Modelo hierárquico bayesiano para a previsão de resultados de futebol

Abstract

This study develops and compares two statistical models to predict match outcomes in Brazil’s top tier football league: a Bayesian hierarchical model and an independent Poisson model. Both approaches model goals scored by each team with Poisson distributions parameterized by offensive strength, defensive strength, and a home‑field effect. Model assessment was conducted on two fronts: (i) in‑sample goodness of fit for the full season and (ii) out‑of‑sample predictive performance, using a sequential updating scheme to forecast the second half of the championship. Results reveal a clear trade‑off. The hierarchical model, through shrinkage, produced more stable and consistent forecasts but oversmoothed the extremes, underestimating the performance of the strongest and weakest teams. The independent Poisson model was more sensitive to team differences, achieving better overall fit at the cost of higher predictive variability. Both models exhibited limitations, most notably poor discrimination of draws. A scenario analysis further illustrated how each model captured the evolution of title, top four, and relegation probabilities during the final rounds. Finally, we discuss extensions to enhance predictive accuracy. These include adopting more flexible distributions, such as Negative Binomial to handle overdispersion, and draw‑inflated models, as well as incorporating betting market information either as informative priors, external benchmarks, or to simulate the financial return of betting strategies. Overall, this work advances applied football analytics by detailing practical challenges and outlining promising modeling directions for future research.