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

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, enabling efficient computation of distance. Then, building on this frame-level analysis,we use 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 successfully retrieve relevant clusters of game situations and calculate the similarity matrix between teams in terms of style of play. Additionally, we demonstrate the effectiveness of the embedding as a preprocessing tool for prediction tasks. Likewise, we apply our framework to analyze the dynamics in the first half of the NBA season in 2015–2016.