Performance rating in chess, tennis, and other contexts
Abstract
In this note, I introduce Estimated Performance Rating (PR), a novel system for evaluating player performance in sports and games. PR 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 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 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 has broad applicability in domains where Elo ratings are used, from college rankings to the evaluation of large language models.
Keywords
Cite
@article{arxiv.2312.12700,
title = {Performance rating in chess, tennis, and other contexts},
author = {Mehmet S. Ismail},
journal= {arXiv preprint arXiv:2312.12700},
year = {2023}
}