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.

翻译：排球中每一分的推进始于发球，随后在双方之间交替进行，每方最多可触球三次。利用2022年NCAA一级女子排球赛季的图表数据（4147场比赛、60万+分、超过500万次记录触球），我们将每一分的推进建模为马尔可夫链，其状态空间由当前回合的触球序列定义。我们估计每支队伍赢得该分的概率，该概率随每次触球而变化。我们将分概率的变化归因于每次触球的球员，从而便于在分数尺度上衡量不同技能的表现。传统排球统计数据无法实现不同技能之间的直接比较，也无法衡量表现对团队成功的影响。对于对抗性触球（发球/接发球以及进攻/拦网/防守），我们估计了一个分层线性模型以预测结果，其中包含相关球员的随机效应；并且我们不仅从球队层面，还从单个球员层面调整了赛程强度对表现的影响。利用这些结果，我们可以为排球教练的实际问题提供答案。