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JOURNAL OF SPORTS ECONOMICS / May 20 2 Humphreys / COMPETITIVE BALANCE IN SPORTS LEAGUES Alternative Measures of Competitive Balance in Sports Leagues BRAD R. HUMPHREYS UMBC The most commonly used measures of competitive balance in sports leagues do not cap- ture season-to-season changes in relative standings. This article describes an alternative measure of competitive balance, the Competitive Balance Ratio (CBR), that reflects team- specific variation in winning percentage over time and league-specific variation. Based on estimation of a model of the determination of annual attendance in professional base- ball during the past 100 years, variation in the CBR explains more of the observed varia- tion in attendance than other alternatives measures of competitive balance, suggesting that CBR is a useful metric. C ompetitive balance is thought to be an important determinant of demand for sporting events. Competitive balance reflects uncertainty about the outcomes of professional sporting events. The conventional wisdom holds that to induce fans to purchase tickets to a game or tune in to a broadcast, there must be some uncertainty regarding the outcome. Neale (1964) called this the League Standing Effect. If a league lacks competitive balance, fan interest in the weaker teams will fall and, eventually, fan interest in the stronger teams will also decline. Thus, greater com- petitive balance should lead to greater demand, other things held equal. Quirk and Fort (1997) attribute the demise of the All American Football Conference, which started play in 1946 and merged with the National Football Conference in late 1949, to a lack of competitive balance. One commonly used measure of competitive balance is the dispersion of win- ning percentage within sports leagues. This measure of competitive balance has been used extensively by Scully (1989), Quirk and Fort (1997), and others to assess the performance of teams in sports leagues. Formally, this measure of competitive balance uses the standard deviation of winning percentage ( WPCT ), defined as the ratio of wins to total games played, as a measure of competitive balance. Consider a 133 AUTHOR’S NOTE: Mike Bradley, Kathleen Carroll, Dennis Coates, Alan Sorkin, Stefan Szymanski, and especially Andy Zimbalist provided helpful comments on this article . JOURNAL OF SPORTS ECONOMICS, Vol. 3 No. 2, May 2002 133–148 © 2002 Sage Publications
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league with N teams during a period of T seasons. If WPCT i,t is the winning percent- age of team i in season t , and i =1,. .., N indexes teams and t T indexes sea- sons, then the standard deviation of winning percentages for this league is () σ L it t T i N WPCT NT = = = , . 0 500 2 1 1 . σ L has a convenient comparison value based on the dispersion of winning percent- ages in an idealized league where each team is of equal strength; thus, the probabil- ity of winning any particular game is 0.5. The standard deviation of winning per- centages in an idealized league would be σ I G = 0 500 .
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This note was uploaded on 09/21/2011 for the course ECON 33974 taught by Professor Barbaraross during the Spring '09 term at Hawaii.

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