Performance rating in chess, tennis, and other contexts

Mehmet S. Ismail
12/20/2023
econ.THcs.MA

No official code found. Best implementation: drmehmetismail/Estimated-Performance-Rating (5 stars, last commit 2025-04-21).

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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Code Implementations(1)

drmehmetismail/Estimated-Performance-RatingCommunity100%

Extension of Tournament Performance Rating (TPR) to zero and perfect scores. The script also implements the standard TPR and FIDE's Performance Rating.

50PythonDec 19, 20231 years ago

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Cite this paper

@article{ismail2023performance,
  title  = {Performance rating in chess, tennis, and other contexts},
  author = {Mehmet S. Ismail},
  year   = {2023},
  eprint = {2312.12700},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2312.12700v1}
}

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