The Bobby Cox Effect
Thomas Lake has a nice retrospective article on Bobby Cox’s ejections in the current issue of Sports Illustrated. If you have read it, you might have seen my brief contribution.
FEW HUMAN endeavors have been studied so closely by so many people with such fascination for such a long time as the game of baseball. Historians, economists and statisticians scrutinize everything that happens and compare it with everything else that already happened, going back to 1871. This ocean of numbers can tell us a lot about Bobby Cox. For example: He makes pitchers better. J.C. Bradbury, author of the 2008 book The Baseball Economist: The Real Game Exposed, looked at pitchers who had thrown for multiple teams and compared their performances for Cox with their performances for other teams. Using a sophisticated technique called multiple regression analysis, Bradbury factored out variables such as hitter-friendly ballparks, league ERA differences, team defense and pitchers’ ages. What remained was a meaningful Cox Effect, worth about a quarter of a run every nine innings. (True, the Leo Mazzone Effect was even larger, but the Cox Effect existed even in the 14 years Mazzone wasn’t Cox’s pitching coach.)
I looked at pitchers with more than 30 innings pitched in a season and hitters with more than 100 plate appearances who played for Bobby Cox and at least one other manager. The tables below report the estimates. The performance numbers are park corrected.
ERA
Bobby Cox -0.256
(3.95)**
Career ERA 0.833
(16.36)**
LgERA 0.249
(2.71)**
Tm BABIP 10.839
(4.12)**
Age -0.341
(6.10)**
Age2 0.006
(6.28)**
Constant 1.686
(1.61)
Observations 1519
R-squared 0.29
Robust t statistics in parentheses
* significant at 5%; ** significant at 1%
OPS
Bobby Cox -0.006
(1.24)
Career OPS 0.935
(42.88)**
LgOPS 0.415
(6.48)**
Age 0.028
(4.98)**
Age2 -0.00046
(5.01)**
Constant -0.670
(7.00)**
Observations 1833
R-squared 0.52
Robust t statistics in parentheses
* significant at 5%; ** significant at 1%
PrOPS Leaders at the All-Star Break
Here are the PrOPS leaders for the first half of the season (minimum 250 PAs). Introduction to 2010 PrOPS. Introduction to PrOPS.
Top performers:
PrOPS Leaders Player Team PrAVE PrOBP PrSLG PrOPS 1 Carlos Gonzalez COL 0.321 0.411 0.572 0.984 2 Miguel Cabrera DET 0.316 0.386 0.594 0.980 3 Joey Votto CIN 0.297 0.388 0.567 0.955 4 Justin Morneau MIN 0.308 0.392 0.563 0.955 5 Vladimir Guerrero TEX 0.309 0.374 0.570 0.943 6 Corey Hart MIL 0.285 0.371 0.570 0.941 7 Albert Pujols STL 0.305 0.381 0.559 0.940 8 Adrian Beltre BOS 0.317 0.405 0.524 0.929 9 Carlos Quentin CHW 0.284 0.376 0.553 0.929 10 Paul Konerko CHW 0.292 0.368 0.553 0.921 11 Josh Hamilton TEX 0.286 0.358 0.557 0.915 12 Andre Ethier LAD 0.301 0.379 0.528 0.907 13 Ian Stewart COL 0.300 0.395 0.512 0.907 14 Torii Hunter LAA 0.311 0.386 0.520 0.907 15 Jose Bautista TOR 0.261 0.351 0.555 0.906 16 Magglio Ordonez DET 0.332 0.386 0.519 0.905 17 David Ortiz BOS 0.264 0.364 0.539 0.903 18 Robinson Cano NYY 0.306 0.386 0.516 0.903 19 Miguel Olivo COL 0.290 0.378 0.521 0.899 20 Vernon Wells TOR 0.288 0.362 0.537 0.899 21 Matt Holliday STL 0.301 0.379 0.517 0.897 22 Adrian Gonzalez SDP 0.288 0.370 0.524 0.894 23 Kevin Youkilis BOS 0.277 0.374 0.519 0.894 24 Adam Dunn WSN 0.255 0.359 0.534 0.894 25 Aubrey Huff SFG 0.292 0.368 0.520 0.888 26 Ryan Howard PHI 0.281 0.375 0.512 0.887 27 Mike Napoli LAA 0.277 0.378 0.507 0.885 28 Brennan Boesch DET 0.294 0.364 0.517 0.881 29 Scott Rolen CIN 0.276 0.360 0.521 0.880 30 Prince Fielder MIL 0.273 0.367 0.512 0.880
Second-half rebounds coming?
Top-30 Under-Performers Player Team OPS PrOPS Diff 1 Yadier Molina STL 0.595 0.744 -0.149 2 Justin Smoak TOT 0.657 0.789 -0.132 3 Adam Lind TOR 0.640 0.768 -0.128 4 Carlos Lee HOU 0.682 0.807 -0.125 5 Hunter Pence HOU 0.743 0.867 -0.124 6 Jose Lopez SEA 0.610 0.732 -0.122 7 Ian Stewart COL 0.788 0.907 -0.119 8 Skip Schumaker STL 0.642 0.761 -0.119 9 Juan Rivera LAA 0.708 0.818 -0.110 10 Carlos Gonzalez COL 0.878 0.984 -0.106 11 Derek Jeter NYY 0.732 0.836 -0.104 12 Pedro Feliz HOU 0.546 0.648 -0.102 13 Cesar Izturis BAL 0.569 0.670 -0.101 14 Aaron Hill TOR 0.631 0.732 -0.101 15 Mike Napoli LAA 0.786 0.885 -0.099 16 Kurt Suzuki OAK 0.716 0.812 -0.096 17 Aramis Ramirez CHC 0.648 0.743 -0.095 18 Todd Helton COL 0.646 0.737 -0.091 19 Aaron Rowand SFG 0.681 0.764 -0.083 20 Alcides Escobar MIL 0.630 0.713 -0.083 21 Orlando Cabrera CIN 0.612 0.690 -0.078 22 Carlos Pena TBR 0.737 0.812 -0.075 23 Russell Martin LAD 0.679 0.752 -0.073 24 Clint Barmes COL 0.721 0.791 -0.070 25 Miguel Tejada BAL 0.691 0.761 -0.070 26 Howie Kendrick LAA 0.708 0.778 -0.070 27 Ty Wigginton BAL 0.768 0.837 -0.069 28 Shane Victorino PHI 0.766 0.835 -0.069 29 Jorge Cantu FLA 0.734 0.798 -0.064 30 Juan Uribe SFG 0.758 0.821 -0.063
Second-half declines on the way?
Top-30 Over-Performers Player Team OPS PrOPS Diff 1 Ian Kinsler TEX 0.831 0.688 0.143 2 Carl Crawford TBR 0.901 0.774 0.127 3 Andres Torres SFG 0.861 0.736 0.125 4 Nick Markakis BAL 0.847 0.726 0.121 5 Brennan Boesch DET 0.990 0.881 0.109 6 Justin Morneau MIN 1.055 0.955 0.100 7 Rafael Furcal LAD 0.898 0.798 0.100 8 Josh Hamilton TEX 1.014 0.915 0.099 9 Evan Longoria TBR 0.895 0.796 0.099 10 David DeJesus KCR 0.855 0.760 0.095 11 Miguel Cabrera DET 1.074 0.980 0.094 12 Fred Lewis TOR 0.779 0.689 0.090 13 Cliff Pennington OAK 0.726 0.637 0.089 14 Kevin Youkilis BOS 0.981 0.894 0.087 15 Jayson Werth PHI 0.881 0.796 0.085 16 Ben Zobrist TBR 0.783 0.699 0.084 17 Ichiro Suzuki SEA 0.785 0.704 0.081 18 Angel Pagan NYM 0.845 0.769 0.076 19 Troy Tulowitzki COL 0.877 0.806 0.071 20 Andrew McCutchen PIT 0.798 0.727 0.071 21 David Wright NYM 0.924 0.854 0.070 22 Billy Butler KCR 0.873 0.805 0.068 23 Adam Dunn WSN 0.959 0.894 0.065 24 Daric Barton OAK 0.772 0.708 0.064 25 Jason Bay NYM 0.779 0.720 0.059 26 Blake DeWitt LAD 0.728 0.670 0.058 27 Kelly Johnson ARI 0.870 0.813 0.057 28 Joey Votto CIN 1.011 0.955 0.056 29 Josh Willingham WSN 0.913 0.857 0.056 30 Lastings Milledge PIT 0.739 0.686 0.053
Valuing Prince Fielder
Buster Onley ($) has a piece this morning in which he discusses the potential free-agent valuePrince Fielder after his agent Scott Boras made some comparisons to Mark Teixeira. Olney points to the Fielder in the living room when making such comparisons, and notes that several MLB insiders feel his weight is going to prevent him from aging as gracefully as most players. Fielder is so heavy that it’s hard to know what to expect. I think he will ultimately be a DH, and this may keep him in the game longer.
Yet despite his weight, which many talent evaluators thought would keep him from excelling at all, he has been an elite and valuable hitter. If he ages like the average players (possibly a dubious assumption, but it’s hard to know what to expect) and signs a five-year deal (equivalent in length to Ryan Howard’s extension) after the 2011 season, I estimate the value of the deal in total dollars paid out would be $104 million, or a little under $21 million per year. It’s not quite Teixeira money, but it’s in the neighborhood. Concerns about his weight, justified or not, will probably prevent him from signing a deal this long, but I guess we’ll just have to “weight” and see.
2010 PrOPS Over- and Under-Performers (Through 07/01)
PrOPS updated through July 1 (minimum 240 PA). I report the top-30 over- and under-performers. Introduction to 2010 PrOPS. Introduction to PrOPS.
Top-30 Over-Performers Rank Player Team OPS PrOPS Diff PA 1 Andres Torres SFG 0.814 0.680 0.134 269 2 Ian Kinsler TEX 0.811 0.684 0.127 244 3 Carl Crawford TBR 0.869 0.742 0.127 322 4 Nick Markakis BAL 0.821 0.699 0.122 340 5 Justin Morneau MIN 1.059 0.938 0.121 327 6 David DeJesus KCR 0.875 0.756 0.119 330 7 Andrew McCutchen PIT 0.825 0.710 0.115 332 8 Josh Hamilton TEX 0.993 0.880 0.113 328 9 Jayson Werth PHI 0.919 0.813 0.106 308 10 Daric Barton OAK 0.798 0.692 0.106 352 11 Kevin Youkilis BOS 0.983 0.878 0.105 322 12 Ichiro Suzuki SEA 0.813 0.716 0.097 351 13 Ben Zobrist TBR 0.797 0.710 0.087 336 14 Franklin Gutierrez SEA 0.767 0.681 0.086 311 15 Lastings Milledge PIT 0.715 0.634 0.081 263 16 Jason Bay NYM 0.812 0.732 0.080 323 17 Fred Lewis TOR 0.774 0.695 0.079 272 18 Brandon Phillips CIN 0.841 0.766 0.075 357 19 Troy Tulowitzki COL 0.877 0.806 0.071 265 20 Evan Longoria TBR 0.870 0.803 0.067 342 21 Colby Rasmus STL 0.921 0.856 0.065 275 22 Miguel Cabrera DET 1.040 0.976 0.064 325 23 Brett Gardner NYY 0.811 0.747 0.064 278 24 Cliff Pennington OAK 0.704 0.644 0.060 296 25 Adam Dunn WSN 0.917 0.858 0.059 327 26 Johnny Damon DET 0.753 0.695 0.058 302 27 Elvis Andrus TEX 0.706 0.649 0.057 344 28 David Wright NYM 0.929 0.874 0.055 338 29 Martin Prado ATL 0.857 0.803 0.054 367 30 Albert Pujols STL 0.989 0.936 0.053 346
Top-30 Under-Performers Rank Player Team OPS PrOPS Diff PA 1 Hunter Pence HOU 0.730 0.876 -0.146 313 2 Ian Stewart COL 0.738 0.866 -0.128 270 3 Yadier Molina STL 0.615 0.742 -0.127 267 4 Carlos Lee HOU 0.669 0.796 -0.127 319 5 Jose Lopez SEA 0.603 0.726 -0.123 325 6 Adam Lind TOR 0.608 0.729 -0.121 322 7 Skip Schumaker STL 0.655 0.768 -0.113 288 8 Justin Smoak TEX 0.697 0.800 -0.103 250 9 Derek Jeter NYY 0.754 0.857 -0.103 361 10 Carlos Gonzalez COL 0.825 0.925 -0.100 301 11 Juan Rivera LAA 0.725 0.820 -0.095 258 12 Pedro Feliz HOU 0.572 0.664 -0.092 255 13 Todd Helton COL 0.657 0.749 -0.092 281 14 Aaron Hill TOR 0.642 0.719 -0.077 287 15 Carlos Pena TBR 0.728 0.804 -0.076 323 16 Clint Barmes COL 0.706 0.781 -0.075 257 17 Mike Napoli LAA 0.838 0.912 -0.074 262 18 Derrek Lee CHC 0.699 0.772 -0.073 334 19 Miguel Tejada BAL 0.695 0.768 -0.073 325 20 Jason Bartlett TBR 0.631 0.702 -0.071 258 21 Alcides Escobar MIL 0.640 0.710 -0.070 282 22 Orlando Cabrera CIN 0.625 0.692 -0.067 337 23 Russell Martin LAD 0.678 0.743 -0.065 300 24 Carlos Quentin CHW 0.784 0.848 -0.064 279 25 Shane Victorino PHI 0.767 0.829 -0.062 346 26 Melky Cabrera ATL 0.653 0.715 -0.062 265 27 Howie Kendrick LAA 0.718 0.779 -0.061 336 28 A.J. Pierzynski CHW 0.651 0.711 -0.060 250 29 Ty Wigginton BAL 0.808 0.865 -0.057 299 30 Mark Teixeira NYY 0.757 0.812 -0.055 354
What Edwin Jackson’s Pitch Count Hath Wrought
Edwin Jackson threw a bit of a lame no-hitter on Friday. I’m sorry if it offends you when I call such a hallowed feat lame, but eight walks in a game for a major-league pitcher is bad (see Pulling a Homer). But aside from this, one aspect of his performance has gotten a lot of attention: 149 pitches thrown. This is the highest pitch count allowed in a game since 2005 (see my previous post on how pitch counts have changed over the past two decades).
I have been conducting a study of pitch counts with Sean Forman, and we will be presenting our findings at the upcoming SABR convention in Atlanta. But since it’s applicable to Jackson’s situation, I’ll reveal some of the findings. Our study uses past pitching performances to estimate the impact of pitch counts on future performance, controlling for numerous factors, using fractional polynomial regression analysis to capture potential non-linear relationships. The results indicate that the impact of the pitch count in a single game on the following game is real but small; and, the impact is linear, not increasing as some analysts have theorized.
On average, every pitch thrown raises a pitcher’s ERA by 0.007 in the following game. Jackson’s ERA was 5.05 going into Friday’s game averaging 104 pitches per game; thus, based on the historical response of pitchers to pitch counts Jackson’s expected performance in his next start is about 5.37. So, Jackson can be expected to pitch worse, but not that much worse. Really, it’s not that big of a deal as a one-time event. Should Jackson continue to average around 150 pitches a game, the impact will grow, but I doubt that is going to happen. As for the impact on injuries, we didn’t look into it in this study. However, I have previously found little correlation between pitching loads and injury.
My take: if you have a pitcher going for a no-hitter—not matter how bad he’s pitching—the benefit of the excitement and media coverage of letting a pitcher throw more pitches is probably worth the cost. Let’s stop freaking out about pitch counts until we understand their influence a little better.
Update: In response to Jackson’s high pitch count, the Diamondbacks will push back his next start a day or two. How much will this help him recover? No much. On average, each day of rest lowers a pitcher’s ERA by approximately 0.015. Thus, his expected ERA drops from 5.37 to 5.34 (with two days of extra rest). Why rest days matter so little is an interesting question. A few years ago, I saw an presentation on muscle recovery from exercise, and one of the interesting findings was that most of the healing happens within the first few days. Whether this explains the finding or not, I don’t know.
2010 PrOPS Over- and Under-Performers (Through 6/15)
I have updated PrOPS through June 15 (minimum 200 PA). I report the top-30 over- and under-performers. Here is my previous post on 2010 PrOPS.
Top-30 Over-Performers Rk Player Team OPS PrOPS Diff PA 1 Andres Torres SFG 0.885 0.721 0.164 220 2 Justin Morneau MIN 1.079 0.925 0.154 266 3 Kevin Youkilis BOS 1.043 0.889 0.154 273 4 Ichiro Suzuki SEA 0.830 0.698 0.132 293 5 Jayson Werth PHI 0.904 0.776 0.128 243 6 Nick Markakis BAL 0.818 0.695 0.123 282 7 Andrew McCutchen PIT 0.861 0.741 0.120 271 8 David DeJesus KCR 0.873 0.761 0.112 276 9 Colby Rasmus STL 0.997 0.888 0.109 223 10 Daric Barton OAK 0.818 0.712 0.106 293 11 Evan Longoria TBR 0.964 0.861 0.103 279 12 Carl Crawford TBR 0.831 0.731 0.100 274 13 Adam Dunn WSN 0.951 0.852 0.099 265 14 Johnny Damon DET 0.808 0.711 0.097 262 15 Ben Zobrist TBR 0.824 0.728 0.096 275 16 Billy Butler KCR 0.890 0.798 0.092 278 17 Fred Lewis TOR 0.780 0.689 0.091 218 18 Franklin Gutierrez SEA 0.755 0.666 0.089 273 19 Robinson Cano NYY 1.022 0.936 0.086 278 20 Brett Gardner NYY 0.842 0.763 0.079 236 21 Elvis Andrus TEX 0.722 0.647 0.075 279 22 Aubrey Huff SFG 0.909 0.835 0.074 256 23 David Freese STL 0.809 0.735 0.074 234 24 Jason Bay NYM 0.790 0.719 0.071 272 25 Brandon Phillips CIN 0.849 0.780 0.069 287 26 Andre Ethier LAD 1.021 0.959 0.062 203 27 Josh Hamilton TEX 0.941 0.880 0.061 268 28 Drew Stubbs CIN 0.738 0.678 0.060 242 29 Erick Aybar LAA 0.688 0.629 0.059 292 30 Troy Tulowitzki COL 0.869 0.810 0.059 257
Top-30 Under-Performers Rk Player Team OPS PrOPS Diff PA 1 Casey Kotchman SEA 0.551 0.749 -0.198 200 2 Carlos Lee HOU 0.658 0.823 -0.165 259 3 Hunter Pence HOU 0.751 0.906 -0.155 251 4 Jose Lopez SEA 0.571 0.717 -0.146 271 5 Kendry Morales LAA 0.833 0.970 -0.137 211 6 Skip Schumaker STL 0.613 0.748 -0.135 247 7 Ian Stewart COL 0.758 0.877 -0.119 224 8 Derek Jeter NYY 0.780 0.896 -0.116 301 9 Mike Napoli LAA 0.798 0.912 -0.114 211 10 Juan Rivera LAA 0.746 0.853 -0.107 223 11 Adam Lind TOR 0.636 0.737 -0.101 268 12 Carlos Gonzalez COL 0.824 0.919 -0.095 250 13 Cameron Maybin FLA 0.631 0.726 -0.095 201 14 Clint Barmes COL 0.671 0.761 -0.090 202 15 Carlos Pena TBR 0.736 0.823 -0.087 261 16 Aaron Hill TOR 0.666 0.752 -0.086 230 17 A.J. Pierzynski CHW 0.649 0.734 -0.085 204 18 Pedro Feliz HOU 0.567 0.651 -0.084 224 19 Carlos Quentin CHW 0.681 0.764 -0.083 224 20 Melky Cabrera ATL 0.646 0.724 -0.078 212 21 Nate McLouth ATL 0.577 0.653 -0.076 205 22 Yadier Molina STL 0.666 0.739 -0.073 227 23 Matt Wieters BAL 0.629 0.697 -0.068 231 24 Howie Kendrick LAA 0.712 0.777 -0.065 276 25 Miguel Tejada BAL 0.676 0.741 -0.065 265 26 Alcides Escobar MIL 0.657 0.722 -0.065 233 27 Jerry Hairston SDP 0.618 0.682 -0.064 229 28 Derrek Lee CHC 0.688 0.750 -0.062 270 29 Juan Pierre CHW 0.584 0.645 -0.061 277 30 Brandon Inge DET 0.715 0.774 -0.059 248
A Lesson in Concentrated Benefits and Dispersed Costs
File under: Mancur Olson was right.
From San Francisco Chronicle:
The vote came after the football team spent an astonishing $4 million-plus on a campaign in a city with only 46,000 registered voters. Signs backing the 49ers sprang up in front yards across the community as the team carpet-bombed the city with TV spots, radio ads and campaign mailers.
It was a different story for opponents of the stadium, who managed to collect about $20,000, enough for some yards signs and some campaign handouts for the volunteers who knocked on doors.
Improvement in Fielding: Personal Evidence
In my previous post, I present some data that indicates fielding has improved over time. Here is a partial explanation.
My grandfather’s glove (circa 1910s)
My father’s glove (circa 1950s)
My glove (circa 1980s)
(Forthcoming October 2010)
