A probabilistic approach to the analysis of a volleyball set performance

This paper presents a probabilistic model for predicting the score of a volleyball set that considers the players’ initial positions on court, and the position rotations required by the rules of the game. Each clockwise rotation results in a different team formation that encompasses different probabilistic capabilities. While other models for volleyball games assume a single probability for each team throughout the entire game, the proposed model considers different probabilities as a function of the formation of each rotation. We establish an ergodic Markov chain where each state represents a specific rotation formation; then, the expected final score of a set is estimated. The model is validated using information observed from actual games in several countries (the Australian and Israeli national volleyball teams) in various international competitions. The results show a high correlation between the actual scores and the model’s estimated scores. Sensitivity and error analyses show high robustness to inaccurate estimates of probabilities and to changes in players’ performances during a set. The model can be used as a support-decision tool to assist coaches and managers in selecting the optimal team formation and game tactics, leading to better utilization of resources and an improved success rate.