We study and develop Bayesian models for the analysis of volleyball match outcomes as recorded by the set-difference. Due to the peculiarity of the outcome variable (set-difference) which takes discrete values from $-3$ to $3$, we cannot consider standard models based on the usual Poisson or binomial assumptions used for other sports such as football/soccer. Hence, the first and foremost challenge was to build models appropriate for the set-difference of each volleyball match. Here we consider two major approaches: (a) an ordered multinomial logistic regression model and (b) a model based on a truncated version of the Skellam distribution. For the first model, we consider the set-difference as an ordinal response variable within the framework of multinomial logistic regression models. Concerning the second model, we adjust the Skellam distribution to account for the volleyball rules. We fit and compare both models with the same covariate structure as in Karlis & Ntzoufras (2003). Both models are fitted, illustrated and compared within Bayesian framework using data from both the regular season and the play-offs of the season 2016/17 of the Greek national men’s volleyball league A1.

中文翻译：

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用于预测排球组差的贝叶斯模型

我们研究和开发贝叶斯模型，用于分析由组差记录的排球比赛结果。由于结果变量（集差）的特殊性，它采用从 $-3$ 到 $3$ 的离散值，我们不能考虑基于通常用于其他运动（如足球/足球）的泊松或二项式假设的标准模型。因此，首要的挑战是建立适合每场排球比赛的组差的模型。在这里，我们考虑两种主要方法：（a）有序多项逻辑回归模型和（b）基于 Skellam 分布的截断版本的模型。对于第一个模型，我们将集合差异视为多项逻辑回归模型框架内的序数响应变量。关于第二个模型，我们调整 Skellam 分布以考虑排球规则。我们使用与 Karlis & Ntzoufras (2003) 中相同的协变量结构来拟合和比较这两个模型。使用来自希腊国家男子排球联赛 A1 的 2016/17 赛季常规赛和季后赛的数据，在贝叶斯框架内对两种模型进行拟合、说明和比较。