Super Size Soccer - Alterations of pitch dimensions reveal hysteresis in teams' collective behavior

INTRODUCTION:
Sports teams are frequently interpreted as (dynamical) systems to examine their collective behaviors, (CB; i.e., states) under stable environmental conditions (1). However, it is unknown whether the states of such a system are time-dependent, i.e., sensitive to previous environmental conditions (2). One particularly suitable system to study this dependency is soccer teams, where variations in pitch dimensions across contexts, e.g., from training to competition, are pervasive. The present study examines time-dependency by investigating hysteresis effects in the spatial organization of soccer teams responding to systematic changes in pitch dimensions.
METHODS:
Twenty-two male soccer players (6th division or higher) participated in a 11-vs-11 crossover, controlled, trial-based approach (3). They were instructed to perform an organized attack in 4-4-2 formation. Following six warm-up trials on an official-sized pitch (105x68 m; 7,140 m²), twelve experimental trials were conducted across four pitch size conditions (50%, 100%, 150%, 200%). To observe time-dependent adaptations in CB, each team performed three experimental trials per condition, scaling UP from 50% pitch size to 100%, 150%, and 200%. After a short break, this procedure was reversed, scaling DOWN from 200% back to 50%, totaling 54 trials. Player positions were tracked using GPS (10Hz) and verified with video footage. For each trial, effective playing space (EPS), team spread, stretch index, and relative field usage were calculated as parameters of CB. Multiple linear regression was employed to assess the influence of pitch size (50%, 100%, 150%, 200%), scaling direction (UP, DOWN), and their interaction on the CB.
RESULTS:
Linear regression analysis resulted in significant main effects for pitch size across all calculated CB parameters (EPS, team spread, stretch index, relative field usage; p<.0001). Interaction effects between pitch size and scaling direction were significant for EPS (p=.04), team spread (p=.05), relative field usage (p=.03), and a trend towards significance in the stretch index (p=.06). Hysteresis was particularly present at 50% pitch size, with average differences between UP- and DOWN-scaling as follows: Stretch index delta of 1.07 m, relative field usage of 3.5%, EPS of 127 m², and team spread of 14.5 m. These findings indicate time-dependency of changes in CB.
CONCLUSION:
The discovered hysteresis effects provide empirical evidence for a time-dependency of soccer teams states on historical environmental conditions. This result demonstrates how a (dynamical) systems perspective on soccer teams may lead to important insights, showing that soccer teams CB is highly sensitive and adaptable to previous stimuli. Better understanding the dynamics of team system configuration in sports contexts is a fertile ground for future research.