Tim McGarry

Sport competition as a dynamical self-organizing system

The existence of structure in sport competition is implicated in the widespread practice of using the information gathered from a past contest to prepare for a future contest. Based on this reasoning, we previously analysed squash match-play for evidence of signature traits from among the stochastic relations between the various types of shot. The mixed findings from these analyses led us to re-analyse squash match-play as a dynamical system. Here, we extend this line of investigation with some suggestions as to how various sports might be described further within this theoretical framework. We offer some examples of dynamical interactions in dyadic (i.e. one vs one) and team (e.g. many vs many) sports, as well as some predictions from a dynamical systems analysis for these types of sports contests. This paper should serve to initiate further research into the complex interactions that occur in sport competition.

Space–time coordination dynamics in basketball: Part 2. The interaction between the two teams

Abstract In this article, we examine the space–time coordination dynamics of two basketball teams during competition. We identified six game sequences at random, from which the movement data of each player were obtained for analysis of team behaviours in both the longitudinal (basket-to-basket) and lateral (side-to-side) directions. The central position of a team was measured using its spatial (geometric) centre and dispersion using a stretch index, obtained from the mean distance of team members from the spatial centre. Relative-phase analysis of the spatial centres demonstrated in-phase stabilities in both the longitudinal and lateral directions, with more stability in the longitudinal than lateral direction. As anticipated, this finding is consistent with the results of an analysis of individual playing dyads (see companion article, this issue), as well as the more general principle of complex systems conforming to similar descriptions at different levels of analysis. Phase relations for the stretch index demonstrated in-phase attraction in the longitudinal direction and no attraction to any values in the lateral direction. Finally, the difference between the two stretch indexes at any instant showed phase transitions between two stable patterns when the difference was represented in binary form. This result is attributed to the reciprocity between teams in their amounts of expansion and contraction when possession of the ball is won and lost.

Applied and theoretical perspectives of performance analysis in sport: Scientific issues and challenges

The scientific analysis of sport performance aims at advancing understanding of game behaviour with a view to improving future outcomes. In this article we outline some scientific issues for performance analysis and point towards some possible directions for increased attention in future research. Thus, six inter-linking issues for game analysis are presented for consideration and summarized as follows: First, increased attention should be paid to further developing an understanding of the associations between sports behaviours and sports outcomes; Second, the sports actions observed may not be of equal merit and, instead, some behaviours may be more significant than other behaviours; Third, the interactions between opposing players and/or teams is key for interpreting game behaviour; Fourth, the context in which the sports behaviours are produced offer important information for game analysis; Fifth, the behaviours of players both with and without possession of the sports article must be considered for a complete assessment of game performance, and; Sixth, the player-player dyads constitute a basic unit of analysis for investigating the space-time dynamics of game behaviour. The invitation made here is for a systematic undertaking of each of these inter-linking challenges in future research investigations of sport performance.

On the search for reliable performance indicators in game sports

This article addresses the reliability of performance indicators in game sports. In this context, reliability is invariably treated from a technical point of view as a question of observer agreement i.e. high levels of agreement between observations. That the measurement process itself should yield reliable data, as defined, for sports performance is given. Our considerations of reliability, however, extend from the process of measurement to include the trait (i.e., the performance) being measured. From these considerations, we present the argument that the performance traits, as measured, are inherently unstable and that the performance indicators are therefore necessarily unreliable (or unstable). In this light, the ongoing search for reliable (or stable) measures of sports performance indicators is questioned. Instead, alternative approaches for performance analysis are offered that recognise the dynamic interactions that characterise game sports as key features of sport performance. This notion of dynamic interactions is compatible with sporting experiences and the way that sports practitioners think about sports performance. We conclude that performance analysis for purposes of theoretical advancement should make use of mathematical modelling and simulation techniques, and that performance analysis for practical purposes should include qualitative research methods to arrive at the necessary inferences for sports practice.

Space–time coordination dynamics in basketball: Part 1. Intra- and inter-couplings among player dyads

Abstract We examined space–time patterns of basketball players during competition by analysing movement data obtained from six game sequences. Strong in-phase relations in the longitudinal (basket-to-basket) direction were observed for all playing dyads, especially player–opponent dyads matched for playing position, indicating that these movements were very constrained by the game demands. Similar findings for in-phase relations were observed for the most part in the lateral direction, the main exception being dyads comprising the two wing players from the same team. These dyads instead demonstrated strong attractions to anti-phase, a consequence perhaps of seeking to increase and decrease team width in tandem. Single instances from select dyads and game sequences demonstrated further evidence of phase stabilities and phase transitions on some occasions. Together, these findings demonstrate that space–time movement patterns of playing dyads in basketball, while unique, nonetheless conform to a uniform description in keeping with universal principles of dynamical self-organizing systems as hypothesized.

Interpersonal coordination and ball dynamics in futsal (indoor football).

Here, we report an investigation of the patterned movement behavior of players for a specific sub-phase of the game of futsal, namely when the goalkeeper for the attacking team is substituted with an extra outfield player. The movement trajectories of the ball and players were recorded in both lateral and longitudinal directions and investigated using relative phase analysis. Some differences in phase relations between different playing dyads were noted, indicating specificity of phase attractions, or otherwise, for certain players. In general terms, the defenders demonstrated strong in-phase attractions with the ball and with each other, whereas weaker phase attractions, indicated by increased relative phase variability, were observed for the attackers and ball, as well as between attackers themselves. These results demonstrate different coordination dynamics for the defending and attacking dyads, from which we interpret evidence for different playing sub-systems consistent with different team objectives linked together in an overarching game structure. In keeping with dynamical systems theory for complex systems, we view this sub-phase of futsal as being characterized by coordinated behavior patterns that emerge as a result of self-organizing processes. These dynamic patterns are generated within functional constraints, with players and teams exerting mutual influence on each other.

A stochastic approach to predicting competition squash match‐play

Modelling sport competition is an informative analytic technique for the investigation of athletic behaviour because it focuses attention on the critical aspects of data which characterize sporting success. A stochastic (Markov) model of championship squash match-play is reported which infers prospective behaviour from previous sport performance through forecasting shot response and associated outcome from the preceding shot. The results presently restrict the model to the competing players already analysed because, while a consistent athletic response was established when competing against the same opponent (P > 0.25), an inconsistent response was found when competing against different opponents (P < 0.25). These results may impact the information value traditionally drawn from previous sport analysis. The hypothesis that future squash match-play can be successfully predicted from previous sport performance requires further investigation, since it remains unclear whether the present analysis failed to identify the preceding condition(s) which elicit a reasonably stable behavioural response, or indeed whether athletic behaviour in championship squash is more variant than initially believed. Alternative modelling considerations are discussed and a refinement to the present model is proposed in an effort to improve future model utility and application.

A horse race between independent processes : Evidence for a phantom point of no return in the preparation of a speeded motor response

Electromyographic (EMG) data show that a speeded elbow extension response can be interrupted at any time after its execution. Submaximal, or partial, EMG data are also observed in some cases, from which 2 alternatives were considered. The partial response might in fact be interrupted early in response production or, alternately, it might arise from stopping processes that incompletely suppress the response production processes prior to their execution. An interrupted response is easily accounted for by a horse race between independent response production and stopping processes, whereas a partial response can only be reconciled if leakage between the two processes is allowed for. If the distinction between an interrupted and a partial response is correct, then the data yielded evidence for a phantom point of no return that locates late in the premotor component of the response and, thus, prior to the onset of EMG activity.

On the presence and absence of behavioural traits in sport: An example from championship squash match-play

Here we report two experiments that analysed sport (squash) competition as a non-linear system that transits intermittently between different behavioural states. The first experiment involved a perceptual analysis of 60 rallies in which stable behaviour and unstable behaviour, delineated by behavioural transitions (i.e. shot perturbations), were reliably (kappa = 0.930) and validly (kappa = 0.844) identified by independent observers. In addition, experts were better than non-experts at identifying the type of system behaviour (P < 0.01). These results provide for three alternative descriptions: (a) the system is multi-stable and transits between states via the mechanism of instability; (b) the system is bi-stable and abruptly transits between two states, labelled stable and unstable; or (c) the system is mono-stable and displays variability, marked by transient instability, as a result of system perturbations. The second experiment analysed squash behaviour as expressed in the phase relation between the two players from time-motion analysis. The data, from four rallies, yielded evidence of a tight anti-phase coupling with transient phase shifts, or perturbations, that were quickly damped. These data suggest a mono-stable system with a single (anti-phase) attractor onto which system fluctuations are occasionally written. However, these fluctuations failed to correspond with the short perturbations that were identified from perceptual analysis. Together, these results affirm the presence of transient behaviours in squash match-play, although the information that forms these perceptual judgements has yet to be identified.

Spatiotemporal coordination behaviors in futsal (indoor football) are guided by informational game constraints

This report investigated the behavioral dynamics of teams in futsal game practice when the goalkeeper of the attacking team is substituted for an extra outfield player. To this end, the lateral and longitudinal displacements of the ball and both teams, as well as their kinematics expressed in angles and radial distances from the goal center, were obtained and subjected to relative phase analysis. The results demonstrated (a) stronger phase relations with the ball for the defending team than the attacking team for both coordinate systems, (b) phase relations between each team and ball, and, to a lesser extent, between teams themselves, produced greater stabilities in the lateral (side-to-side) direction than the longitudinal (forward-backward) direction, and (c) phase attractions were most pronounced for the defending team and ball when using angles as a measure of association, indicating ball position and goal location as key informational constraints for futsal game behavior. These findings advance understanding of self-organizing sports game dynamics with implications for sports practice.