An Analysis of Classical and Tie‐breaker Tennis

Summary Expressions for the probability that a player wins a game, set or match of classical or tie‐breaker tennis are obtained. Also, expressions for the distribution, the mean and the variance of the number of points in a game, set or match of classical or tie‐breaker tennis are obtained. These results explain the long matches often previously observed in classical tennis between two players each with very effective serves on fast grass‐court surfaces. The methodology used to derive these expressions could be used to obtain corresponding expressions for other “nested‐type” scoring systems. For example, tennis is 3‐nested (game, set, match) whereas squash is only 2‐nested (game, match).