Simulation-Based Calibration Applied to Sports Modeling

Resumen

This work evaluates five sports prediction models using Simulation-Based Calibration (SBC) [3]: the Bradley–Terry models BT₁ [1] and BT₂, and three Poisson models—Poisson₁ [2], Poisson₂, and the player-based Poisson_v2. SBC results showed strong contrasts: BT₁ and BT₂ displayed substantial miscalibration (60% and 71.4% deviations). Poisson models were far better calibrated: Poisson₁ and Poisson₂ deviated in only 5% and 4.7% of parameters, with ECDF differences mostly inside the confidence bands. Poisson_v2 also showed good calibration (3.3–9.4%), regardless of squad size. Applied to Brazilian Championship data (2014–2023; >3,800 matches; >1,500 players), Poisson models again outperformed Bradley–Terry models. Poisson₁ and Poisson₂ provided robust team level estimates, while Poisson_v2 additionally captured player contributions, albeit with sensitivity to limited playtime. The choice between Poisson₂ and Poisson_v2 depends on whether inference focuses on teams or players. [...]