Performance rating in chess, tennis, and other contexts

Code

• github.com/drmehmetismail/estimated-performance-rating
  OfficialIn papernone★ 5

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.

Reproductions