Validation and Optimisation of Player Motion Models in Football

Modelling the trajectorial motion of humans along the ground is a foundational task in the quantitative analysis of sports like association football. Most existing models of football player motion have not been validated yet with respect to actual data. One of the reasons for this lack is that such a validation is not straightforward, because the validation typically needs to be performed with respect to noisy extreme values rather than expected values. This paper proposes a validation routine for trajectorial motion models that measures and optimises the ability of a motion model to accurately predict all possibly reachable positions by favoring the smallest predicted area that encompasses all observed reached positions up to a manually defined threshold. We demonstrate validation and optimisation on four different motion models, assuming (a) motion with constant speed, (b) motion with constant acceleration, (c) motion with constant acceleration with a speed limit, and (d) motion along two segments with constant speed. Our results show that assuming motion with constant speed or constant acceleration without a limit on the achievable speed is particularly inappropriate for an accurate distinction between reachable and unreachable locations. Motion along two segments of constant speed provides by far the highest accuracy among the tested models and serves as an efficient and accurate approximation of real-world player motion.