An optimal transport based embedding to quantify the distance between playing styles in collective sports

TL;DR

This paper introduces an optimal transport-based embedding method to quantify and compare team playing styles in collective sports using spatial distribution analysis, enabling efficient similarity measurement and predictive analysis.

Contribution

It proposes a novel optimal transport-based embedding for frames and a quantization approach to compare team styles, advancing quantitative sports analysis.

Findings

Successfully clusters game situations and computes team style similarities.

Demonstrates the embedding's effectiveness as a preprocessing tool for prediction tasks.

Analyzes dynamics in NBA and Ligue 1 seasons.

Abstract

This study presents a quantitative framework to compare teams in collective sports with respect to their style of play. The style of play is characterized by the team's spatial distribution over a collection of frames. As a first step, we introduce an optimal transport-based embedding to map frames into Euclidean space, allowing for the efficient computation of a distance. Then, building on this frame-level analysis, we leverage quantization to establish a similarity metric between teams based on a collection of frames from their games. For illustration, we present an analysis of a collection of games from the 2021-2022 Ligue 1 season. We are able to retrieve relevant clusters of game situations and calculate the similarity matrix between teams in terms of style of play. Additionally, we demonstrate the strength of the embedding as a preprocessing tool for relevant prediction tasks. Likewise, we apply our framework to analyze the dynamics in the first half of the NBA season in 2015-2016.