Measuring competitive balance in professional team sports using the Herfindahl-Hirschman index

Competitive balance in sports leagues is essentially concerned with inequality in match and championship outcomes. Measures of inequality or concentration from the income distribution and industrial organization literatures have, therefore, often been used to measure competitive balance. This paper focuses on the use of the Herfindahl-Hirschman Index (HHI) applied to wins. It is shown that variation in the number of teams in the league affects not only the lower bound but also the upper bound of the HHI. An expression is derived for the upper bound and a normalized measure of the HHI, applicable to wins, is proposed. The differences this can make in practice when tracking variations in competitive balance over time are illustrated by considering Depken's (1999) application of the HHI to Major League Baseball.