Simulation Evidence on Herfindahl-Hirschman Indices as Measures of Competitive Balance

Measurement of the degree of competitive balance, how evenly teams are matched, is central to the economic analysis of professional sports leagues. A common problem with competitive balance measures, however, is their sensitivity to the number of teams and the number of matches played by each team, i.e., season length. This paper uses simulation methods to examine the effects of changes in season length on the distributions of several widely used variants of the Herfindahl-Hirschman index applied to wins in a season. Of the measures considered, a normalized measure, accounting for lower and upper bounds, and an adjusted measure perform best, although neither completely removes biases associated with different season lengths