Measuring competitive balance in the major european soccer leagues

Abstract

Competitive balance of a sports competition can be measured by, among others, the standardized Herfindahl- Hirschman index. This index requires knowing its maximum value. So far, its maximum value has been identified with a distribution of competition scores, which we call in cascade. This distribution requires the scoring system to reward victory with twice as many points as ties. However, there are competitions such as the major soccer leagues that have a different remuneration pattern. Therefore, the cascade distribution does not generate the maximum value of the index. In this article, we show that: (i) solutions such as recalculating the results are not suitable; (ii) we redefine the distribution and (iii) we obtain the maximum index values for the major European soccer leagues. Thus, we can construct the standardized Herfindahl-Hirschman indexes for the 1997/98-2016/17 leagues and conclude that, overall, competitive balance has decreased.