Income Inequality and Baseball

After doling out $137.5 million for über-ace Johan Santana last month, the last place the New York Mets' clubhouse could be a reminder of is the tiny African kingdom of Swaziland.

But when you compare how the team's payroll is split up between the Mets' high-priced players like Santana and center fielder Carlos Beltran at the top and the lowly rookies making the league minimum at the bottom, a hallmark of equity the Amazin's are not.

In fact, when you look at all of baseball, income inequality is even worse. In 2007, pay disparity in the majors was on par with that of Haiti, one of the most inequitable countries in the world, according to one of the more popular methods of measuring inequality, the Gini coefficient.

But that's not necessarily a bad thing. The "tournament theory," put forth in the 1980's by Edward Lazear, the current head of President Bush's Council of Economic Advisers, says the high wages at the top of the food chain in competitive endeavors are there to motivate the rank-and-file.

In this world, you work hard at the beginning of your career to reap the rewards at the end. (This also means that you get underpaid when you first start out and overpaid when you reach the top. Sound familiar?)

But what level of inequality is optimal?

That and similar questions have been tackled by a number of researchers in recent years using data from baseball, where salary and productivity information are easy to find. Most of this work has found a negative relationship between income inequality and how well a team does on the field.

A new working paper by Octavian Vasilescu of Clemson University, however, says that it's not that simple. He argues for an inverted U-shaped relationship between inequality and output: As wage disparity increases the tournament effect is dominant and the chances of winning increase -- up to a point. Then the negative effects of income inequality (such as poor allocation of resources) take over and the chances of winning decrease.

In a separate paper, he estimates this point to be around 0.43 to 0.50 on the Gini scale (0 on the Gini means complete equality, 1 complete inequality, the U.S. has a Gini of 0.41), which is actually a lot lower than the current Gini coefficient for all of baseball -- 0.61. In 2007 there was only one team in that range, the Baltimore Orioles, who won a pitiful 69 games.

So by this measure, it looks like teams are not spreading the wealth in the most efficient manner possible. It's important to note however, that most ballplayers don't really get paid market wages until they qualify for free agency after six years. To proxy for that, I calculated a Gini for 2007 which only looks at players who make more than $500,000, just above the league minimum of a little under $400,000. That number comes out to 0.48, implying that when it comes to spending free agent dollars, general managers might be more on the mark. Last year, both World Series teams had adjusted Ginis that fell in Vasilescu's range: Boston Red Sox, 0.43, and Colorado Rockies, 0.49.

Looking ahead to this season, the teams with Ginis (for players making above $500,000) between Vasilescu's optimum are: (Vegas over-under for season wins and country with matching Gini in parentheses)

(The Marlins are far-and-away the most equitable team in baseball with a Gini of 0.25, making them the Sweden of the MLB. They're also projected to have only a $19 million team salary this season. On the other end of the spectrum the Houston Astros have an adjusted Gini of 0.52, similar to the Dominican Republic.)

There are some really bad teams on the list besides favorites like the Red Sox, Mets and Tigers, implying that while salary distribution is one component in putting together a winning ball club, it's not the only factor.

An interesting question arises from a Gini analysis of baseball. The Major League Baseball Player's Association, the ballplayers' union, has often been called the strongest in America. But more than two-thirds of players earn less than the average salary. You'd have to think that most players don't think they're going to be Alex Rodriguez-es, so given their larger numbers, why haven't they pushed the union for more equitable wages?

(Photo credit: Doug Benc/Getty Images)