Clustering algorithm for formations in football games

This paper develops a clustering algorithm for formations in team sports, with a focus on football games. Our method first clusters formations into several average formations: `442,' `4141,' `433,' `541,' and `343.' Then, each average formation is further divided into more specific patterns in which the configurations of players are slightly different. The latter step is based on hierarchical clustering and the Delaunay method, which defines the formation of a team as an adjacency matrix of Delaunay triangulation. A formation clustered using our method is expressed in a form such as `442-C1'.