Score-Driven Rating System for Sports
This provides a theoretical foundation for dynamic sports performance models, benefiting researchers and practitioners in sports analytics, though it is incremental as it builds on existing rating systems.
The paper tackles the problem of rating players or teams in sports by generalizing the Elo system to use a score-driven updating mechanism based on the gradient of the log-likelihood, allowing it to handle diverse game outcomes like point differences and rankings, with theoretical properties ensuring consistency and fairness.
This paper introduces a score-driven rating system, a generalization of the classical Elo rating system that employs the score, i.e. the gradient of the log-likelihood, as the updating mechanism for player and team ratings. The proposed framework extends beyond simple win/loss game outcomes and accommodates a wide range of game results, such as point differences, win/draw/loss outcomes, or complete rankings. Theoretical properties of the score are derived, showing that it has zero expected value, sums to zero across all players, and decreases with increasing value of a player's rating, thereby ensuring internal consistency and fairness. Furthermore, the score-driven rating system exhibits a reversion property, meaning that ratings tend to follow the underlying unobserved true skills over time. The proposed framework provides a theoretical rationale for existing dynamic models of sports performance and offers a systematic approach for constructing new ones.