Archive for Business

Income Inequality and Performance in MLB

There’s been a lot of chatter on the economics blogs regarding the subject of income inequality (see Mark Thoma, Brad DeLong, Greg Mankiw, Tyler Cowen for a brief sample of recent commentary). I read through most of it, did some thinking about it, but didn’t dwell on it. Yesterday, I ran across this paper, Relative Income Position And Performance: An Empirical Panel Analysis by Benno Torgler, Sascha L. Schmidt and Bruno S. Frey, and it got me thinking a little more. Here’s the abstract.

Studies have established that people care a great deal about their relative economic position and not solely, as standard economic theory assumes, about their absolute economic position. However, behavioral evidence is rare. This paper provides an empirical analysis on how individuals’ relative income position affects their performance. Using a unique data set for 1114 soccer players over a period of eight seasons (2833 observations), our analysis suggests that the larger the income differences within a team, the worse the performance of the soccer players is. The more the players are integrated in a particular social environment (their team), the more evident this negative effect is.

So, I thought, why not try this with baseball? I wanted to look at how players performed in MLB based on their salary differences from their team and the league as a whole. Using a sample of players with more than 200 plate appearances in a season from 1985-2005, I used the above study of professional soccer as a guide. As a performance metric I used total linear weighted runs produced (LWTS) to capture the player performance in a season. To measure the envy effect, I used the percentage difference in seasonal salary from his team average and the league average (in separate regressions). The model controls for the salary of a player, age (quadratic), salary bargaining status (reserved, arbitration eligible, or free agent—estimated from service time), position played most that season (if tied then I assigned the player to the more difficult position on the defensive spectrum), the year, and team. I used dummy variables to control for the latter four factors. I also estimated the model by each salary bargaining class separately, to see if there were any different effects. I threw out players who switched teams during the year and corrected for serial correlation.

The general hypothesis is that those who make less than their peers may feel inferior and perform worse, and those who make more will perform better as they feel superior. Remember better players should make more than worse players, and the salary variable in the regression is a reasonable control for player quality. Here are the estimated impacts for the percentage difference of in salary from the team and league, along with the standard error of the impacts and the R2 of each regression model.

	Impact	SE	R2
Team 	2.24	0.27	0.34
League	4.89	0.39	0.37

Team 	14.63	2.62	0.27
League	31.81	5.19	0.27

Team 	3.73	0.68	0.35
League	6.73	0.98	0.36

Free Agent		
Team 	1.83	0.34	0.39
League	5.08	0.50	0.42

All of the estimates are statistically significant at the 1% level. It’s interesting that the effect exists, and that it’s more pronounced among reserved and arbitration eligible players than free agents. Also, the effect is greater for league differences, rather than team differences. The coefficients are actually quite small; a ten-percentage-point increase in salary/team average index (disparity is shrinking) increases LWTS by only 0.224. That’s hardly worth noting. However, for purely reserved players the effects are large enough to be interesting. A ten-percentage-point increases in salary/league average index improves performances by 3.18 runs.

Hmm. It seems that there may be some gains to teams bumping up the pay of their reserved players. It might reduce some envy, or maybe it allows them to purchase some lifestyle comforts that help them produce. Maybe teams that buy out young players aren’t just trying to reduce costs in the future, but boost performance in the short-term as well. I need to think some more on this.

Is Oswalt Worth It?

Yesterday, Roy Oswalt signed a 5-year, $73 million deal with the Houston Astros, which averages out to $14.6 million per year. That’s quite a contract, and the obvious question is: “how much is Roy Oswalt worth?” Last year, I developed a method for valuing players based on player contributions to winning and what those wins translate into in terms of team revenue. It’s a method that I detail in my book, which will be out in March. Whenever I see a contract like this signed, I pull up the numbers to see what I’ve predicted he’s worth. In 2005, my model predicts that Oswalt was worth $14.9 million dollars, which is pretty darn close to his new annual salary. That made him eighth most valuable player in baseball that year, and only $50,000 less than Roger Clemens, who threw 30 fewer innings.

Oswalt has been consistent over the past three seasons, so I think it’s reasonable to expect him to continue at his current level of performance over the next few years. The bad news for the Astros is that they didn’t get a bargain. The good news is you get what you pay for, and Oswalt is pretty darn good.

Do Southpaws Get a Fair Shake in MLB? Part 2: Pitchers

My first attempt to look at the compensation of lefties in the big leagues focused solely on hitters. I found, contrary to findings in “the real world,” that lefty hitters earned about a quarter of a million dollars less than equally skilled right-handed batters. However, there are few problems with the analysis; the biggest one being that I only used hitting stats and lefties don’t play a few positions of high defensive importance. I can think of some ways to control for this, but all of them are a royal pain. Instead, let’s look at pitchers.

Just like in the analysis of hitters, I include only pure left and right-handed players—no switch hitters or players who throw and bat with opposite hands. I estimate the impact of pitching performance (estimated through strikeouts, walks, home runs, and innings pitched), age, and handedness on yearly salary for free agent eligible pitchers. I used two samples: more than 100 innings pitched and less than 100 but with a minimum of 30 innings pitched. This should roughly capture starters and relievers. I care less about that starter/reliever designation than I do about getting an adequate sample size.

The results are interesting. For the starters sample, lefties earn about $233,000 more than equally skilled right-handed pitchers. This fits with the findings from the general work force. Again, the relationship is not statistically significant, but it’s close, with a t-statistic of 1.55 (p-value of 0.12). This is about 7.5%, which is about half as large as the effect found in the general labor force. I find it interesting that you often hear left starters described as “crafty.” Maybe there is something to it. These guys are deceptive and smart, and have higher opportunity costs outside of baseball. I’d be curious to see the handedness of pitchers turned TV commentators, scouts, instructors, etc.

For relievers, the findings are nearly the mirror image, and the estimate is statistically significant. Southpaw relievers earn about $209,000 less than equally skilled right-handed pitchers, which is similar to what I found for position players. Hmm, maybe this has to do with LOOGY duties of lefty relievers. Because many left-handed relievers are used only against other lefties there are a lot of marginal pitchers who hang around. This may reduce the bargaining strength of each other because teams can just say, “look, if you don’t sign this contract I’m just going to bring up some random kid from triple-A or sign Mike Remlinger.” And because there are very few ROOGYs, marginal righties are more likely to find a real job if they are on the margin. OK folks, this is what is called a stretch, but it seems somewhat plausible.

I post the results below. Feel free to add comments.

Var.	Coef.		T-stat
K9	$408,358	7.29
BB9    	-$294,948	-3.78
HR9    	-$865,822	-3.65
Age    	$371,375	1.59
Age2	-$4,417		-1.27
IP    	$8,410		5.37
Lefty	$230,654	1.57
R2    	0.47	
Var.	Coef.		T-stat
K9    	$219,657	6.92
BB9    	-$186,071	-3.74
HR9    	$269,649	1.81
Age    	$645,741	2.52
Age2	-$9,295		-2.43
IP    	$8,468		2.41
Lefty	-$209,337	-1.98
R2    	0.25
(Constant and year effects not reported)

Do Southpaws Get a Fair Shake in MLB?

There have been a few blog posts recently on a new NBER article Handedness and Earnings (Everyday Economics, Marginal Revolution, and Greg Mankiw). The general results are reported in The Washington Post.

“Among the college-educated men in our sample, those who report being left-handed earn 13 percent more than those who report being right-handed,” said economist Christopher S. Ruebeck of Lafayette College. Ruebeck and his research partners, Joseph E. Harrington Jr. and Robert Moffitt of Johns Hopkins University, reported the findings in a new working paper published by the National Bureau of Economic Research.

However, it’s interesting that there is no concrete theory as to why this gap exists, and why it occurs in men but not women.

While evidence of a wage gap was unequivocal, explanations for the disparity proved more elusive. Differences in biology and brain function are two possibilities. Nor do the researchers know why they didn’t see a similar effect among women.

Tyler Cowen hypothesizes that there is something special about being left-handed, which I think fits with the conventional wisdom.

Left-handers have idiosyncrasies, obsessions, and downright insanities which lift some of them into productivity heaven.

But I’m curious. Left-handedness is not something traditionally viewed positively by society. The Latin term for left is sinister. Are modern day lefties overcoming a past bias and now surpassing righties?

Anyway, I wanted to see how left-handedness plays out in baseball. Because handedness plays a role in the success of players—because of the platoon effect— I had to be careful to control for other characteristics.

So, I went to the trusty Lahman Baseball Database and looked at all batters from 1985-2005. I estimated the impact of hitting performance, age, and handedness on yearly earnings of free agent eligible players using multiple linear regression. Also, I used a sample of only pure left-handed and right-handed players, taking out all switch hitters and players who throw and bat with opposite hands. Here is what I found.

Left-handers earn about $225,000 less than right-handers, but the difference is not statistically significant, meaning the estimate is within the expected variation. However, that’s nearly 6% less than the average player in this sample, which is nothing to sneeze at. But, more importantly, there does not seem to be evidence of lefties earning more than righties among hitters. This certainly isn’t perfect, and I can think of a few problems. The main weakness is that lefties are barred from playing four defensive positions: catcher, third, shortstop, and second. Because I’m using only offensive stats, equally good-hitting lefties may not be as valuable as righties. I’ll post the results below if you’re interested. I’m not sure what it means about why left-handers earn more in the general workforce, but this doesn’t seem to hold for baseball hitters. Maybe I’ll do pitchers next.

Variable	Coefficient	T-stat
AVG		$10,800,000	4.21
Walk Rate	$13,300,000	6.17
Iso-Power	$11,600,000	9.07
Left-Handed	-$225,676	-1.35
Age		-$297,196	-0.81
Age2		$4,337		0.79
R2		.51 
(year effects and constant not reported)

Addendum: See Part 2 for analysis of pitchers.

A Bright Day for Sports Economics

There are two stories about sports economics in the national media today.

Sue Kirchhoff writes of the recent rise of the field of sports economics in USA Today. This is the most thorough review of the field that I’ve seen.

Economists have long been intrigued by the numbers-rich world of sports. The interest is no longer a sideline, but an expanding field of study that offers insights on such broad topics as labor-management relations and racial disparities in pay and hiring.

It also examines questions such as whether football teams punt too often in fourth-down situations (yes, with implications for business risk taking) and the lack of left-handed catchers in baseball (it’s complex, but one reason is that most people who would be left-handed catchers become left-handed pitchers).

About 100 to 120 professors teach courses on sports economics, according to MKTG Services, a marketing firm. Textbooks on the subject sell well here and overseas. Dozens of sports-related papers were prepared for the recent Western Economic Association meeting in San Diego analyzing the impact of stadium announcements on property values, the winner’s curse in baseball’s free-agent market and other issues.

Here is my contribution.

John-Charles Bradbury of Kennesaw State University near Atlanta felt compelled to defend himself and fellow economists after Chicago Sun-Times columnist Greg Couch implied that some of those delving into sports statistics were frustrated geeks or grown-up versions of the “kid who always was forced to play right field, standing there pushing the glasses back up off his nose.”

“First, I don’t wear glasses,” Bradbury good-naturedly retorted on his blog. “Second, I was a power-hitting first baseman who once hit two home runs — the kind that go over the fence — in one game. I batted third and made my league’s All-Star team.”

Bradbury has a book coming out next year. “When I wrote about public finance and designed fiscal policy that would work, no one really called,” Bradbury says. “I get calls from reporters all the time now. … The market is giving me a signal.”

If you’d like some proof of by little league prowess, here’s a picture of me in my Dilworth Little League All-Star uniform.

JC All-Star Pic

The other article is by Bill Syken at It’s for subscribers only, so I can’t tell you what’s in it beyond a nice picture of Skip Sauer of The Sports Economist. If you can read the whole thing, feel free to give a brief summary in the comments (no quotes, please).

One of the beauties of sport is that it can be enjoyed by so many kinds of people, from little girls to grandfathers, from face-painted yahoos to deep thinkers like Skip Sauer and his cohorts. Sauer, 50, is chair of the economics department at Clemson and the brains behind The Sports Economist, a two-year-old blog. On the site Sauer and nine other professors put their decades in academe to use dissecting the sports news of the day. Think of as a highbrow version of Around the Horn.

Definitely a good day for sports economics. If you’re considering a career in the field, here’s my advice.

Addendum: Sabernomics gets a brief mention in the Sports Illustrated article. I don’t think anyone will mind if I quote it.
Economic thinking applied to baseball. You’ll get statistical analysis on such subjects as why, since pitching coach Leo Mazzone left the Braves for the Orioles, both teams’ staffs have stunk.

The article is quite flattering to The Sports Economist crew, and it’s hard not to be. I read it every day. I think the blog as been instrumental as a focal point for economists interested in sports.

Gladwell on The Wages of Wins

Malcolm Gladwell reviews The Wages of Wins in this week’s New Yorker.

It’s hard not to wonder, after reading “The Wages of Wins,” about the other instances in which we defer to the evaluations of experts. Boards of directors vote to pay C.E.O.s tens of millions of dollars, ostensibly because they believe—on the basis of what they have learned over the years by watching other C.E.O.s—that they are worth it. But so what? We see Allen Iverson, over and over again, charge toward the basket, twisting and turning and writhing through a thicket of arms and legs of much taller and heavier men—and all we learn is to appreciate twisting and turning and writhing. We become dance critics, blind to Iverson’s dismal shooting percentage and his excessive turnovers, blind to the reality that the Philadelphia 76ers would be better off without him. “One can play basketball,” the authors conclude. “One can watch basketball. One can both play and watch basketball for a thousand years. If you do not systematically track what the players do, and then uncover the statistical relationship between these actions and wins, you will never know why teams win and why they lose.”

The WoW is by three economists—Dave Berri, Martin Schmidt, and Stacey Brook— who have been doing some of the best research in sports economics over the past few years. I happened to end up at a dinner with Dave Berri at the Western Economic Association meeting last July, where I learned about the book. I thought the book had a lot of potential, given the work these economists had done. It reminded me of what William Easterly did in The Elusive Quest for Growth with his amazing academic work on economic growth.

Because of our similar research interests Dave sent me a few finished chapters, and it was even better than I thought. I’ve mentioned it a few times over the past few months, because of my excitement over what I have read. I think the readers of Sabernomics will enjoy its discussion of not only baseball, but other sports as well. The chapters on basketball are exceptional. Now that I have the entire book in front of me, I find that it has exceeded my already high expectations. Sometimes I wonder if my opinion is the exception or the consensus, but it turns out to be the latter. In addition to Mr. Gladwell, the book has also received praise from Alan Schwarz (cover blurb) and Tyler Cowen.

I’ll try and post a more thorough review of the book soon, but I’m a bit tied up with some other projects, so I can’t make promises. If you read the book, or find other reviews, and want to post comments in this thread, go right ahead. Also, check out the authors’ blog.

Why Don’t More GMs Do This?

Josh Byrnes, the GM of the Arizona Diamondbacks, just signed Chad Tracy to a 4-year $13.25 million deal (guaranteed) with an option for a fifth year at an additional $6 million ($7 million minus the $1 million buyout that is guaranteed). Mark Shapiro, of the Cleveland Indians, did something similar with several of his young players earlier this season, and it’s something his predecessor, John Hart, did as well.

As a general rule, individuals tend to be risk averse while firms are risk neutral. Baseball teams can diversify away risk—by signing many players—while players have their financial nest-egg in one basket. For a reserved player who has the potential to be a star, he’s likely to forgo some of his expected future earnings for a guarantee of stability. This represents a huge opportunity for teams to free up financial resources. As David Pinto puts it:

Tracy is a solid offensive player who is now locked up through his peak years. Not too long that he can cost the team a lot of money with a career ending injury, and they don’t need to worry about arbitration.

The league minimum may seem like a lot of money, but it’s not over the course of a lifetime. I expect, as must the D-backs, that Tracy is going to be worth more than $3.5 million/year for the next four years—I estimate that Tracy was worth $8.15 million in 2005—and Tracy is happy to trade some of that potential income for stability.

I also wonder how players behave after signing deals like this. You might think that a player who gets some guaranteed money over the next few years would shirk, but I think the exact opposite might happen. There is still the potential for a bigger payday down the road, and I’m sure Tracy wants to win. Maybe he’ll be more likely to do some little things that might injure his chances of getting a long run payoff—like dive for balls or get into collisions, or do strenuous weight-training. He might also be willing to share knowledge with younger teammates who could compete for his job. And let’s not forget generating good will with players.

Non-Credible Relocation Threats

Two weeks ago I pointed out that Jeffrey Loria’s threat to move the Marlins to San Antonio isn’t credible. Today, Maury Brown summarizes all of the prospective baseball markets and why none of them are viable alternatives at The Hardball Times.

When looking over this research, it becomes clear that relocation for franchises, at this time, is not favorable. The economics of franchises in existing markets is much better than the last time a serious discussion on relocation occurred, which places less stress and strain on clubs to force themselves into changing markets.

Also relevant to the discussion is my post The Extortion Game from two years ago.

This leads me to believe that MLB is more likely to use available market for expansion rather than extortion….If the probability of departure is perceived to be greater than the actual probability, then extortion may be preferable to expansion. But, if cities overestimate the probability of team relocation, then leaving a city open for extortion is not necessary. Owners can extract subsidies by threatening to move the team to unqualified markets AND obtain revenues from expanding into a qualified market.

Sorry for the clip show.

Payroll and Wins

Dave Berri, coauthor of The Wages of Wins, is today’s DH at The Baseball Analysts. Berri, an economist at Cal. St.-Bakersfield, answers the question: Can Money Buy Love in Baseball?

Contrary to popular perception, payroll in professional sports is not strongly linked to wins. A $100 million team does not win twice as many games as a $50 million team – not even close. Our own work has shown that only about 18% of a team’s regular season wins can be attributed to its payroll. In other words, more than 80% of a team’s regular season record cannot be tied to team spending. We would add that this is what we see when we look at teams in Major League Baseball from 1988 to 2005. In other words, the lack of a link between spending and wins is not a recent phenomenon. Across time more spending is not an elixir that leads automatically to success on the field. As the saying goes, games are not won on paper. Moreover, they are not won just because you spent a pile of paper.

Also, check out the site for the book. I received a copy of the book recently, and I have been loving it. Berri, Schmidt, and Brook do some of the most interesting work in the field of sports economics. I think the book is going to be a big hit, so pick up a copy of the book when it comes out in May. And look out for the authors’ blog, which is just getting started.

Marlins to San Antonio? Please

This is ridiculous.

Florida Marlins owner Jeffrey Loria said before the home opener Tuesday that he believes San Antonio is a viable market for a team and he must determine the club’s future “very, very, very soon.”

“San Antonio is a very viable market, and they’re very serious,” Loria said. “Read my lips: They’re very serious.”

2000 MSA Population and % change from 1990

Miami: 5,007,564 (23.5% increase from 1990)
San Antonio: 1,711,703 (21.6% increase from 1990)

When you see statements as non-credible as this one, it’s hard to take anything the speaker says seriously. Shut-up and market your damn team. This reminds me of that Simpson’s episode where the men of Springfield attempt to sabotage Apu’s Valentine’s Day surprises for his wife. Ned Flanders correctly points out that all the effort they are using could have gone to their wives—it’s rent seeking loss— before he’s told to pipe down. South Florida should be a great place for baseball. You have two of the best players in baseball on your team—Dontrelle Willis and Miguel Cabrera—playing for peanuts. Yeah, Jeff, you’d make more money if the city bought you a new stadium, but it’s not like you’ve got a bad situation. But no one believes you’re going to move the team from a top-10 market to a city three times smaller. The owners certainly won’t allow it either.

I hope the citizens of Miami do the right thing and dare him to leave. The citizens of Charlotte did the same thing to George Shinn with the Hornets, and look what it got them. The jerk owner left town, and the city got a new team and a downtown arena. Threatening to leave a city is a dangerous strategy. If you don’t get what you want, it can cost you in the long run.