Dusty's pitcher abuse - a numerical study

After Monday night's senseless 121-pitch outing by Carlos Zambrano, many of us were enraged at Baker's pointless overworking of his "caballo". Furthermore, there is ample evidence that Baker thinks this sort of work is good for Zambrano's career. For example:

"I talked to him about being himself and doing what he's capable of doing," Baker said. "To be a horse, to be a caballo, like an iron man under adverse conditions.

"If you're going to be truly great eventually, you're going to have to be that kind of person."

To me, this stinks of Dusty throwing his horse under the bus in order to save his ass...

However, despite Dusty's usage of Zambrano this year, despite his frightening comments from Monday, and despite his horrible track record of pitcher abuse, i was still skeptical of Dusty's real effect on pitch counts, as i recalled a recent Hardball Times article that claimed Dusty's "abuse" only added up to ~3-4 pitches per start. That article, written by David Gassko, attempted to determine how many pitches per start Dusty's starters were expected to throw:

"Let's take every pitcher season beginning in 2000, 394 in total, with six seasons worth of data, and try to predict pitch counts while controlling for everything in the universe that needs to be controlled for. In this case, "everything" means hits, walks, strikeouts, league, and year. Essentially what we're asking is this: 'Given that a pitcher allowed this many hits and this many walks, struck out this many batters, played in this season, and in this league, how many pitches per start would we expect him to throw?'"

More rigorously, he used the following methodology:

"I used an ordinary least-squares regression with Pitches/Start as my dependent variable, and Year, Hits/BFP, BB/BFP, K/BFP, NL, and 'Baker' as my independent variables. The Years were there essentially as constants. Hits had a negative relationship with Pitches/Start, as you might expect, so the more hits a pitcher allows per plate appearance, the more likely he is to be pulled early. Walks and Strikeouts both had a positive relationship, though the coefficient for walks was somewhat unexpected. The most likely explanation is a combination of the following three things: (1) Walks have a positive correlation with Ks, and high-K pitchers will generally be the ones who stay in for longest, (2) It takes a lot of pitches to walk a batter, and (3) A walk are not as costly as a hit, so a high-BB pitcher can still be good. The results of my regression are listed below. All estimates were significant at the 1% level."

The results? Gassko's model predicted the "Dusty" variable was worth 3.67 pitches/start. That's not a horrible number, but it is significant. However, i had some concerns about his analysis. Specifically, it seems to be answering the wrong question. The question Gassko answered was basically "On average, how many extra pitches per outing is the result of Dusty being the manager?" I think a more appropriate question would be "For Dusty's stable of 'caballos,' how many pitches per outing is the result of Dusty being the manager?" Fortunately, it is fairly simple to reproduce Gassko's method. In this case, we'll make a least squares regression model for every season during Dusty's tenure with the Cubs (2003-2006), and will use the same variables Gassko used, except we will exclude Dusty as a variable. We can then compare the expected number of pitches per game for Dusty-managed starting pitchers to the actual number of pitches/game they threw. Here are the results (GS=Games started, P/GS=Pitches/GS, Exp. P/GS=model prediction for P/GS, "Dusty effect"=(Exp P/GS)-P/GS. The important number is the "Dusty effect" which is a measure of the pitches Dusty "added" to an average start by a particular pitcher over the course of a given season. Positive numbers mean the pitcher threw more than would be expected given his performance that season; negative numbers mean the opposite.)

Year Last Name First Name GS P P/Start EXP P/GS "Dusty effect"
2006 Zambrano Carlos 26 2913 112.04 100.059 11.979
2006 Marmol Carlos 12 1174 97.83 91.621 6.212
2006 Hill Rich 8 736 92.00 89.794 2.206
2006 Prior Mark 9 835 92.78 93.398 -0.620
2006 Mateo Juan 1 88 88.00 85.082 2.918
2006 Maddux Greg 25 2104 84.16 94.259 -10.099
2006 Marshall Sean 19 1665 87.63 92.944 -5.313
2006 Guzman Angel 5 446 89.20 92.243 -3.043
2006 Rusch Glendon 9 752 83.56 93.083 -9.527
2006 Wood Kerry 4 317 79.25 94.405 -15.155
2006 Williams Jerome 2 147 73.50 81.295 -7.795
2006 Ryu Jae Kuk 1 28 28.00 73.591 -45.591
2005 Zambrano Carlos 33 3558 107.82 101.136 6.682
2005 Rusch Glendon 19 1873 98.58 92.776 5.803
2005 Prior Mark 27 2827 104.70 103.621 1.083
2005 Mitre Sergio 7 680 97.14 93.077 4.066
2005 Williams Jerome 20 1890 94.50 92.750 1.750
2005 Koronka John 3 284 94.67 103.445 -8.778
2005 Dempster Ryan 6 593 98.83 97.470 1.363
2005 Maddux Greg 35 3099 88.54 95.416 -6.873
2005 Wood Kerry 10 880 88.00 104.668 -16.668
2005 Hill Rich 4 323 80.75 92.168 -11.418
2005 Leicester Jon 1 59 59.00 84.859 -25.859
2004 Zambrano Carlos 31 3471 111.97 99.292 12.676
2004 Rusch Glendon 16 1609 100.56 95.902 4.661
2004 Wood Kerry 22 2221 100.95 100.357 0.598
2004 Clement Matt 30 2992 99.73 100.511 -0.778
2004 Prior Mark 21 2061 98.14 101.200 -3.057
2004 Maddux Greg 33 2925 88.64 96.904 -8.268
2004 Mitre Sergio 9 764 84.89 89.005 -4.116
2003 Prior Mark 30 3391 113.03 104.561 8.473
2003 Zambrano Carlos 32 3396 106.13 95.033 11.092
2003 Wood Kerry 32 3540 110.63 104.392 6.233
2003 Clement Matt 32 3142 98.19 97.536 0.651
2003 Estes Shawn 28 2591 92.54 87.428 5.108
2003 Cruz Juan 6 571 95.17 96.335 -1.169
2003 Mitre Sergio 2 136 68.00 77.782 -9.782
2003-2006 Total 610 60081 98.49 97.312 1.182

What can we glean from this data? Well, there does seem to be a fairly consistent pattern: every year, Dusty picks a horse or two (cough, Z, cough), who he overworks significantly, while letting the other members of the staff take on a lighter load. This keeps the average "Dusty effect" less than 2 pitches per start even though Dusty is really abusing his best pitchers. Remember, this data is already corrected for performance. In other words, although one would expect Mark Prior, Kerry Wood, and Carlos Zambrano to throw more pitches due to their effectiveness, one would not expect their load to increase nearly as much as it does under Baker. Conversely, the pitchers at the back of Baker's rotations have pitched less than one would expect, even when their sub-standard performances are taken into account. The numbers for Zambrano are particularly disconcerting. It seems that, with the lone exception of a "gentle" 2005, Dusty has left Zambrano in for 11-12 pitches more than one would predict given Zambrano's performance in those seasons. That's a lot. Keep in mind that those 10 extra pitches are the ones that will do the most damage to Zambrano's arm. (For those of you wondering how pitcher abuse points are calculated, its the number of triple digit pitches in an outing cubed, and then summed over each start.) If Zambrano were to see 10 pitches less per outing, his pitcher abuse points would be way down and i for one would be far less concerned about his future health. It may be that Zambrano's arm truly is indestructible, and that it can take year after year of overuse. However, a lost season in which Zambrano's team has an atomically-small chance of making the playoffs would be a good time to rest his arm for the future, not to test the hypothesis that it is made of adamantium.

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