Performance rating in chess, tennis, and other contexts

TY - UNPB

T1 - Performance rating in chess, tennis, and other contexts

AU - Ismail, Mehmet

PY - 2024/10/2

Y1 - 2024/10/2

N2 - This note introduces two novel performance rating systems to address the limitations of the Tournament Performance Rating (TPR), which is undefined for zero or perfect scores. The first, Estimated Performance Rating (EPR), is based on solving a constrained optimization problem related to scoring probabilities, and the main result establishes that it is equivalent to TPR when the latter is defined. The second, Complete Performance Rating (CPR), provides a practical alternative to calculating performance ratings without a computer. CPR is the hypothetical rating at which a player, after scoring m points in n games in a tournament, and drawing against an opponent with the same rating, would keep their initial rating unchanged. These systems are applied to analyze historical win streaks across various sports and show broader applicability in any domain that uses Elo ratings, from academic rankings to LLM evaluation.

AB - This note introduces two novel performance rating systems to address the limitations of the Tournament Performance Rating (TPR), which is undefined for zero or perfect scores. The first, Estimated Performance Rating (EPR), is based on solving a constrained optimization problem related to scoring probabilities, and the main result establishes that it is equivalent to TPR when the latter is defined. The second, Complete Performance Rating (CPR), provides a practical alternative to calculating performance ratings without a computer. CPR is the hypothetical rating at which a player, after scoring m points in n games in a tournament, and drawing against an opponent with the same rating, would keep their initial rating unchanged. These systems are applied to analyze historical win streaks across various sports and show broader applicability in any domain that uses Elo ratings, from academic rankings to LLM evaluation.

M3 - Working paper

BT - Performance rating in chess, tennis, and other contexts

ER -