On the mathematical modeling of soccer dynamics

- The paper addresses the modelling and dynamical analysis of soccer sport teams.
- First, the power law behaviour and fractional-order integration are explored.
- Second, a league season is interpreted in the light of a system of particles.
- Real data is processed.
- The models lead to the emergence of patterns that are analysed and interpreted.

This paper addresses the modeling and dynamical analysis of soccer teams. Two modeling perspectives based on the concepts of fractional calculus are adopted. In the first, the power law behavior and fractional-order integration are explored. In the second, a league season is interpreted in the light of a system where the teams are represented by objects (particles) that evolve in time and interact (collide) at successive rounds with dynamics driven by the outcomes of the matches. The two proposed models embed implicitly details of players and coaches, or strategical and tactical maneuvers during the matches. Therefore, the scale of observation focuses on the teams behavior in the scope of the observed variables. Data characterizing two European soccer leagues in the season 2015-2016 are adopted and processed. The model leads to the emergence of patterns that are analyzed and interpreted.