Dynamics of attacker–defender dyads in Association Football : parameters influencing decision-making

Previous work on pattern-forming dynamics of team sports has investigated sub-phases of basketball and rugby union by focussing on one-versus-one (1v1) attacker-defender dyads. This body of work has identified the role of candidate control parameters, interpersonal distance and relative velocity, in predicting the outcomes of team player interactions. These two control parameters have been described as functioning in a nested relationship where relative velocity between players comes to the fore within a critical range of interpersonal distance. The critical influence of constraints on the intentionality of player behaviour has also been identified through the study of 1v1 attacker-defender dyads. This thesis draws from previous work adopting an ecological dynamics approach, which encompasses both Dynamical Systems Theory and Ecological Psychology concepts, to describe attacker-defender interactions in 1v1 dyads in association football. Twelve male youth association football players (average age 15.3 ± 0.5 yrs) performed as both attackers and defenders in 1v1 dyads in three field positions in an experimental manipulation of the proximity to goal and the role of players. Player and ball motion was tracked using TACTO 8.0 software (Fernandes & Caixinha, 2003) to produce two-dimensional (2D) trajectories of players and the ball on the ground. Significant differences were found for player-to-ball interactions depending on proximity to goal manipulations, indicating how key reference points in the environment such as the location of the goal may act as a constraint that shapes decision-making behaviour. Results also revealed that interpersonal distance and relative velocity alone were insufficient for accurately predicting the outcome of a dyad in association football. Instead, combined values of interpersonal distance, ball-to-defender distance, attacker-to-ball distance, attacker-to-ball relative velocity and relative angles were found to indicate the state of dyad outcomes.

Proximity-to-goal as a constraint on patterns of behaviour in attacker–defender dyads in team games

The aim of this study was to determine whether spatiotemporal interactions between footballers and the ball in 1 vs. 1 sub-phases are influenced by their proximity to the goal area. Twelve participants (age 15.3 ± 0.5 years) performed as attackers and defenders in 1 vs. 1 dyads across three field positions: (a) attacking the goal, (b) in midfield, and (c) advancing away from the goal area. In each position, the dribbler was required to move beyond an immediate defender with the ball towards the opposition goal. Interactions of attacker-defender dyads were filmed with player and ball displacement trajectories digitized using manual tracking software. One-way repeated measures analysis of variance was used to examine differences in mean defender-to-ball distance after this value had stabilized. Maximum attacker-to-ball distance was also compared as a function of proximity-to-goal. Significant differences were observed for defender-to-ball distance between locations (a) and (c) at the moment when the defender-to-ball distance had stabilized (a: 1.69 ± 0.64 m; c: 1.15 ± 0.59 m; P < 0.05). Findings indicate that proximity-to-goal influenced the performance of players, particularly when attacking or advancing away from goal areas, providing implications for training design in football. In this study, the task constraints of football revealed subtly different player interactions than observed in previous studies of dyadic systems in basketball and rugby union.

Overview of complex systems in sport

The complex systems approach offers an opportunity to replace the extant pre-dominant mechanistic view on sport-related phenomena. The emphasis on the environment-system relationship, the applications of complexity principles, and the use of nonlinear dynamics mathematical tools propose a deep change in sport science. Coordination dynamics, ecological dynamics, and network approaches have been successfully applied to the study of different sport-related behaviors, from movement patterns that emerge at different scales constrained by specific sport contexts to game dynamics. Sport benefit from the use of such approaches in the understanding of technical, tactical, or physical conditioning aspects which change their meaning and dilute their frontiers. The creation of new learning and training strategies for teams and individual athletes is a main practical consequence. Some challenges for the future are investigating the influence of key control parameters in the nonlinear behavior of athlete-environment systems and the possible relatedness of the dynamics and constraints acting at different spatio-temporal scales in team sports. Modelling sport-related phenomena can make useful contributions to a better understanding of complex systems and vice-versa.

Competing together : assessing the dynamics of team-team and player-team synchrony in professional association football

This study investigated movement synchronization of players within and between teams during competitive association football performance. Cluster phase analysis was introduced as a method to assess synchronies between whole teams and between individual players with their team as a function of time, ball possession and field direction. Measures of dispersion (SD) and regularity (sample entropy – SampEn – and cross sample entropy – Cross-SampEn) were used to quantify the magnitude and structure of synchrony. Large synergistic relations within each professional team sport collective were observed, particularly in the longitudinal direction of the field (0.89 ± 0.12) compared to the lateral direction (0.73 ± 0.16, p < .01). The coupling between the group measures of the two teams also revealed that changes in the synchrony of each team were intimately related (Cross-SampEn values of 0.02 ± 0.01). Interestingly, ball possession did not influence team synchronization levels. In player–team synchronization, individuals tended to be coordinated under near in-phase modes with team behavior (mean ranges between −7 and 5° of relative phase). The magnitudes of variations were low, but more irregular in time, for the longitudinal (SD: 18 ± 3°; SampEn: 0.07 ± 0.01), compared to the lateral direction (SD: 28 ± 5°; SampEn: 0.06 ± 0.01, p < .05) on-field. Increases in regularity were also observed between the first (SampEn: 0.07 ± 0.01) and second half (SampEn: 0.06 ± 0.01, p < .05) of the observed competitive game. Findings suggest that the method of analysis introduced in the current study may offer a suitable tool for examining team’s synchronization behaviors and the mutual influence of each team’s cohesiveness in competing social collectives.

Power law distributions in pattern dynamics of attacker-defender dyads in the team sport of Rugby Union : phenomena in a region of self-organized criticality?

In the region of self-organized criticality (SOC) interdependency between multi-agent system components exists and slight changes in near-neighbor interactions can break the balance of equally poised options leading to transitions in system order. In this region, frequency of events of differing magnitudes exhibits a power law distribution. The aim of this paper was to investigate whether a power law distribution characterized attacker-defender interactions in team sports. For this purpose we observed attacker and defender in a dyadic sub-phase of rugby union near the try line. Videogrammetry was used to capture players’ motion over time as player locations were digitized. Power laws were calculated for the rate of change of players’ relative position. Data revealed that three emergent patterns from dyadic system interactions (i.e., try; unsuccessful tackle; effective tackle) displayed a power law distribution. Results suggested that pattern forming dynamics dyads in rugby union exhibited SOC. It was concluded that rugby union dyads evolve in SOC regions suggesting that players’ decisions and actions are governed by local interactions rules.

Insights from ecological psychology and dynamical systems theory can underpin a philosophy of coaching

The aim of this paper is to show how principles of ecological psychology and dynamical systems theory can underpin a philosophy of coaching practice in a nonlinear pedagogy. Nonlinear pedagogy is based on a view of the human movement system as a nonlinear dynamical system. We demonstrate how this perspective of the human movement system can aid understanding of skill acquisition processes and underpin practice for sports coaches. We provide a description of nonlinear pedagogy followed by a consideration of some of the fundamental principles of ecological psychology and dynamical systems theory that underpin it as a coaching philosophy. We illustrate how each principle impacts on nonlinear pedagogical coaching practice, demonstrating how each principle can substantiate a framework for the coaching process.

How small-sided and conditioned games enhance acquisition of movement and decision-making skills

This article summarizes research from an ecological dynamics program of work on team sports exemplifying how small-sided and conditioned games (SSCG) can enhance skill acquisition and decision-making processes during training. The data highlighted show how constraints of different SSCG can facilitate emergence of continuous interpersonal coordination tendencies during practice to benefit team game players.

Dynamics of multi-articular coordination in neurobiological systems

Although previous work in nonlinear dynamics on neurobiological coordination and control has provided valuable insights from studies of single joint movements in humans, researchers have shown increasing interest in coordination of multi-articular actions. Multi-articular movement models have provided valuable insights on neurobiological systems conceptualised as degenerate, adaptive complex systems satisfying the constraints of dynamic environments. In this paper, we overview empirical evidence illustrating the dynamics of adaptive movement behavior in a range of multi-articular actions including kicking, throwing, hitting and balancing. We model the emergence of creativity and the diversity of neurobiological action in the meta-stable region of self organising criticality. We examine the influence on multi-articular actions of decaying and emerging constraints in the context of skill acquisition. We demonstrate how, in this context, transitions between preferred movement patterns exemplify the search for and adaptation of attractor states within the perceptual motor workspace as a function of practice. We conclude by showing how empirical analyses of neurobiological coordination and control have been used to establish a nonlinear pedagogical framework for enhancing acquisition of multi-articular actions.

The organisation of action in complex neurobiological systems

This chapter elucidates key ideas behind neurocomputational and ecological dynamics and perspectives of understanding the organisation of action in complex neurobiological systems. The need to study the close link between neurobiological systems and their environments (particularly their sensory and movement subsystems and the surrounding energy sources) is advocated. It is proposed how degeneracy in complex neurobiological systems provides the basis for functional variability in organisation of action. In such systems processes of cognition and action facilitate the specific interactions of each performer with particular task and environmental constraints.

The constraints-based approach to motor learning : Implications for a non-linear pedagogy in sport and physical education

Recently, a constraints- led approach has been promoted as a framework for understanding how children and adults acquire movement skills for sport and exercise (see Davids, Button & Bennett, 2008; Araújo et al., 2004). The aim of a constraints- led approach is to identify the nature of interacting constraints that influence skill acquisition in learners. In this chapter the main theoretical ideas behind a constraints- led approach are outlined to assist practical applications by sports practitioners and physical educators in a non- linear pedagogy (see Chow et al., 2006, 2007). To achieve this goal, this chapter examines implications for some of the typical challenges facing sport pedagogists and physical educators in the design of learning programmes.

Identifying constraints on children with movement difficulties : implications for pedagogues and clinicians

A constraints- based framework for understanding processes of movement coordination and control is predicated on a range of theoretical ideas including the work of Bernstein (1967), Gibson (1979), Newell (1986) and Kugler, Kelso & Turvey (1982). Contrary to a normative perspective that focuses on the production of idealized movement patterns to be acquired by children during development and learning (see Alain & Brisson, 1986), this approach formulates the emergence of movement co- ordination as a function of the constraints imposed upon each individual. In this framework, cognitive, perceptual and movement difficulties and disorders are considered to be constraints on the perceptual- motor system, and children’s movements are viewed as emergent functional adaptations to these constraints (Davids et al., 2008; Rosengren, Savelsbergh & van der Kamp, 2003). From this perspective, variability of movement behaviour is not viewed as noise or error to be eradicated during development, but rather, as essentially functional in facilitating the child to satisfy the unique constraints which impinge on his/her developing perceptual- motor and cognitive systems in everyday life (Davids et al., 2008). Recently, it has been reported that functional neurobiological variability is predicated on system degeneracy, an inherent feature of neurobiological systems which facilitates the achievement of task performance goals in a variety of different ways (Glazier & Davids, 2009). Degeneracy refers to the capacity of structurally different components of complex movement systems to achieve different performance outcomes in varying contexts (Tononi et al., 1999; Edelman & Gally, 2001). System degeneracy allows individuals with and without movement disorders to achieve their movement goals by harnessing movement variability during performance. Based on this idea, perceptual- motor disorders can be simply viewed as unique structural and functional system constraints which individuals have to satisfy in interactions with their environments. The aim of this chapter is to elucidate how the interaction of structural and functional organismic, and environmental constraints can be harnessed in a nonlinear pedagogy by individuals with movement disorders.

Interacting constraints shape emergent decision-making of referees

How and why football referees made decisions was investigated. A constructivist grounded theory methodology was undertaken to tap into the experiential knowledge of referees. The participant cohort comprised 7 A-League referees (aged 23 to 35) and 8 local Brisbane league referees (aged 20 to 50), spanning the lowest to highest levels of competition in men’s football in Australia. Results found that referees used ‘four pillars’ to underpin their judgments, these were conceptual notions of: safety, fairness, accuracy and entertainment. A fifth pillar ‘consistency’ referred to the referee’s ‘contextual sensitivity’. Results were explained using an ecological dynamics framework that emphasises the individual-environment scale of analysis. It was concluded that interacting constraints shape emergent decision-making in referees which are nested in task goals.

Science of winning soccer : emergent pattern-forming dynamics in association football

Quantitative analysis is increasingly being used in team sports to better understand performance in these stylized, delineated, complex social systems. Here we provide a first step toward understanding the pattern-forming dynamics that emerge from collective offensive and defensive behavior in team sports. We propose a novel method of analysis that captures how teams occupy sub-areas of the field as the ball changes location. We used the method to analyze a game of association football (soccer) based upon a hypothesis that local player numerical dominance is key to defensive stability and offensive opportunity. We found that the teams consistently allocated more players than their opponents in sub-areas of play closer to their own goal. This is consistent with a predominantly defensive strategy intended to prevent yielding even a single goal. We also find differences between the two teams' strategies: while both adopted the same distribution of defensive, midfield, and attacking players (a 4:3:3 system of play), one team was significantly more effective both in maintaining defensive and offensive numerical dominance for defensive stability and offensive opportunity. That team indeed won the match with an advantage of one goal (2 to 1) but the analysis shows the advantage in play was more pervasive than the single goal victory would indicate. Our focus on the local dynamics of team collective behavior is distinct from the traditional focus on individual player capability. It supports a broader view in which specific player abilities contribute within the context of the dynamics of multiplayer team coordination and coaching strategy. By applying this complex system analysis to association football, we can understand how players' and teams' strategies result in successful and unsuccessful relationships between teammates and opponents in the area of play.

The dynamics of expertise acquisition in sport : the role of affective learning design

Objectives The aim of this position paper is to discuss the role of affect in designing learning experiences to enhance expertise acquisition in sport. The design of learning environments and athlete development programmes are predicated on the successful sampling and simulation of competitive performance conditions during practice. This premise is captured by the concept of representative learning design, founded on an ecological dynamics approach to developing skill in sport, and based on the individual-environment relationship. In this paper we discuss how the effective development of expertise in sport could be enhanced by the consideration of affective constraints in the representative design of learning experiences. Conclusions Based on previous theoretical modelling and practical examples we delineate two key principles of Affective Learning Design: (i) the design of emotion-laden learning experiences that effectively simulate the constraints of performance environments in sport; (ii) recognising individualised emotional and coordination tendencies that are associated with different periods of learning. Considering the role of affect in learning environments has clear implications for how sport psychologists, athletes and coaches might collaborate to enhance the acquisition of expertise in sport.