Skill Importance in Women's Volleyball

The purpose of this paper is to demonstrate two methods to quantify skill importance for teams in general, and women's volleyball in particular. A division I women's volleyball team rated each skill (serve, pass, set, etc.) and recorded rally outcomes during all home games in a competitive season. The skills were only rated when the ball was on the home team's side of the net. Events followed one of these three patterns: serve-outcome, pass-set-attack outcome, or block-dig-set-attack-outcome. These sequences of events were assumed to be first-order Markov chains, meaning the quality of the performance of the current skill only depended on the quality of the performance of the previous skill. We analyze the volleyball data using two different techniques: one uses a Markovian transition matrix, while the other is an implementation of logistic regression. To estimate the Markovian transition matrix, we assumed a multinomial likelihood with a Dirichlet prior on the transition probabilities. The logistic regression model also uses a Bayesian approach. The posterior distributions of parameters associated with skill performance are used to calculate importance scores. Importance scores produced by the two methods are reasonably consistent across skills. The importance scores indicate, among other things, that the team would have been well rewarded by improving transition offense. Importance scores can be used to assist coaches in allocating practice time, developing new strategies, and optimizing team performance relative to player selection.