Degree distribution of position-dependent ball-passing networks in football games

Abstract: We propose a simple stochastic model describing the position-dependent ball-passing network in football games. In this network, a player on a certain area in the divided fields is a node, and a pass between two nodes corresponds to an edge. Our model is characterized by the consecutive choice of a node dependent on its intrinsic fitness. We derive the explicit expression of the degree distribution, and find that the derived distribution reproduces the real data quit well.