# Measuring Skill Importance in Women's Soccer and Volleyball

## Abstract

The purpose of this study is to demonstrate how to measure skill importance for two sports: soccer and volleyball. A division I women's soccer team filmed each home game during a competitive season. Every defensive, dribbling, first touch, and passing skill was rated and recorded for each team. It was noted whether each sequence of plays led to a successful shot. A hierarchical Bayesian logistic regression model is implemented to determine how the performance of the skill affects the probability of a successful shot. A division I women's volleyball team rated each skill (serve, pass, set, etc.) and recorded rally outcomes during 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 dig-set-attack-outcome. We analyze the volleyball data using two different techniques, Markov chains and Bayesian logistic regression. These sequences of events are assumed to be first-order Markov chains. This means the quality of the current skill only depends on the quality of the previous skill. The count matrix is assumed to follow a multinomial distribution, so a Dirichlet prior is used to estimate each row of the count matrix. Bayesian simulation is used to produce the unconditional posterior probability (e.g., a perfect serve results in a point). The volleyball logistic regression model uses a Bayesian approach to determine how the performance of the skill affects the probability of a successful outcome. The posterior distributions produced from each of the models are used to calculate importance scores. The soccer data importance scores revealed that passing, first touch, and dribbling skills are the most important to the primary team. The Markov chain model for the volleyball data indicates setting 3–5 feet off the net increases the probability of a successful outcome. The logistic regression model for the volleyball data reveals that serves have a high importance score because of their steep slope. Importance scores can be used to assist coaches in allocating practice time, developing new strategies, and analyzing each player's skill performance.

MS

## College and Department

Physical and Mathematical Sciences; Statistics

2009-03-11

Selected Project

## Handle

http://hdl.lib.byu.edu/1877/etd2809

## Keywords

volleyball, Markov chain, transition matrix, Markov chain Monte Carlo, Gibbs sampling, multinomial distribution, Bayesian model, soccer, hierarchical logistic regression

English

COinS