Estimating individual contributions to team success in women's college volleyball

TL;DR

This paper models volleyball point progression as a Markov chain to attribute success probabilities to individual player actions, enabling detailed performance measurement and comparison across skills.

Contribution

It introduces a novel Markov chain model for volleyball points that attributes success probabilities to individual actions, improving performance assessment.

Findings

Effective at estimating individual skill contributions

Adjusts for opponent strength and schedule effects

Provides actionable insights for coaching strategies

Abstract

The progression of a single point in volleyball starts with a serve and then alternates between teams, each team allowed up to three contacts with the ball. Using charted data from the 2022 NCAA Division I women's volleyball season (4,147 matches, 600,000+ points, more than 5 million recorded contacts), we model the progression of a point as a Markov chain with the state space defined by the sequence of contacts in the current volley. We estimate the probability of each team winning the point, which changes on each contact. We attribute changes in point probability to the player(s) responsible for each contact, facilitating measurement of performance on the point scale for different skills. Traditional volleyball statistics do not allow apples-to-apples comparisons across skills, and they do not measure the impact of the performances on team success. For adversarial contacts (serve/receive and attack/block/dig), we estimate a hierarchical linear model for the outcome, with random effects for the players involved; and we adjust performance for strength of schedule not only on the conference/team level but on the individual player level. We can use the results to answer practical questions for volleyball coaches.