A Bayesian quest for finding a unified model for predicting volleyball games

Volleyball is a team sport with unique and specific characteristics. We introduce a new two-level hierarchical Bayesian model which accounts for these volleyball-specific characteristics. In the first level, we model the set outcome with a simple logistic regression model. Conditionally on the winner of the set, in the second level, we use a truncated negative binomial distribution for the points earned by the losing team. An additional Poisson-distributed inflation component is introduced to model the extra points played in the case that the two teams have a point difference less than two points. The number of points of the winner within each set is deterministically specified by the winner of the set and the points of the inflation component. The team-specific abilities and the home effect are used as covariates on all layers of the model (set, point and extra inflated points). The implementation of the proposed model on the Italian SuperLega 2017–2018 data shows exceptional reproducibility of the final league table and satisfactory predictive ability.