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The distribution of soccer leagues scores that generates the minimum of competitive balance: Truncated-Cascade Distribution

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  • Antonio Ávila-Cano

    (Department of Economics, University of Málaga)

  • Francisco Triguero-Ruiz

    (Department of Languages and Computer Science, University of Málaga)

Abstract

Competitive balance can be measured using standardized indexes, such as the Herfindahl-Hirschman index (HHI). The standardized HHI calculus is based on knowing the maximum value of HHI. This value corresponds to the minimum value of the competitive balance. Measuring competitive balance is affected by the scoring system used. There are competitions that have scoring systems that do not award twice as many points for winning as they award for ties. In this case, the scores distribution representative of the minimum competitive balance is unstable because the total points at the end of the championship can vary. This issue has been addressed by reconstructing the results obtained in leagues. Nevertheless, this solution generates cardinal and ordinal negative effects, that we verify for the major European soccer leagues over twenty seasons. The aim of this article is to redefine the perfectly unbalanced distribution in order to construct a new one that generates the maximum level of concentration: we call this truncated-cascade distribution. Thus, we show that the instability problem does not involve recalculating the scoring based on the results. The minimum value of competitive balance is generated by a truncated-cascade distribution of results at a level that can be previously calculated. Thus, we calculate the cut-off point of the truncated-cascade distribution using a 5-grade polynomial equation obtained by recurrent calculation. Besides, we provide the cut-off points and maximum HHI values for leagues with different number of teams.

Suggested Citation

  • Antonio Ávila-Cano & Francisco Triguero-Ruiz, 2018. "The distribution of soccer leagues scores that generates the minimum of competitive balance: Truncated-Cascade Distribution," Working Papers 2018-04, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center.
    • Handle: RePEc:mal:wpaper:2018-4
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    Cited by:

    1. Antonio Avila-Cano & Amparo Ruiz-Sepulveda & Francisco Triguero-Ruiz, 2021. "Identifying the Maximum Concentration of Results in Bilateral Sports Competitions," Mathematics, MDPI, vol. 9(11), pages 1-19, June.
    2. Nicolas Scelles & Aurélien François, 2021. "Does a country’s income inequality affect its citizens’ quest for equality in leisure? Evidence from European men’s football," Economics and Business Letters, Oviedo University Press, vol. 10(2), pages 133-139.
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    More about this item

    Keywords

    Competitive balance; Herfindahl-Hirschman index; Perfectly unbalanced distribution; major European soccer leagues;
    All these keywords.

    JEL classification:

    • Z20 - Other Special Topics - - Sports Economics - - - General
    • Z21 - Other Special Topics - - Sports Economics - - - Industry Studies

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