Metodologie moderne per la match-up analysis: un'applicazione alla Superlega italiana di Pallavolo

In volleyball, the goal of match-up analysis is to highlight teams’ strengths and weaknesses and describe the possible configuration of the starting line-ups of the two teams in terms of the probability of scoring points during a set. This information is nowadays provided as a pointwise estimate of this probabilitiy, based on two elements: how many times a team performs a perfect good negative etc. service or reception, and what is the efficacy of the two teams in such situations. Our goal is to provide a model-based approach to match-up analysis, which can be used to validate these estimations. Therefore we introduce the Bradley-Terry models, a well known class of models for pair comparison data. We present both a logistic and a loglinear formulation for this model. In the logistic model, each comparison represents an observation and the response variable is a binary variable which indicates which player wins the comparison. On the other hand, the log-linear model is fit on a contingency table whose entries are the number of comparisons won by each player in each comparison. Bradley Terry models provide a list of parameters representing players' strenght. The difference between these parameters corresponds to the log-odds of the probability of winning the comparison for the two considered players. In our model, we provide an ability parameter for each rotation (P1, P6, P5 etc.) and each phase (side-out, break-point) of the two considered teams. Therefore, we can calculate an interval estimation of the probability of winning a rally in each combination of phase and rotation of the two teams. This information can be used by teams to chose the optimal starting line-up of a set or to highlight strenghts and weaknesses of the team in a given configuration in order to decide tactical substitutions and team strategies.