An Elo-type rating model for players and teams of variable strength

TL;DR

This paper extends the Elo rating system to better model variable performance in players and teams, providing a formal mean-field model and computational insights into its dynamics.

Contribution

It generalizes the kinetic Elo model to account for performance variability and derives a formal mean-field model for this extended system.

Findings

The model converges towards true player or team strength under certain conditions.

Computational results illustrate the dynamics of the generalized Elo system.

The approach offers a more flexible framework for rating in variable-performance settings.

Abstract

The Elo rating system, which was originally proposed by Arpad Elo for chess, has become one of the most important rating systems in sports, economics and gaming nowadays. Its original formulation is based on two-player zero-sum games, but it has been adapted for team sports and other settings. In 2015, Junca and Jabin proposed a kinetic version of the Elo model, and showed that under certain assumptions the ratings do converge towards the players' strength. In this paper we generalise their model to account for variable performance of individual players or teams. We discuss the underlying modelling assumptions, derive the respective formal mean-field model and illustrate the dynamics with computational results.