The distance to competitive balance: a cardinal measure

Francisco Triguero Ruiz and Antonio Avila-Cano ()

Applied Economics, 2019, vol. 51, issue 7, 698-710

Abstract: Competitive balance is a key variable in the analysis of sports competitions. There are several indexes that measure competitive balance but, either they are not a mathematical metric or they do not have the unit interval as a range. Therefore, these indexes do not indicate the magnitude of the differences, and the measurements cannot be interpreted as percentages. We characterize the space of all admissible configurations of the results of a competition. Then, we construct a new index, based on the concept of distance, whose range is the unit interval, and define it as a function in a metric space. So, it solves issues linked to the limited cardinality of most existing indexes, and we can answer this question: What is the meaning of the differences between the levels of competitive balance? We applied this index to the major European soccer leagues over the last twenty seasons.

Date: 2019
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DOI: 10.1080/00036846.2018.1512743

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