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

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