What is the best serving strategy? - Pollard, G. (Medicine and Science in Tennis, 2008)
A player can get a high percentage of first serves into court by taking a low risk on first service, or can get a lower percentage of first serves into court (with a higher probability of winning the resultant point if the serve goes into court) by taking a higher risk on service. This characteristic also applies to second serves. In this paper the relationship between the risks taken (on first and second serves) and the probability of winning the point is considered. Using Wimbledon Championships Men`s Singles data, it is shown that the relationship between the risk taken on a serve and the probability of winning that point (if the serve goes into court), is typically not a linear one. It appears that for most players quadratic relationships are needed to model this type of data. Finally, some practical suggestions are made as to where the server might best focus his/her attention on how to increase the probability of winning a point on service.