Mathematical Analysis of a Soccer Game. Part II: Energy, Spectral, and Correlation Analyses

Abstract

Following the calculations on the individual and collective behaviors of players and the ball in Part I, further calculations are carried out in Part II concerning (i) the specific kinetic energy of each player, (ii) the power densities of various quantities for different groups of players (forwards, defenders) and for the geometrical centers of the two teams, as well as for the ball, and (iii) the correlations of various quantities among different groups of players and the ball, as well as among the geometrical centers and the ball. Some parameters are compared between the two teams. The relation between these parameters and the potential indicators and all the influencing factors to the final result of a soccer match are discussed. Advantages and limitations of the present approach and some ideas for the future research are outlined.