Simulation evidence on Herfindahl-Hirschman measures of competitive balance in professional sports leagues

Abstract

Measurement of the degree of competitive balance, how evenly teams are matched, is central to the analysis of professional sports leagues. A common problem with within-season 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. Accounting for both the lower and upper bounds of the index improves its robustness to variation in the numbers of teams or games played per season, but does not completely remove overestimation of imbalance associated with shorter season lengths. Overall, McGee’s balance measure significantly mitigates the dependence on the number of matches and, of the measures considered, is recommended as the most robust to variation in season length.