The importance of the serve in winning points in tennis

Abstract

The Reverend Thomas Bayes, an 18 th 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.