How to account for changes in the size of Sports Leagues: The Iso Competitive Balance Curves

The issue of Competitive Balance is a central issue in the literature on the economics of professional sports. The basic idea is that the managers of professional sports leagues must maintain a certain level of competitive balance in their league if they want it to remain attractive (Rottenberg (1956), El Hodiri & Quirk (1971), Fort & Quirk (1995), Vrooman (1995), Kesenne (2000), ...). An important part of literature is also devoted to the mechanisms to restore a satisfactory level of competitive balance: salary caps, luxury taxes, draft rules, gate revenue sharing... Although some authors challenge the idea that a decrease in competitive balance necessarily leads to a weakening of fan interest (Szymanski (2001)), all agree on the need to measure adequately the balance. As mentioned by Zymbalist (2002), the most commonly used index is the standard deviation of win percentage. But other indexes can be used as the ratio of the actual to the idealized standard deviation of win percentages, the Gini coefficient of win percentages, the Hirshman-Herfindahl index of competitive balance, the Concentration Ratio, the ratio of the top to bottom win percentages, the index of dissimilarity...