Markov-chain Modelling and Simulative Assessment of the Impact of Selected Tactical Behaviours in Modern Tennis

Keywords: finite Markov chain modelling, state transitions modelling, tennis performance indicators, theoretical performance analysis, tactical behaviour

Abstract

Game behaviour in net games or other sports is often captured in the form of discrete performance indicators which represent frequencies or relative frequencies of key behavioural variables. In this regard however, discrete performance indicators are often of low practical relevance as they lack information on the sequence of actions and the underlying interaction of players in a match. Thereby, establishing a connection between performance indicators and sport success also remains an open challenge. In tennis, finite Markov chain modelling based on a transition matrix has shown promise in circumventing these issues. The transition matrix allows the capture of equivalent classes of strokes as a sequence of states with the possibility of transitions between them, basically representing a rally. Furthermore, finite Markov chain modelling enables the determination of the relevance of state transitions regarding performance. Since existing state transition models may be outdated a major aim of the current study was to establish a newly designed transition matrix which is representative of the game structure of tennis. The sufficiency of the transition matrix as a descriptive tool was demonstrated using actual match data. Furthermore, the relevance of selected state transitions was determined using finite Markov chain modelling. Match data and emerging values for performance relevance were analysed with regard to the influencing factors of sex and court surface. This revealed only minor differences regarding both factors, specifically indicating a convergence of game structure in men and women.

References

Blanca Mena, M. J., Alarcón Postigo, R., Arnau Gras, J., Bono Cabré, R., & Bendayan, R. (2017). Non-normal data: Is ANOVA still a valid option?. Psicothema, 29(4), 552-557.

Bortz, J., & Schuster, C. (2011). Statistik für Human-und Sozialwissenschaftler: Limitierte Sonderausgabe: Springer-Verlag.

Gillet, E., Leroy, D., Thouvarecq, R., & Stein, J.-F. (2009). A Notational Analysis of Elite Tennis Serve and Serve-Return Strategies on Slow Surface. The Journal of Strength & Conditioning Research, 23(2), 532-539. doi:10.1519/JSC.0b013e31818efe29

Haake, S. J., Allen, T. B., Choppin, S., & Goodwill, S. R. (2007). The Evolution of the Tennis Racket and its Effect on Serve Speed. Paper presented at the Tennis Science and Technology 3, London.

Herzog, M. H., Francis, G., & Clarke, A. (2019). Understanding Statistics and Experimental Design: How to Not Lie with Statistics: Springer Nature.

Hughes, M., & Bartlett, R. (2002). The use of performance indicators in performance analysis. Journal of Sports Sciences, 20, 739-754. doi:10.1080/026404102320675602

Kemeny, J. G., & Snell, J. L. (1976). Markov chains: Springer-Verlag, New York.

Lames, M. (1991). Leistungsdiagnostik durch Computersimulation: Ein Beitrag zur Theorie der Sportspiele am Beispiel Tennis: Deutsch.

Lames, M. (1994). Systematische Spielbeobachtung: Philippka.

Lames, M. (2020). Markov Chian Modelling And Simulations In Net Games. In C. Ley & Y. Dominicy (Eds.), Science Meets Sports: When Statistics Are More Than Numbers (pp. 147-170): Cambridge Scholars Publisher.

Lames, M., Hohmann, A., Daum, M., Dierks, B., Fröhner, B., Seidel, I., & Wichmann, E. (1997). Top oder Flop: Die erfassung der Spielleistung in den Mannschaftssportspielen. Sport-Spiel-Forschung Zwischen Trainerbank und Lehrstuhl, 101-117.

Lames, M., & McGarry, T. (2007). On the search for reliable performance indicators in game sports. International Journal of Performance Analysis in Sport, 7(1), 62-79.

Liu, T., & Hohmann, A. (2013). Applying the Markov Chain Theory to Analyze the Attacking Actions between FC Barcelona and Manchester United in the European Champions League Finale. International Journal of Sports Science and Engineering, 7(2), 79-86.

Ma, S. M., Liu, C. C., Tan, Y., & Ma, S. C. (2013). Winning matches in Grand Slam men's singles: an analysis of player performance-related variables from 1991 to 2008. J Sports Sci, 31(11), 1147-1155. doi:10.1080/02640414.2013.775472

McGarry, T. (2009). Applied and theoretical perspectives of performance analysis in sport: Scientific issues and challenges. International Journal of Performance Analysis in Sport, 9(1), 128-140.

McGarry, T., & Franks, I. M. (1996). In search of invariant athletic behaviour in sport: an example from championship squash match-play. J Sports Sci, 14(5), 445-456. doi:10.1080/02640419608727730

Meyer, D., Forbes, D., & Clarke, S. R. (2006). Statistical analysis of notational AFL data using continuous time Markov Chains. Journal of sports science & medicine, 5(4), 525.

Miller, S. (2006). Modern tennis rackets, balls, and surfaces. Br J Sports Med, 40(5), 401-405. doi:10.1136/bjsm.2005.023283

O’Donoghue, P. (2013). Sports Performance Profiling. In Routledge handbook of sports performance analysis: Routledge.

O’Donoghue, P., & Ballantyne, A. (2004). The impact of speed of service in Grand Slam singles tennis. In Science and racket sports III (pp. 223-229): Routledge.

O’Donoghue, P., & Brown, E. (2008). The Importance of Service in Grand Slam Singles Tennis. International Journal of Performance Analysis in Sport, 8(3), 70-78. doi:10.1080/24748668.2008.11868449

O’Donoghue, P., & Ingram, B. (2001). A notational analysis of elite tennis strategy. Journal of Sports Sciences, 19(2), 107-115. doi:10.1080/026404101300036299

Pfeiffer, M., Zhang, H., & Hohmann, A. (2010). A Markov chain model of elite table tennis competition. International Journal of Sports Science & Coaching, 5(2), 205-222.

Read, B., & Edwards, P. (1992). Teaching Children to Play Games. Leeds: White Line Publishing

Reid, M., Morgan, S., & Whiteside, D. (2016). Matchplay characteristics of Grand Slam tennis: implications for training and conditioning. J Sports Sci, 34(19), 1791-1798. doi:10.1080/02640414.2016.1139161

Sampaio, J., & Leite, N. (2013). Performance indicators in game sports. In T. McGarry, P. O’Donoghue, & J. Sampaio (Eds.), Routledge handbook of sports performance analysis (pp. 115-126): Routledge.

Vergne, N. (2008). Drifting Markov models with polynomial drift and applications to DNA sequences. Statistical applications in genetics and molecular biology, 7(1).

Vygen-Bonnet, S., Koch, J., Bogdan, C., Harder, T., Heininger, U., Kling, K., . . . Mertens, T. (2021). Beschluss der STIKO zur 1. Aktualisierung der COVID-19-Impfempfehlung und die dazugehörige wissenschaftliche Begründung.

Wang, J., Zhao, K., Deng, D., Cao, A., Xie, X., Zhou, Z., . . . Wu, Y. (2020). Tac-Simur: Tactic-based Simulative Visual Analytics of Table Tennis. IEEE transactions on visualization and computer graphics, 26(1), 407-417. doi:10.1109/TVCG.2019.2934630

Wenninger, S., & Lames, M. (2016). Performance analysis in table tennis-stochastic simulation by numerical derivation. International Journal of Computer Science in Sport, 15(1), 22-36.

Published
2023-08-08
How to Cite
Rothe, F., & Lames, M. (2023). Markov-chain Modelling and Simulative Assessment of the Impact of Selected Tactical Behaviours in Modern Tennis. International Journal of Racket Sports Science, 5(1). Retrieved from https://journal.racketsportscience.org/index.php/ijrss/article/view/81