Previous work on dynamics of interpersonal interactions in 1 vs. 1 sub-phases of basketball has identified changes in interpersonal distance between an attacker and defender as a potential control parameter for influencing organizational states of attacker–defender dyads. Other studies have reported the constraining effect of relative velocity between an attacker and defender in 1 vs. 1 dyads. To evaluate the relationship between these candidate control parameters, we compared the impact of both interpersonal distance and relative velocity on the pattern-forming dynamics of attacker–defender dyads in the sport of rugby union. Results revealed that when interpersonal distance achieved a critical value of less than 4 m, and relative velocity values increased or were maintained above 1 m · s⁻¹, a successful outcome (i.e. clean attempt) for an attacker was predicted. Alternatively, when values of relative velocity suddenly decreased below this threshold, at the same critical value of interpersonal distance, a successful outcome for the defender was predicted. Data demonstrated how the coupling of these two potential, nested control parameters moved the dyadic system to phase transitions, characterized as a try or a tackle. Observations suggested that relative velocity increased its influence on the organization of attacker–defender dyads in rugby union over time as spatial proximity to the try line increased.

Ecological dynamics characterizes adaptive behavior as an emergent, self-organizing property of interpersonal interactions in complex social systems. The authors conceptualize and investigate constraints on dynamics of decisions and actions in the multiagent system of team sports. They studied coadaptive interpersonal dynamics in rugby union to model potential control parameter and collective variable relations in attacker–defender dyads. A videogrammetry analysis revealed how some agents generated fluctuations by adapting displacement velocity to create phase transitions and destabilize dyadic subsystems near the try line. Agent interpersonal dynamics exhibited characteristics of chaotic attractors and informational constraints of rugby union boxed dyadic systems into a low dimensional attractor. Data suggests that decisions and actions of agents in sports teams may be characterized as emergent, self-organizing properties, governed by laws of dynamical systems at the ecological scale. Further re...

The authors examined whether, similar to collective agent behaviors in complex, biological systems (e.g., schools of fish and colonies of ants), performers in team sports displayed functional coordination tendencies, based on local interaction rules during performance. To investigate this issue, they used videogrammetry and digitizing procedures to observe interpersonal interactions in common 4 versus 2 + 2 subphases of the team sport of rugby union, involving 16 participants aged between 16 and 17 years of age. They observed pattern-forming dynamics in attacking subunits (n = 4 players) attempting to penetrate 2 defensive lines (n = 2 players in each). Data showed that within each attacking subunit, the 4 players displayed emergent functional grouping tendencies that differed between the 2 defensive lines. Results confirmed that grouping tendencies in attacking subunits of team games are sensitive to different task constraints, such as relative positioning to nearest defenders. It was concluded that running correlations were particularly useful for measuring the level of interpersonal coordination in functional grouping tendencies within attacking subunits.

In team sports, the spatial distribution of players on the field is determined by the interaction behavior established at both player and team levels. The distribution patterns observed during a game emerge from specific technical and tactical methods adopted by the teams, and from individual, environmental and task constraints that influence players’ behaviour. By understanding how specific patterns of spatial interaction are formed, one can characterize the behavior of the respective teams and players. Thus, in the present work we suggest a novel spatial method for describing teams’ spatial interaction behaviour, which results from superimposing the Voronoi diagrams of two competing teams. We considered theoretical patterns of spatial distribution in a well-defined scenario (5 vs 4+ GK played in a field of 20×20m) in order to generate reference values of the variables derived from the superimposed Voronoi diagrams (SVD). These variables were tested in a formal application to empirical data collected from 19 Futsal trials with identical playing settings. Results suggest that it is possible to identify a number of characteristics that can be used to describe players’ spatial behavior at different levels, namely the defensive methods adopted by the players.

When considering time series data of variables describing agent interactions in social neurobiological systems, measures of regularity can provide a global understanding of such system behaviors. Approximate entropy (ApEn) was introduced as a nonlinear measure to assess the complexity of a system behavior by quantifying the regularity of the generated time series. However, ApEn is not reliable when assessing and comparing the regularity of data series with short or inconsistent lengths, which often occur in studies of social neurobiological systems, particularly in dyadic human movement systems. Here, the authors present two normalized, nonmodified measures of regularity derived from the original ApEn, which are less dependent on time series length. The validity of the suggested measures was tested in well-established series (random and sine) prior to their empirical application, describing the dyadic behavior of athletes in team games. The authors consider one of the ApEn normalized measures to generate the 95th percentile envelopes that can be used to test whether a particular social neurobiological system is highly complex (i.e., generates highly unpredictable time series). Results demonstrated that suggested measures may be considered as valid instruments for measuring and comparing complexity in systems that produce time series with inconsistent lengths.