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Snooker Statistics and Zipf’s Law

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  • Wim Hordijk

    (SmartAnalytiX, 1015 Lausanne, Switzerland)

Abstract

Zipf’s law is well known in linguistics: the frequency of a word is inversely proportional to its rank. This is a special case of a more general power law, a common phenomenon in many kinds of real-world statistical data. Here, it is shown that snooker statistics also follow such a mathematical pattern, but with varying parameter values. Two types of rankings (prize money earned and centuries scored), and three different time frames (all-time, decade, and year) are considered. The results indicate that the power law parameter values depend on the type of ranking used, as well as the time frame considered. Furthermore, in some cases, the resulting parameter values vary significantly over time, for which a plausible explanation is provided. Finally, it is shown how individual rankings can be described somewhat more accurately using a log-normal distribution, but that the overall conclusions derived from the power law analysis remain valid.

Suggested Citation

  • Wim Hordijk, 2022. "Snooker Statistics and Zipf’s Law," Stats, MDPI, vol. 5(4), pages 1-8, October.
    • Handle: RePEc:gam:jstats:v:5:y:2022:i:4:p:58-992:d:950022
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    References listed on IDEAS

    as
    1. Wim Hordijk & Arie Hordijk & Bernd Heidergott, 2015. "A Genetic Algorithm for Finding Good Balanced Sequences in a Customer Assignment Problem with no State Information," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(03), pages 1-20.
    2. 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.
    3. J. M. Samuels, 1965. "Size and The Growth of Firms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 105-112.
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