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.

中文翻译：

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贝叶斯寻求寻找排球比赛的统一模型的追求

排球是一项具有独特特色的团体运动。我们引入了一个新的两级分层贝叶斯模型，该模型考虑了这些排球特定的特征。在第一级中，我们使用简单的逻辑回归模型对设定的结果进行建模。在第二级中，有条件地以组合的获胜者为准，对输掉的团队所获得的积分使用截断的负二项式分布。在两支球队的得分差小于两分的情况下，引入了一个额外的泊松分布的通货膨胀成分来模拟加分。每组中获胜者的点数由该组获胜者和通货膨胀成分的点确定性地指定。特定于团队的能力和主场效应在模型的所有层（集合，点和额外充气点）。拟议模型在意大利SuperLega 2017-2018数据上的实施显示了最终联赛表的出色再现性和令人满意的预测能力。