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In this paper, we investigate the ability of traditional indices of Competitive Balance to properly measure the attractiveness of professional sports leagues, differentiating Closed leagues and Promotion & Relegation leagues. Using an original device that allows to build hypothetical configurations of final rankings of clubs, we highlight the inability of traditional indices, and especially that of the Gini index, to account for the attractiveness of the different types of leagues. When adopting the approach based on the “parallel” between decision under risk and measurement of inequalities (following Yaari [1987]), we propose a generalization of the Gini index that properly reflects the attractiveness of different types of leagues.Classification JEL : L83, D63, D81