System approach to games and competitive playing: Reply to Lebed (2006)

Abstract

In this article, we respond to some criticisms by Lebed (2006) of our previous research (McGarry, Anderson, Wallace, Hughes, & Franks, 2002) in which we reported that (a) the space–time interactions of players in sports (squash) contests might usefully be considered as a dynamical system, (b) that the other racket sports of tennis and badminton might likewise subscribe to a similar description, and (c) that doubles-play in these same racket sports might further be explained using the same self-organizing principles. From there, we speculated that team sports (taking soccer as an example) might ultimately also subscribe to similar principles, thus offering the possibility of a common underpinning for the space–time movements of sports players that seemingly give rise to patterned behaviours that are nonetheless unique. Lebed (2006) criticized this interpretation of sports (squash) contests as a dynamical system and instead offered a different account, though unfortunately these criticisms are inaccurate and unfounded. The most important point overlooked by Lebed (2006), and thus reiterated here, is that the essentials for a dynamical system – namely, the presence of coupled oscillators that comprise the system, as well as the sharing of information among the coupled oscillators that produces the patterned formations – are present in the racket sports for both singles-play and doubles-play. The presence of these essentials for team sports, however, must remain a matter of speculation for the time being as noted previously (McGarry et al., 2002).

Keywords:

• Sports contests
• dynamical self-organizing systems

This research was funded by separate grants from the Social Sciences and Humanities Research Council of Canada awarded to Tim McGarry and Ian M. Franks.

Notes

¹This comment on the description of a dynamical system in terms of coupled oscillators is made in respect of the formal descriptions thus far presented in the literature regarding the coordinated pattern dynamics of human (and animal) rhythmic actions.

²There are important differences in the structure of sports such as squash where possession is traded in equal measure, and sports such as soccer where possession is exchanged in unequal fashion, a point noted in McGarry et al. (2002). In that article, we suggested (p. 778) that the squash, tennis, and badminton players each move back and forth around a “locus of oscillation”, with that locus being “public” for squash (the “T”) and “private” for tennis (mid-baseline) and badminton (mid-court). We made no explicit suggestions of loci of oscillations for soccer players, although we would of course expect such loci to be present if the space–time patterns of soccer behaviours are to subscribe to similar dynamical descriptions as the racket sports, as hypothesized. Unlike the racket sports, however, there is no good reason to suppose at the outset that such loci for soccer (and other team sports) would be stationary. Further theoretical considerations on the possibility of sports contests – both individual and team – as dynamical systems are presented in McGarry (2004).

³Lebed is non-committal on whether a match consists of two (or more) dynamic systems, as well as on what the nature of these dynamic systems might represent. Lebed is likewise non-committal on whether a player in a sports contest should be considered as an “ordered system” (not defined by Lebed) or as a “chaotic system” (not defined by Lebed) and so instead opts for some unexplained combination of the two before continuing to describe a player, or a “game player” (i.e. team), as being on the “edge of chaos”. Thus, in so far as we can tell, Lebed views a sports contest as a “conflict” of (at least) two “ordered-chaotic” systems (our phrase for want of a better one), and looks to support this supposition using ill-defined concepts with phrases such as “edge of chaos” and “equifinality of a collective ‘game player’ [i.e. team]” (p. 38), albeit with brief explanatory footnotes of these terms [our inserts in brackets]. If such a position regarding sports behaviour is to be supported, however, then instead what would seem to be required is a formal description of a chaotic system (i.e. a formal description of a complex system using chaos theory) and then, a demonstration, preferably using empirical data, of game behaviour of each opponent from a sports contest seemingly conforming to the aforementioned principles of chaotic systems. Then, somehow, a conflict of these chaotic behaviours should be demonstrated as being co nsistent with the behaviours observed in sports contests.