Tennis match time Series do not exhibit long term correlations

Han Eol Kim, Fuwen Cai, Joong Hyun Ryu, Jeffrey M. Haddad and Howard N. Zelaznik

Department of Health and Kinesiology, Purdue University, Indiana, USA


Eol Kim, H., Cai, F., Hyun Ryu, J., M. Haddad, J., N. Zelaznik, H. (2015). Tennis match time Series do not exhibit long term correlations. International Journal of Sport Psychology, 46(6), 542-554. doi:10.7352/IJSP.2015.46.542


Many researchers have examined expert performance in competition in dual sports such as squash and tennis. The focus of those studies has been either on short term shot dependencies, or the movements of the players. In these dual sports, player movements usually oscillate, because the player usually returns to the center of the baseline(tennis) or court (squash) to provide maximum court coverage. Thus, a traditional phase analysis of player movements provides evidence of in phase and anti-phase behavior. In our present work we explore the long term structure of a tennis match. Video data from two grand-slam semi-final tennis matches (Australian Open, 2012), one between Roger Federer and Rafael Nadal and the other between Maria Sharapova and Petra Kvitova were captured. The time series of ball bounce locations was computed and subjected to Detrended Fluctuation Analysis (DFA). The ball location time series did not show evidence of long-term correlations, typical of a dynamical system. We recommend that other potential signatures of dynamical systems should be studied in the future to better understand expert dual-sport performance.

Keywords: Complex Systems, Detrended, Expertise, Fluctuation, Tennis