Probability Formulas and Statistical Analysis in Tennis

In this paper an expression for the probability of winning a game in a tennis match is derived under the assumption that the outcome of each point is identically and independently distributed. Important properties of the formula are evaluated and presented pictorially. The accuracy of this formula is tested by comparing observed proportions against predicted values using data from the 2007 Wimbledon Tennis Championships. We also derive expressions for the probability of several other milestones in a tennis match including winning a tiebreaker, winning a set, winning a match, and recovering from a break of serve down to win a set. The resulting "tennis formulas" are used to evaluate the implications of possible rule changes, to demonstrate how broadcasts of tennis matches could be made more interesting and informative, and to potentially improve a player's chance of winning a match.