Heteroscedastic TrueSkill: Modeling Match Noise and Player Consistency

TrueSkill is a widely used Bayesian rating system for inferring latent player skill from game outcomes. However, its standard formulation assumes a fixed global performance-noise parameter, making it sensitive to atypical outcomes and unable to distinguish skill from player-specific consistency. We propose two heteroscedastic extensions: a match-specific precision model that yields a robust heavy-tailed comparison likelihood, and a player-specific precision model that captures differences in performance consistency among players. Both extensions use Gamma-distributed precision variables and retain a modular factor-graph representation. Because the introduced Gaussian-Gamma factors do not admit the same closed-form expectation-propagation updates as vanilla TrueSkill, we derive an efficient hybrid message-passing scheme that combines expectation-propagation updates for outcome truncation factors with variational updates for latent precision factors. Experiments on synthetic and real match data show that the proposed models improve robustness to anomalous outcomes and provide interpretable estimates of player consistency.