Identifying the Maximum Concentration of Results in Bilateral Sports Competitions

Antonio Avila-Cano (), Amparo Ruiz-Sepulveda and Francisco Triguero-Ruiz
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Amparo Ruiz-Sepulveda: Department of Languages and Computer Science, University of Malaga, 29071 Málaga, Spain
Francisco Triguero-Ruiz: Department of Languages and Computer Science, University of Malaga, 29071 Málaga, Spain

Mathematics, 2021, vol. 9, issue 11, 1-19

Abstract: There are situations in which a monopoly solution cannot be reached. In these cases, which situation represents the maximum concentration (minimum competitive balance)? It is a relevant question, given that in sports economics, measuring the competitive balance of a league is done through normalized indices. These indices require that the maximum level of concentration be known. Until now, the distribution of results that generates the maximum level of concentration has been identified in the literature as Complete cascade distribution. However, if the scoring system used does not fulfil the stability condition, which implies that the total number of points of a championship is constant, it can be demonstrated that the Complete cascade distribution does not generate the maximum level of concentration. This is the case, for example, with major European football leagues. In this article, we constructed a perfectly unbalanced distribution, which we called a Truncated cascade distribution. This distribution generates the maximum concentration level. Therefore, if we do not use Truncated cascade distribution, there is an overestimation of the concentration measured with normalized indices. Then, the calculated competitive balance will be wrong, that is, underestimated. We provided a spreadsheet for identifying this distribution.

Keywords: operational research in sport; exact solution procedure; sports economics; maximum concentration; bilateral sports competitions; competitive balance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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