P\'olya urn model for analysis of football passes

TL;DR

This paper introduces a Pólya urn-based stochastic model to analyze football pass networks, revealing how preferential selection influences network evolution and correlates with pass accuracy and difficulty.

Contribution

It presents a novel application of the Pólya urn model to football pass networks and proposes a data analysis method for evolving networks.

Findings

The model characterizes network evolution with a single parameter.

The preferential-selection parameter correlates with pass accuracy.

The method applies broadly to various evolving networks.

Abstract

This study analyzes pass networks in football (soccer) using a stochastic model known as the P\'olya urn. By focusing on preferential selection, it theoretically demonstrates that the time evolution of networks can be characterized by a single parameter. Building on this result, a data analysis method is proposed and applied to a large-scale public dataset of professional football matches. The statistical properties of the preferential-selection parameter are examined, demonstrating its correlation with pass accuracy and with mean pass difficulty. This method is applicable to various evolving networks.