Multifractality in Antagonistic Couplings: Cross-Scale Interactions in 1v1 Futsal Dyads

The coordination of competitively coupled systems is notoriously complex. One-v.-one attacker-defender interactions (1v1s), common in team sports, provide a vehicle for investigating the role of nonlinear interactions between timescales during competitive coordination. This study tracked movements of 20 amateur players in a 1v1 futsal task, modelling the attacker’s leading role and the dyad’s nonlinear interactivity with an anticipatory-synchronisation metric and multifractality, respectively. Anticipatory synchronisation encoded how well an attacker could pre-empt a defender’s movements. Multifractality encoded variability and comparison to linear surrogates encoded nonlinear interactions across scales. Generalised linear mixed-effects modelling showed that attackers scored more points when they anticipatorily synchronised with defenders’ movements and promoted greater multifractal variability in defenders, as well as in a collective variable pooling dyadic variability. Attackers scored more when they themselves constrained their own multifractal nonlinearity to generate targeted attacks. Thus, competitive coordination in invasion games rests on nonlinear cross-timescale interactions, not just linear sequences of perceptual, cognitive, and motor processes. Explanations of 1v1s may need to address both independent-player contributions and shared nonlinear interactivity. Finally, we discuss avenues for future research on the multiscale dynamics of competitive co-adaptation in sport and related contexts.