Modeling soccer by means of relative phase

Soccer is a complex system. Therefore, appropriate (nontrivial) models have to be applied to be able to analyze the behavior of the teams on the pitch. This study analyzed the World Cup Final 2006 between France and Italy by means of relative phase. Mean longitudinal and lateral positions of all 20 outfield players were used to calculate relative phase by Hilbert transformation. Whole team-, group-, and attacker-fullbacks couplings showed that soccer is clearly an in-phase game. Perturbations of the relative phase structure helped to identify scoring opportunities of the attacking team. Moreover, analyses of the relative phase structure can help to understand the complexity of soccer.