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The distance to competitive balance: a cardinal measure

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  • Francisco Triguero Ruiz
  • Antonio Avila-Cano

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.

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  • Francisco Triguero Ruiz & Antonio Avila-Cano, 2019. "The distance to competitive balance: a cardinal measure," Applied Economics, Taylor & Francis Journals, vol. 51(7), pages 698-710, February.
    • Handle: RePEc:taf:applec:v:51:y:2019:i:7:p:698-710
    DOI: 10.1080/00036846.2018.1512743
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    1. Dubois, Marc, 2022. "Dominance criteria on grids for measuring competitive balance in sports leagues," Mathematical Social Sciences, Elsevier, vol. 115(C), pages 1-10.
    2. Antonio Avila‐Cano & Francisco Triguero‐Ruiz, 2023. "On the control of competitive balance in the major European football leagues," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 44(2), pages 1254-1263, March.
    3. Triguero-Ruiz, Francisco & Avila-Cano, Antonio & Trujillo Aranda, Francisco, 2023. "Measuring the diversification of energy sources: The energy mix," Renewable Energy, Elsevier, vol. 216(C).
    4. 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.
    5. Avila-Cano, Antonio & Owen, P. Dorian & Triguero-Ruiz, Francisco, 2023. "Measuring competitive balance in sports leagues that award bonus points, with an application to rugby union," European Journal of Operational Research, Elsevier, vol. 309(2), pages 939-952.
    6. L'aszl'o Csat'o & D'ora Gr'eta Petr'oczy, 2024. "The myth of declining competitive balance in the UEFA Champions League group stage," Papers 2406.19222, arXiv.org, revised Sep 2024.
    7. Francisco Triguero‐Ruiz & Antonio Avila‐Cano, 2023. "On competitive balance in the group stage of the UEFA Champions League," Scottish Journal of Political Economy, Scottish Economic Society, vol. 70(3), pages 231-248, July.
    8. 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.
    9. Marc Dubois, 2022. "Dominance criteria on grids for measuring competitive balance in sports leagues," Post-Print hal-04692979, HAL.
    10. Marco Di Domizio & Raul Caruso & Bernd Frick, 2020. "Intelligenza Collettiva E Valore Di Mercato Dei Calciatori: Il Caso Transfermarkt," Rivista di Diritto ed Economia dello Sport, Centro di diritto e business dello Sport, vol. 16(2), pages 155-172, novembre.

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