Modelování pravděpodobnosti výhry v ledním hokeji

This bachelor’s thesis focuses on modeling the probability of victory in National Hockey League (NHL) games using Bayesian statistical methods. The main objective of the thesis is to design and implement a predictive model based on the Bradley–Terry framework that incorporates the latent strength of individual teams, home-ice advantage, and the temporal dynamics of team performance. The analysis is based on historical NHL data from the 2021/2022 season onward, obtained through the official NHL API. Model parameters were estimated using Markov Chain Monte Carlo (MCMC) methods, specifically the No-U-Turn Sampler (NUTS) algorithm implemented in the PyMC library. Three variants of the Bradley–Terry model were proposed and compared, differing primarily in their use of hierarchical structure, prior distributions, and the inclusion of a home-ice advantage parameter. Model performance was evaluated using Bayesian PSIS-LOO cross-validation, MCMC convergence diagnostics, and posterior predictive checks. The results confirm the statistical significance of home-ice advantage in the NHL and demonstrate that the hierarchical Bayesian model provides more stable and robust estimates of latent team strength due to the shrinkage effect. On the other hand, the model with non-informative priors showed greater sensitivity to recent team performance and achieved better results in predicting specific first-round playoff series outcomes. The thesis therefore empirically illustrates the trade-off between stability and flexibility in predictive models applied to highly stochastic sports data.