Sportometrics

by Robert Tollison
About the Author
Until recently, economists who analyzed sports focused on such things as the antitrust exemption, the alleged cartel behavior of sports leagues, and the player draft (see sports). Sportometrics is different. It is the application of economic theories to the behavior of athletes to explain what they do and to see if what they do can help to explain the behavior of people in other professions and settings. Instead of being about the “economics of sports,” sportometrics introduces the idea of “sports as economics.”

In other words, sportometricians view sports as an economic environment in which athletes behave according to incentives and constraints. Economists have, for example, shown how incentives and costs can explain how much effort runners exert in a footrace (see Higgins and Tollison 1990; Maloney and McCormick 2000). Using data from sprint events of the modern Olympics from 1896 to 1980, Richard Higgins and Robert Tollison (1990) found that running times were faster when there were fewer contestants in a race. This makes sense. With fewer runners, each runner’s chance of winning is greater, and, therefore, each runner’s expected gain from putting out additional effort is greater. This cannot be attributed to decreased congestion: because each runner is given a lane, congestion does not diminish when the number of contestants falls.

Higgins and Tollison also found that the harder an Olympic record is to break, the less effort contestants will expend to break it. Can any fan ever forget Carl Lewis’s pass on a third attempt to break Bob Beamon’s long-jump record in the 1984 Olympics? Horse racing is an even better contest to analyze because the prerace odds were used to control for the differential abilities of the racers. The study found similar results: an increase in the number of competitors leads to an increase in average race times.

The economic activity called arbitrage also enters into sports. Arbitrage is what economists call the exploitation of price differences for the same commodity. For example, if wheat sells for $3.00 a bushel in Chicago and $3.30 in Indianapolis, and if it can be transported to Indianapolis for twenty cents per bushel, then an arbitrageur can make ten cents on each bushel he buys in Chicago and sells in Indianapolis.

What does this have to do with professional basketball? A lot. Each player has an incentive to build up his individual performance statistics, particularly the number of points he scores. But a good coach enforces a regime in which shots are allocated—arbitraged—among players to maximize the probability that each shot taken will be made. Players who make a higher percentage of their shots should thus be given more chances to shoot. Moreover, the value of three-point shots must be traded off against two-point shots. Using data from the National Basketball Association, Kevin Grier and I found that coaches who are better at enforcing such an allocation of shots—better arbitrageurs—are more likely to win games and to have longer tenure as head coaches. Among the better coaches, we found, was Cotton Fitzsimmons, the former coach of the Phoenix Suns. He became head coach of the Kansas City Kings in 1977 and, in his first full season, led the Kings to forty-eight wins and a shooting efficiency rating of 66 percent, a very high statistic in the NBA.

In each case studied, economists gain insight not only on the behavior of athletes and coaches, but also on more general economic problems. The behavior of runners is analogous to that of bidders for a government contract: a bidder will expend more effort—lobbying and the like—the fewer competitors it has for a contract. Coaching a team is analogous to managing a company: within a company, managers “arbitrage” tasks among employees.

Analyzing sporting events, moreover, provides insights into the workings of all competition within well-defined rules—just as we see in our economy. Incentives and constraints are spelled out clearly; players behave as rational economic actors; sporting events and seasons can be seen as the operation of miniature economies—and so on. One of the first sportometrics analyses done (see McCormick and Tollison 1984) showed, for example, that basketball players respond rationally when an additional referee is on the court. Using data on the Atlantic Coast Conference Basketball Tournament, the study found that, other things being equal, adding one referee reduced the number of fouls per game by about seventeen, a reduction of 34 percent. A more general application of this research is to the issue of how we can reduce the number of crimes by adding police officers to our police forces.

Most economic analysis is based on the idea that when the incentive to do something increases, people will do more of it. Kenneth Lehn, formerly chief economist at the Securities and Exchange Commission, showed that this idea applies even to the amount of time baseball players spend on the disabled list. After players were signed to multiyear, guaranteed contracts with no extra pay for each game played, their incentive to play diminished. Sure enough, Lehn found that the amount of time players spent on the disabled list increased from 4.7 days in the precontract period to 14.4 days after—an increase of 206 percent.

Sports data have been used to understand other interesting issues. Brian Goff, Robert McCormick, and I analyzed the process of racial integration in Major League Baseball and college basketball (Goff et al. 2002). We wanted to know what type of teams integrated first—winners or losers. Using data on team rosters and other information about teams and schools, we found that winning teams were the first to acquire and use the more productive black players. Thus, entrepreneurship and not competitive pressure played the key role in the racial integration of sports.

Goff, William Shughart, and I analyzed the designated hitter rule in the American League of Major League Baseball (Goff et al. 1997). Under this rule, in force since 1973, American League pitchers do not have to bat. Thus, a pitcher in the American League does not have to fear direct retaliation for hitting a batter on the other team. In economic jargon, the pitcher’s cost of plunking a batter is lower in the American League. As economists would have predicted, after the rule change there was a significant increase in hit batters in the American League.

Yet other studies have examined sports data to test hypotheses from game theory. P. A. Chiappori, Steve Levitt, and Tim Groseclose (2002) studied penalty kicks in soccer to see if goalies and kickers play a “mixed-strategy equilibrium”—that is, one in which the direction of the kick and the initial movement of the goalie are random. Such a result had previously been difficult to find in experimental studies, but they found it on the soccer field. Mark Waller and John Wooders (2001) found a similar result for the placement of tennis serves at Wimbledon.

Finally, in what has been hailed as a general contribution to managerial economics as well as being a book about sports, Michael Lewis recounts the story of what he callsMoneyball. This is a story about Billy Beane, general manager of the Oakland Athletics since 1997. By following principles of sabermetrics (the statistical analysis of baseball), Beane has been able to field excellent, competitive teams for far lower expenditures on players than other baseball franchises. Beane and sabermetrics are an example of sportometrics in action.


About the Author

Robert D. Tollison is a professor of economics at Clemson University. His specialty is in using economic analysis to explain the behavior of politicians and of athletes.


Further Reading

Chiappori, P. A., Steve Levitt, and Tim Groseclose. “Testing Mixed-Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer.” American Economic Review 92 (September 2002): 1138–1151.
Goff, Brian L., Robert McCormick, and Robert Tollison. “Racial Integration as an Innovation: Empirical Evidence from Sports Leagues.” American Economic Review 92 (March 2002): 16–26.
Goff, Brian L., William Shughart, and Robert Tollison. “Batter Up! Moral Hazard and the Effects of the Designated Hitter Rule on Hit Batsmen.” Economic Inquiry 35 (July 1997): 555–561.
Goff, Brian L., and Robert D. Tollison, eds. Sportometrics. College Station: Texas A&M Press, 1990.
Higgins, Richard S., and Robert D. Tollison. “Economics at the Track.” In Brian L. Goff and Robert D. Tollison, eds., Sportometrics. College Station: Texas A&M Press, 1990.
Lehn, Kenneth. “Property Rights, Risk Sharing, and Player Disability.” Journal of Law and Economics 25 (October 1982): 343–366.
Lewis, Michael. Moneyball: The Art of Winning an Unfair Game. New York: Norton, 2003.
Maloney, Michael, and Robert McCormick. “The Response of Workers to Wages in Tournaments: Evidence from Footraces.” Journal of Sports Economics 1 (May 2000): 99–123.
McCormick, Robert E., and Robert D. Tollison. “Crime on the Court.” Journal of Political Economy 92 (April 1984): 223–235.
Waller, Mark, and John Wooders. “Minimax Play at Wimbledon.” American Economic Review 91 (December 2001): 1521–1538.

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