Simple mechanism rules the dynamics of volleyball

TL;DR

This paper models volleyball rally dynamics using a simple stochastic approach, revealing fundamental probabilistic insights that align with empirical data and enhance understanding of team-sport complexity.

Contribution

It introduces a parsimonious stochastic model for volleyball rally dynamics, providing a closed-form probability expression based on minimal variables.

Findings

Model accurately predicts rally hit distributions

Empirical data supports the stochastic model

Advances understanding of sports competition complexity

Abstract

In volleyball games, we define a rally as the succession of events observed since the ball is served until one of the two teams on the court scores the point. In this process, athletes evolve in response to physical and information constraints, spanning several spatiotemporal scales and interplaying co-adaptively with the environment. Aiming to study the emergence of complexity in this system, we carried out a study focused on three steps: data collection, data analysis, and modeling. First, we collected data from 20 high-level professional volleyball games. Then we conducted a data-driven analysis from where we identified fundamental insights that we used to define a parsimonious stochastic model for the dynamics of the game. On these bases, we show that it is possible to give a closed-form expression for the probability that the players perform n hits in a rally using only two stochastic variables. Our results fully agree with the empirical observations and represent a new advance in the comprehension of team-sports competition complexity and dynamics.