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.

The Last Father’s Day

Some words about my father are below the fold.

»» The Last Father’s Day

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)


Grandfather's glove

My father’s glove (circa 1950s)


Father's glove

My glove (circa 1980s)


My glove

Why More Perfect Games?

Better defense?

Errors and Perfect Games

Just a guess.