The Importance of the Serve in Winning Points in Tennis: A Bayesian Analysis Using Data for the Two winners of the 2019 French Open Singles

Borooah, Vani (2022): The Importance of the Serve in Winning Points in Tennis: A Bayesian Analysis Using Data for the Two winners of the 2019 French Open Singles. Published in: Behavioural Sports Economics: A Research Companion No. H. Altman, M. Altman, and B. Torgler (ed), Routledge (2022): pp. 186-198.

Abstract

The Reverend Thomas Bayes, an 18th century Presbyterian minister, proved what, arguably, is the most important theorem in statistics. Its importance stems from its capacity to transform the answer to a question relating to the likelihood that if a point is won, it will have been preceded by a first service (the probability that if the theory is true, the data will be observed) to an answer to a more interesting and relevant question: if the first serve is good, what is the probability that the point will be won (the probability that if the data is observed, the theory will be true)? Empirical flesh is put on Bayes’ theorem by studying the performance of the winners of the men’s and women’s singles titles at the 2019 French Open: Rafael Nadal and Ashleigh Barty. Whatever the prior likelihood that they would win a point on their service game, this had to be revised upward for both players if the data showed that their first serve was ‘good’ and had to revised downward if the point required that they serve again. On the assumption that the prior probability was 60%, this then allows the analyst to deduce that the probability of winning a point on the first service was 65.9% for Barty and 73.8% for Nadal. Similarly, it could be deduced that the probability of winning a point on the second service was 34.1% for Barty and 26.2% for Nadal. The contribution of the paper lies in applying Bayes’ Theorem to show how, in service games in tennis, evidence can be turned into insight.

• Item Type: MPRA Paper
• Language: English
• Keywords: Bayesian Probability; Tennis; Service; Points
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General; Z - Other Special Topics > Z1 - Cultural Economics ; Economic Sociology ; Economic Anthropology > Z10 - General

References

Aitken, C. (1996), “Lies, Damned Lies, and Expert Witnesses”, Mathematics Today, 32: 76–80.

Cross R, and Pollard G. (2009), “Grand Slam Men's Singles Tennis: Serve speeds and Other Related Data, Coaching & Sport Science Review, 16: :8-10.

Cui, Y., Gomez, M-A, Goncalves, B., Sampaio, J. (2018), “Performance Profiles of Professional Female Tennis Players in Grand Slam Finals, PLOS ONE, 13: 1-18.

Furlong J. (1995), “The Service in Lawn Tennis: How important is it?”, in T. Reilly, M. Hughes, and M. Lees (edited), Science and Racket Sports, London: Taylor and Francis, 266-71.

Hughes M. and Clarke S. (1995), Surface Effect on Elite Tennis Strategy, in T. Reilly, M. Hughes, and M. Lees (edited), Science and Racket Sports , London: Taylor and Francis, 272-78.

Matthews, R. (2005), 25 Big Ideas: The Science That is Changing the World, Oxford: One World.

Moss, B. and O'Donoghue, P. (2015), “Momentum in US Open Men's Singles Tennis”. International Journal of Performance Analysis in Sport. 15: 884-96.

O’Donoghue P. and Ingram, B. (2001), “A Notational Analysis of Elite Tennis Strategy. Journal of Sports Sciences, 19: 107-115.

O’Donoghue P, Ballantyne A (2004), “The impact of speed of service in Grand Slam singles tennis”, in Science and Racket Sports III in A.Lees, J. Kahn, and I. Maynard (edited), Science and Racket Sports III, London: Routledge179-84.

O'Donoghue, P. Brown, E. (2008), “The Importance of Service in Grand Slam Singles Tennis”, International Journal of Performance Analysis in Sport, 8:70-78.

O'Donoghue, P. Brown, E. (2009), “Sequences of Service points and the Misperception of Momentum in Elite Tennis”, International Journal of Performance Analysis in Sport, 9:113-27.

Thompson, W.C. and Schumann, E.L. (1987), “Interpretation of Statistical Evidence in Criminal Trials: The Prosector’s Fallacy and the Defense Attorney’s Fallacy”, Law and Human Behavior, 11: 167–187.

Unierzyski, P. and Wieczorek (2004), “Comparison of Tactical Solutions and Game Patterns in the Finals of Two Grand Slam Tournaments”, in Science and Racket Sports III in A.Lees, J. Kahn, and I. Maynard (edited), Science and Racket Sports III, London: Routledge,169-74.

Zackrisson, S., Andersson, I., Janzon, L., Manjer, J. and Garne, J.P. (2006), “Rate of Over-Diagnosis of Breast Cancer 15 Years after End of Malmo Mamographic Screening”, British Medical Journal, 33: 689–692.