Testing styles of play using triad census distribution: an application to men’s football

Summary statistics of football matches such as final score, possession and percentage of completed passes are not satisfyingly informative about style of play seen on the pitch. In this sense, networks and graphs are able to quantify how teams play differently from each others. We study the distribution of triad census, i.e., the distribution of local structures in networks and we show how it is possible to characterize passing networks of football teams. We describe the triadic structure and analyse its distribution under some specific probabilistic assumptions, introducing, in this context, some tests to verify the presence of specific triadic patterns in football data. We firstly run an omnibus test against random structure to asses whether observed triadic distribution deviates from randomness. Then, we redesign the Dirichlet-Multinomial test to recognize different triadic behaviours after choosing some reference patterns. The proposed tests are applied to a real dataset regarding 288 matches in the Group Stage of UEFA Champions League among three consecutive seasons.