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Statistical Properties Of Rankings In Sports And Games

Author

Listed:
  • JOSÉ ANTONIO MORALES

    (Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, 04510, Mexico)

  • JORGE FLORES

    (Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, 04510, Mexico)

  • CARLOS GERSHENSON

    (Instituto de Investigaciones en Matemáticas Aplicadas y Sistemas, Universidad Nacional Autónoma de México, Mexico City, 04510, Mexico3Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Mexico City, 04510, Mexico4Lakeside Labs GmbH, Lakeside Park B04, 9020 Klagenfurt am Wörthersee, Austria)

  • CARLOS PINEDA

    (Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, 04510, Mexico)

Abstract

Any collection can be ranked. Sports and games are common examples of ranked systems: players and teams are constantly ranked using different methods. The statistical properties of rankings have been studied for almost a century in a variety of fields. More recently, data availability has allowed us to study rank dynamics: how elements of a ranking change in time. Here, we study the rank distributions and rank dynamics of 12 datasets from different sports and games. To study rank dynamics, we consider measures that we have defined previously: rank diversity, change probability, rank entropy, and rank complexity. We also introduce a new measure that we call “system closure†that reflects how many elements enter or leave the rankings in time. We use a random walk model to reproduce the observed rank dynamics, showing that a simple mechanism can generate similar statistical properties as the ones observed in the datasets. Our results show that while rank distributions vary considerably for different rankings, rank dynamics have similar behaviors, independently of the nature and competitiveness of the sport or game and its ranking method. Our results also suggest that our measures of rank dynamics are general and applicable for complex systems of different natures.

Suggested Citation

  • Jos㉠Antonio Morales & Jorge Flores & Carlos Gershenson & Carlos Pineda, 2021. "Statistical Properties Of Rankings In Sports And Games," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 24(02), pages 1-15, March.
    • Handle: RePEc:wsi:acsxxx:v:24:y:2021:i:02:n:s0219525921500077
    DOI: 10.1142/S0219525921500077
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    Cited by:

    1. Wim Hordijk, 2022. "Snooker Statistics and Zipf’s Law," Stats, MDPI, vol. 5(4), pages 1-8, October.
    2. Wołoszyn, Maciej & Kułakowski, Krzysztof, 2023. "Status achieved in an organization—Rank dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 610(C).

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