A spectral analysis of team dynamics and tactics in Brazilian football

Abstract

The purposes of this study were to characterise the total space covered and the distances between players within teams over ten Brazilian First Division Championship matches. Filmed recordings, combined with a tracking system, were used to obtain the trajectories of the players (n = 277), before and after half-time. The team surface area (the area of the convex hull formed by the positions of the players) and spread (the Frobenius norm of the distance-between-player matrix) were calculated as functions of time. A Fast Fourier Transform (FFT) was applied to each time series. The median frequency was then calculated. The results of the surface area time series median frequencies for the first half (0.63 ± 0.10 cycles · min⁻¹) were significantly greater (P < 0.01) than the second-half values (0.47 ± 0.14 cycles · min⁻¹). Similarly, the spread variable median frequencies for the first half (0.60 ± 0.14 cycles · min⁻¹) were significantly greater (P < 0.01) than the second-half values (0.46 ± 0.16 cycles · min⁻¹). The median frequencies allowed the characterisation of the time series oscillations that represent the speed at which players distribute and then compact their team formation during a match. This analysis can provide insights that allow coaches to better control the team organisation on the pitch.

Keywords:

• spectral analysis
• tactics
• surface area
• spread
• time series

Acknowledgements

The authors would like to thank FAPESP, CAPES, CNPq and Rede Globo de Televisão.