Archive for General

Interesting Facts about My Dad

Please excuse my personal post. My father died yesterday after a long battle with Progressive Supranuclear Palsy (PSP).

Tom Bradbury, journalist and advocate, dies

Paul Thomas “Tom” Bradbury, 67: Journalist and ham-radio whiz

»» Interesting Facts about My Dad

Revenue Sharing, Incentives, and Competitive Balance

Rob Neyer takes issue with the conclusions of my NY Times column on revenue sharing and competitive balance, in which I suggested MLB abandon revenue sharing for the purpose of aiding competitive balance.

I can’t say that I’m convinced, but then again I can’t say I’m objective, either. Because it makes me happy to see the rich giving to the poor. It makes me happy to see the Yankees and the Red Sox writing checks to the Rays and the Royals.

Also, Bradbury’s argument isn’t terribly convincing. Maybe competitive balance hasn’t improved with more revenue-sharing … but that doesn’t mean it wouldn’t be worse without revenue sharing. Bradbury points out that the balance has hovered around 1.8 — as measured by the Noll-Scully ratio — since the early ’90s … but can anyone prove that it wouldn’t be lower than 1.8 without revenue sharing?

Maybe someone can. Economists love to play around with models. But I haven’t yet seen a model that gets the Rays into the playoffs twice in three years without a little help. And I suspect they’re happy, this year at least, with Commissioner Robin Hood and his Merry Men.

Let me clarify a few things and extend my argument to possibly convince Rob and other skeptics that revenue sharing isn’t a useful policy instrument for manipulating competitive balance. 800 words isn’t a lot of space to make an argument, and the book chapter which contains much of my argument is too long to include here. Although, as the son of a newspaper editor, I have to admit that I have a soft spot for short policy pieces.

First, I am not opposed to revenue sharing, per se. As a collective profit-maximizing entity, MLB may find guaranteeing payments to all franchises, regardless the level of locally-generated revenue, is the optimal business strategy. By having teams in Pittsburgh, Miami, etc., MLB receives media attention and retains interest in baseball among potential fans in the area. Even if local receipts aren’t sufficient to keep the franchise in the black, the net benefit to the league is positive. Therefore, in order to encourage an owner to own and operate a franchise in the area, a subsidy may be required. I have no problem with such an arrangement, nor do I have a problem with owners pocketing such transfers.

Where I see the issue as problematic is when we tie revenue sharing to competitive balance. Below is a revenue function that I have estimated for an average MLB team, based solely on winning. The left-side of the function shows “the loss trap” bump that I highlight in the article, which is consistent with revenue sharing creating a disincentive to win. However, the bump is slight, and I don’t think it’s even necessary for explaining why revenue sharing hasn’t improved competitive balance (more on that in a moment). The fact that earnings are relatively flat until wins reach the mid-80s in wins means that there is very little incentive for poor-and-losing teams to invest any money into the club. Whether that money comes from transferred wealth or a pot at the end of the rainbow, investing the funds into a club doesn’t generate sufficient return to justify it. The Pirates and Marlins weren’t being excessively greedy, their behavior reflected a sound business decision. For a team like the Rays, however, putting that money into the club does make sense. The returns to winning are increasing, likely higher than alternative investments. It’s getting to that point that is the difficult part. If you’re in the loss trap, spending many millions of dollars to improve the club doesn’t help much. And revenue sharing doesn’t help you out.

Revenue Function

Teams that have garnered success on small budgets in the recent past (e.g., Rays, Twins, Indians, A’s, and Marlins) haven’t used revenue sharing to get where they are. Instead, another baseball institution has served to give these teams a fighting chance: the reserve system that allow teams to pay players wages below their revenue-generating capability. The amateur draft gives every team in the league rights to valuable player-assets that teams can use to build winners. This mechanism is far more effective at promoting competitive balance and it lacks the disincentives of revenue sharing. Only teams who draft wisely and properly develop their players are rewarded.

Now, to Neyer’s second point. He argues that because competitive balance is no better than it was in the mid-1990s, when revenue-sharing for competitive balance purposes was first instituted, it doesn’t mean that measured imbalance wouldn’t have been worse without revenue sharing. This is certainly a possibility. The graph below shows the Noll-Sully measure of competitive imbalance from 1921-2009, smoothed with a lowess fit to map the trend.
Competitive Balance Over Time

The graph shows that competitive balance improved from the 1930s until leveling off in the late-1980s and early-1990s. Much of this improvement was likely a natural consequence of more high-quality talent becoming available to more clubs, the addition of the amateur draft in 1965 (the mechanism Branch Rickey felt was most important for leveling the financial playing field across teams), and other minor structural tweaks to the league. Why would the improving trend disappear just as revenue sharing came into existence? While I’m not certain that revenue sharing stopped the progress, I doubt it was instituted just in time to counteract a trend reversal.

In my view, if revenue sharing worked, there would be some evidence of it working over the past two decades that it’s been tried under various formats. How much longer are we supposed to give it, especially when what we observe is exactly what theory predicts we should observe? If we think it’s important to correct inherent differences in revenue potential across teams, I think revenue sharing is a poor tool for achieving that goal.


I’ll be attending SABR 40 for the next few days. If you would like to talk, please approach me and introduce yourself. This is my first SABR convention.

I am giving two research presentations, one oral and one poster.

Resting the pitcher: How useful are pitch counts and days of rest? (with Sean Forman): Thursday, August 5, 2:30 – 2:55pm, Georgia 7,8,9

Many individuals believe that limiting pitch counts and increasing days of rest can improve performance and reduce injuries. Though the belief that overuse can hamper pitchers is widespread, there exists little evidence that adjusting pitch counts and rest has much effect on pitcher performance. In this study, Bradbury and Forman use newly available game-level pitch count data from 1988 to 2009 to evaluate the impact of pitch counts and rest days on future performance. They discuss their employment of linear and non-linear multiple regression analysis techniques to estimate the impact of pitch counts — in recent games and cumulatively over a season — and days of rest on pitcher performances while controlling for the effects of other factors.

Here are the presentation slides (pdf). Here is a draft of the paper (revised 10/18/2010).

Putting a dollar sign on the muscle: What are baseball players worth?: I’ll be by the poster on Thursday from 4-6pm.

In the 1970s, using team revenue and player performance data, Gerald Scully employed the standard marginal revenue product framework frequently used by labor economists to estimate the financial contributions of players. Bradbury’s study employs new information about baseball’s economic structure and sabermetric performance metrics in an updated Scully framework to estimate the dollar value of current major league baseball players. He compares player salaries and estimated worth by service class, presents a method for projecting player worth over the duration of long-term contracts, identifies some of baseball’s best and worst deals, and ranks teams according to their abilities to manage their budgets.

For more see my forthcoming book Hot Stove Economics.

Was There a Canseco Effect?

In today’s Slate, Ray Fishman says yes. I disagree. What follows is repeat of a post that I wrote two years ago on the study that Fishman believes supports the effect. (Thanks to Alex for the pointer.)

— — —

Was Jose Canseco the Johnny Appleseed of Steroids?

Last week, I became aware of a study by economists Eric Gould and Todd Kaplan that evaluates at the impact of Jose Canseco on his teammates. They examine the belief that Canseco distributed his knowledge about steroids throughout baseball by introducing many of his teammates to performance-enhancing drugs. If this was the case, the authors hypothesize that he ought to have left a trail of improved performance among teammates in his wake.

The authors look at the careers of Canseco’s teammates to investigate this claim. Their method is to examine players to see how well they perform as a Canseco teammate and afterwards, relative to the years preceding involvement with Canseco. The idea is somewhat similar to what I did with my analysis of Leo Mazzone’s impact on pitchers (see Chapter 5 of my book).

After reading the study, I am not convinced by the authors’ conclusions. It’s not just one thing, but a collection of issues that form my opinion. I have problems with both the study’s design and the interpretation of the reported results. My disagreement does not mean that the effect does not exist, only that I do not see a pattern consistent with Canseco spreading steroids to his teammates.

First, I want to start with the sample. The authors look at players from from 1970–2003. I find this an odd range of seasons to select. Canseco’s career spans from 1985–2001. Why start a decade and a half before Canseco enters the league and stop two years after he exits? The asymmetry bothers me largely because the run-scoring environment preceding Canseco was much lower than it was during the latter part of his career. But even without this, it is a strange choice to make. I can only guess that there is some teammate of Canseco’s whose career extends back this far, but I still don’t agree with the choice. And why not extend the sample until the present?

Next, the authors set the cutoffs for examining player performance at 50 at-bats for hitters and 10 games for pitchers. These minimums are far too low even when stats are normalized for playing time, but the impact is much worse when looking at absolute statistics like total home runs, which the authors do. For pitchers—who I will not examine here—it’s possible to get pitchers who pitched very few innings.

The authors also make a strange choice to break hitters into two classes: power and skilled players. The idea is that we might see different effects on the different styles of play. I don’t agree with this, but that is not the weird part. The way they differentiate power and skilled players is by position played, weird but moderately defensible. The power positions are first base, designated hitters, outfielders, and catchers. The skilled positions are second base, shortstop, and third base. And it becomes clear that the authors are not all that familiar with baseball. Catcher is a “power” position? Third base is a skill position? I suspect that the catcher and shortstop positions produce the least offense of all the positions. Sure, you can point to a power-hitting catcher like Mike Piazza, but you can also point to a punchless first basemen like Doug Mientkiewicz, but in general catcher and first base are at the opposite ends of defensive skill with very different offensive expectations. Center field is also a defensive position that should not be lumped in with the corner positions. This highlights the problem of separating power potential by position. And, it’s not so much that the way that the sample spliced—which don’t like—but the fact that it is being spliced at all makes me suspicious.

The choice of dependent variables is also bit strange. While the authors are mainly looking for changes in power, they pick only a few metrics that measure power: HR, SLG, and HR/AB. The other statistics include AVG, RBI, K, BB, IBB, at-bats, fielding percentage, errors, and steals. I have no problem with AVG. RBI is completely useless since it is largely dependent on teammates. K, BB and IBB are chosen because they correlate with home run hitting. But, performance in this area is also correlated with other things such as plate discipline, and the authors are already looking at home runs. This just adds columns to the regression table, that would have been better-used doing robustness checks on the sample and control variables. I would have liked to have seen isolated power (SLG–AVG), HR/H, OBP, and OPS.

As for the control variables, many of the choices are not intuitive. The batting average of the division (subtracting out own-team performance), the manager’s lifetime winning percentage, the batting park factor, years of experience (listed as a continuous variable in the text, but reported as a matrix of dummies in the regression tables), year effects, and dummies for each division. Also, the equation is estimated with fixed effects to control for individual player attributes.

I wouldn’t have chosen some of these same variables, but I don’t think they make much difference. However, I am perplexed by the inclusion of manager’s winning percentage and division dummies. I don’t see any obvious potential bias from the quality of the manager. In any event, managerial dummies are probably the better choice. Mangers with players who perform better will have higher winning percentages, so a positive correlation is to be expected, but the causality is difficult to determine. However, this isn’t a huge issue.

The division dummies make no sense. The divisions changed their compositions at several points during the sample—the most extreme change occurs when a Central Division was added to both leagues in 1994—and there are no common rules or kinds of play that are really unique to any division. If there was such an effect, the batting average of the division and year effects should catch this. It would have made more sense to include league dummies, because of the significant differences in play between the leagues after the introduction of the DH in 1973. In any event, the authors state that the control variables do not alter the results. I would have liked to see some results with different controls.

Now, to the variable(s) of interest. When I initially looked at the study, flipped to the regression tables first and noticed that there did not appear to be a “Canseco effect,” because the estimate on playing with Canseco was not statistically significant. But, that is not what the authors use to quantify Canseco’s impact; we are supposed to look at a second variable that identifies the seasons after playing with Canseco. The intuition is that “even if he did learn steroids from Canseco, we do not know when he learned about it during his time with Canseco, but we can be sure that he already acquired the knowledge after player with Canseco” (p. 10). I just don’t buy this. I understand that it might take a while for the effect to kick in, but this should still manifest itself in the “played with” variable, especially because many players played with Canseco for multiple seasons. At best this story makes sense only for guys who might have played one season with Canseco (more on this below). Second, anabolic steroids work quickly, so it’s unlikely that there would be a delayed effect.

After reading the paper, I came to the conclusion that the results are probably fragile. So, I designed a similar, but not identical, dataset. I did almost everything the authors did, except I did not break the sample into power and skilled players, and I included league dummies instead of division dummies, because I feel this is a superior choice. I also kicked out some partial seasons when guys switched teams to make life easier in developing the dataset. Thus, what I am doing is “replication” in the sense of looking for a similar result in the data, rather than trying to recreate the previous estimates. If the result is real, then I should find something similar. Here is what I found looking at raw home run totals (control variable estimates not reported).

		50 AB	200 AB	50 AB		200 AB		Corrected
With Canseco	-0.297	-0.199	-1.28E-03	-9.39E-04	-0.449
		[0.66]	[0.35]	[1.41]		[0.93]		[0.87]
After Canseco	0.667	0.737	3.49E-04	6.28E-04	-0.204
		[1.58]	[1.34]	[0.41]		[0.65]		[0.34]
Observations	15,644	9,234	15,644		9,234		12,759
Players		2,885	1,717	2,885		1,717		2,265
R-squared	0.13	0.14	0.09		0.13		0.08
Absolute value of t statistics in brackets					

The coefficient on for playing with Canseco is negative and insignificant and the after Canseco coefficient is positive with a p-value of 0.12, which is above the standard (0.05) and lenient (0.1) thresholds for statistical significance. That is the best that I could get. When I up the at-bat minimum to the more appropriate 200, normalize home runs for at-bats, and both, “played with” is negative and never significant, and “after’s” p-value is never as low as it was in the specification that most-closely resembles the study. Another potential problem that I encountered was serial correlation in the data. This is sometimes difficult to detect, and it is possible that it is a problem unique to my sample. However, when I correct for the problem, both Canseco variables consistently have high insignificant p-values. So, though the authors find some evidence of an effect in the after variable in their sample, the finding appears not be all that robust.

The one thing that bothers me most about this study is that we have to interpret why the “after Canseco” variable is important, but the “during” variable is not as important. And I think the author’s story really only applies to players who are with Canseco for one season. So, I ran some regressions using players who played with Canseco for only one year.

		One-year	One-year 
				10+ Career
With Canseco	-2.656		-3.450
		[3.02]**	[3.17]**
After Canseco	-2.562		-3.027
		[2.84]**	[2.95]**
Observations	1,200		940
Players		186		100
R-squared	0.18		0.23
Absolute value of t statistics in brackets		
* significant at 5%; ** significant at 1%		

The effects of during and after playing with Canseco are strongly negative, about 2.5 less homers. However, if they only played on year with him it could reflect that these players were not very good and were on their way out of the league. So, I limited the sample to players with careers of 10 or more seasons; and, the result is a decline in homers of about 3 HRs both with and after.

My point of offering this “replication” isn’t so much to say that my specifications are superior. I just want to show that the findings do not appear to be robust. To concur with the conclusions presented in the study you have to interpret the findings in a way that I do not believe is correct. Upon further examination, I believe the significant effect on home runs after playing with Canseco identified in the Gould and Kaplan study is a product of spurious correlation, and thus this tells us little about Canseco impact on disseminating steroids throughout baseball.

Why the Oswalt Deal Worked

Yesterday, the Philadelphia Phillies acquired Roy Oswalt for J.A. Happ, Anthony Gose, and Jonathan Villar from the Houston Astros. The general reaction of to the deal has been quite negative toward the return to Houston. Oswalt is an ace starter. Gose (whom the team immediately sent to Toronto for Brett Wallace) and Villar are low-minors prospects. How could Astros GM Ed Wade get so little in return?

It’s interesting that several years ago Ed Wade was on the other side of one of these supposed heists for the Phillies, acquiring Kevin Millwood for Johnny Estrada. It just so happens that the opening chapter of my book on valuing players Hot Stove Economics (forthcoming in October) is titled: “Why Johnny Estrada Is Worth Kevin Millwood: Valuing Players as Assets.” In the chapter, I explain how players so different in ability were swapped for each other without bringing stupidity into the equation. The difference was their salary requirements. While I can’t go into the details here, Millwood would receive $11 million the following year (which was way more than his expected worth), while Estrada would get less than $1 for two years of service before being traded for two relievers.

Now we have Oswalt, who is owed just under $25 million for the remainder of his contract (the Phillies are kicking in and extra million for the buyout of his option). The Phillies are winning team and thus value his performance much more than the Astros, because there are increasing returns to winning. I estimate his expected performance through 2011 is worth about $28 million to the Phillies—a little over $3 million more than his salary obligations. The Astros are also sending along $11 million, which seems excessive until you remember the prospects. A year ago, Happ was pitching decently in the majors, and considered untouchable commodity. He’s been injured, but injuries heal. Let’s assume that Happ pitched at his true performance last year for the Phillies. Based on the value of his performance, and his expected salary obligations (one more purely-reserved year and three arbitration years), I estimate he’s worth about $12 million (discounted present value of performance for four years under team control). But, his injury risk lowers his expected return somewhat. Then the other prospect come into the deal. They are at such a low level that I won’t try and project them from minor league stats (stats below high-A are close to useless), but they certainly have value.

My point here isn’t to calculate the exact value to see whom got the better end of this deal. I want to understand why this trade was made. And while a lot of people aren’t high on Ed Wade, he and his baseball people have some sense of what players are worth. I think the deal is defensible from the Astros perspective, especially considering that Oswalt has some post-season value to the Phillies that the Astros can’t capture without trading him to where his services are more highly valued.

Addendum: Bottom line, Osawlt is the superior player, but expensive. Happ and the other prospects are inferior, but cheap.

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	

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