Score-Driven Rating System for Sports
TLDR
This paper introduces a score-driven rating system that generalizes Elo, using gradient-based updates to handle diverse sports outcomes beyond simple wins/losses.
Key contributions
- Generalizes Elo with a score-driven update mechanism based on log-likelihood gradients.
- Handles diverse game outcomes beyond win/loss, including point differences and rankings.
- Establishes theoretical properties for fairness, consistency, and skill reversion.
- Offers a systematic framework for constructing new dynamic sports performance models.
Why it matters
This system offers a robust, theoretically sound alternative to traditional Elo, capable of modeling complex sports outcomes. It provides a systematic approach for developing new, fair, and consistent rating models.
Original Abstract
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.
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