A mathematical model for evaluating scoring systems with specific reference to tennis.

Abstract The purpose of this investigation was twofold: (a) to examine the feasibility of using mathematical probability models to evaluate scoring systems; and (b) to actually examine, by use of the model, the relative merits of various tennis scoring systems. The hypothesized model was a Markov chain with stationary transition probabilities, the total chain being divided into an initial process and a random walk. By assessing a constant probability p that player A would win a point against his opponent B, and applying probability theory to the initial Markov process and the random walks, the probability that A would win the match was calculated. This was done for each of the various scoring systems. Under the assumption that the “best” player was the one with the highest probability of winning a point, the scoring method which would most frequently result in this best player being declared the winner was ascertained. Further analysis yielded the expected number of points that would be played in a match,...