Title:Computational Biomechanics, Stochastic Motion and Team Sports

Abstract: The objective of the present study is to present a computational model of the motion of a single athlete in a team and to compare the resulting trajectory with experimental data obtained in the field during competitions by match analysis software. To this purpose, some results related to a paths ensemble of a single player are discussed. Between each interaction it is assumed that he follows a straight line and his motion is characterized by viscous, pushing and pedestrian like force. A random force is supposed to influence only the trajectory direction after each interaction. Furthermore it is assumed that the time step between each interaction is a random variable belonging to a Gaussian distribution. The main criteria is a selection of a function correlated to the strategy of the player, around which, in a necessarily randomly way, a tactic function should be added. The strategy depends on the players role: for the numerical simulations in this paper, a forward player was selected, with the average target to score. So it is straightforward to assume that the line direction joining the player position and a point related to the goal, would be the main strategy objective function around which a random angle A rand, expression of the tactic objective function, influencing the direction selected by the player until a next interaction could be introduced. The comparison between both single and multiple experimental paths and figures obtained by the numerical methodology proposed in this paper are very interesting, showing common Brownian path structures.