PAP totals above average for their pitch counts.

It's important to grasp the details here. High pitch counts increase injury risk. On top of that, being used in a way that generates more PAP than average increases the injury risk further. An example should illustrate the point. A 20-year-old phenom has two starts - in one corner you can pitch him for 110 pitches in each start, and the other is to pitch him 120 and 100. Both have the same high pitch count which represents a small injury risk (especially for only two starts), but the scenario where he throws 120 pitches is worse than two 110 pitch starts. Extending the above example out, the same PAP number would be achieved in three 110 pitch starts as the 120 followed by two 100 pitch starts. Having established that, what we really want is a correlation between PAP and injury rate that tells us what the relative risk is of increasing PAP.

Enter workload stress, which is simply PAP/ the number of pitches. Another handy graph is provided at . Those who bothered to look were probably intrigued that at very high stress loads, the injury risk starts to decline. This is essentially the Randy Johnson effect. To accumulate those kinds of stress loads, you essentially have to demonstrate you can pitch well with that kind of workload consistently and stay healthy enough to keep on accumulating those PAP points. If you've had enough, you can stop right here because the graph gives you everything you need to know to make your own judgements. If you intend to use the BP PAP system, note that later in the article they break down the starts by pitch count into five categories (from no risk to very high risk).

Getting back to the graph, I found that Keith's remaining analysis was just plain silly. He attempted to get a function for the probability of injury risk. That is, he tried to fit a line to the data (see this link) . I don't know about you, but I think that line stinks. It's just a simple natural logarithm of the workload multiplied by a constant. It does all right at low to moderate stress levels but is way off at the higher levels. If we can agree that the decrease at very high levels is related to the pitchers, we don't have to worry about workload. It would be better to cut off the data after the stress load of 60 (where it seems to plateau), and find a better equation for the first part of the data, giving everyone the same injury risk or increasing it slightly for stress loads above 60. Alternatively, you could just always estimate your pitcher of interest from the graph.

Player of the Week Wow, what a week it's been...ten in a row baby! I haven't had this much fun in quite awhile. Doug Davis pitched a complete game for the victory and Player of the Week loves complete games (when they aren't ruining young arms), but other players contributed much more to this week. It was neck and neck between Podzilla and Jenkins. Each player was great the entire week, but in the end Jenkins put up more RBIs plus Runs by a fair margin. He was also instrumental in pulling out win #10 before being removed from the game, and he had so many big hits and multi-hit games that he wouldn't be denied.

Jason Belter:
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