Tennis as a dynamical self-organizing system

• Published in: Journal of sports sciences 2006-04, Vol.24 (4), p.346-347
• Main Authors: Palut, Y, Zanone, P G
• Format: Article
• Language: English
• ISSN: 0264-0414

Classical analytic and probabilistic methods used to predict players' behaviour in racket sports have yielded different outcomes. Recently, some authors proposed another approach using dynamical self-organizing systems. In their view, the game is no longer a mere addition of each player's individual behaviour, but rather a complex system arising from the interaction between the two players and the environment. Accordingly, the study of such a system requires the definition of a relevant collective variable capturing invariance and change in the coupled activity between the two players involved in the game. In racket sports, the position of the two players relative to each other is of critical importance. As a first approximation, each player exhibits to-and-fro motion about a reference position located in the middle of the baseline. Thus, we posit that relative phase (or phase lag) between the two players' displacement is a pertinent variable to characterize the various modes of collective behaviour exhibited in a racket sport such as tennis. Four male tennis players ranked at a national level were videotaped while they were instructed to play long games. Forty trials lasting more than seven strokes were thus collected. After digitization, two-dimensional displacements were decomposed according to their Cartesian coordinates. As x-motion (viz. back and forth, from the baseline) was very seldom and/or of very small amplitude, only y-motion (viz. laterally, along the baseline) was analysed. A cross-correlation within a moving 5 s window was carried out between the y-motion of both players. The lag value close to a lag 0 with the most significant correlation dividing the window length yielded an index of the relative phase between the two time series. Results showed that among all relative phase modes exhibited across all trials, 0 degree and 180 degree are the most frequent and stable. For the first two time windows, however, relative motion hovered about 180 degree . Then, two evolutions of relative phase were observed. For 40% of the trials, relative phase did not change from 180 degree . An analysis of variance (ANOVA) with repeated measures failed to reveal any significant effect on relative phase across time windows (P > 0.05). For another 40% of the trials, relative phase exhibited a marked shift. An ANOVA with repeated measures detected a significant effect across time windows (F sub(5,5) = 20.03, P < 0.01). In the last 20% of the trials, no significa