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Performance rating in chess, tennis, and other contexts

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  • Mehmet S. Ismail

Abstract

In this note, I introduce Estimated Performance Rating (PR$^e$), a novel system for evaluating player performance in sports and games. PR$^e$ addresses a key limitation of the Tournament Performance Rating (TPR) system, which is undefined for zero or perfect scores in a series of games. PR$^e$ is defined as the rating that solves an optimization problem related to scoring probability, making it applicable for any performance level. The main theorem establishes that the PR$^e$ of a player is equivalent to the TPR whenever the latter is defined. I then apply this system to historically significant win-streaks in association football, tennis, and chess. Beyond sports, PR$^e$ has broad applicability in domains where Elo ratings are used, from college rankings to the evaluation of large language models.

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  • Mehmet S. Ismail, 2023. "Performance rating in chess, tennis, and other contexts," Papers 2312.12700, arXiv.org.
    • Handle: RePEc:arx:papers:2312.12700
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    References listed on IDEAS

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    1. Scarf, Philip & Yusof, Muhammad Mat & Bilbao, Mark, 2009. "A numerical study of designs for sporting contests," European Journal of Operational Research, Elsevier, vol. 198(1), pages 190-198, October.
    2. Jose Apesteguia & Ignacio Palacios-Huerta, 2010. "Psychological Pressure in Competitive Environments: Evidence from a Randomized Natural Experiment," American Economic Review, American Economic Association, vol. 100(5), pages 2548-2564, December.
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    Cited by:

    1. Mehmet S. Ismail, 2024. "Performance Rating Equilibrium," Papers 2410.19006, arXiv.org, revised Oct 2024.

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