  The aim of this paper is to 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-differences 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 in order 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.
