# Probability of Winning at Tennis I. Theory and Data

```@article{Newton2005ProbabilityOW,
title={Probability of Winning at Tennis I. Theory and Data},
author={P. Newton and J. Keller},
journal={Studies in Applied Mathematics},
year={2005},
volume={114},
pages={241-269}
}```
• Published 2005
• Mathematics
• Studies in Applied Mathematics
The probability of winning a game, a set, and a match in tennis are computed, based on each player's probability of winning a point on serve, which we assume are independent identically distributed (iid) random variables. Both two out of three and three out of five set matches are considered, allowing a 13-point tiebreaker in each set, if necessary. As a by-product of these formulas, we give an explicit proof that the probability of winning a set, and hence a match, is independent of which… Expand
41 Citations

#### Figures and Tables from this paper

Rule of Tangent for Win-By-Two Games
• Mathematics
• 2011
Our study of win-by-two tie games is motivated by a famous 2010 Wimbledon tennis match whose final set was decided by the improbable score of 70-68. We introduce a trigonometric interpretation of theExpand
A point-based Bayesian hierarchical model to predict the outcome of tennis matches
Abstract A well-established assumption in tennis is that point outcomes on each player’s serve in a match are independent and identically distributed (iid). With this assumption, it is enough toExpand
The Winning Probability of a Game and the Importance of Points in Tennis Matches
• Computer Science, Medicine
• Research quarterly for exercise and sport
• 2019
A stochastic model of a discrete-time Markov chain (DTMC) that fits well with a dataset of professional playing records and reveals interesting properties in professional tennis matches is built. Expand
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.Expand
On the winning probabilities and mean durations of volleyball
• 2014
In this paper we consider the volleyball under the assumption that the probability of winning a single rally is independent of the other rallies and constant during the game. Fixing two parametersExpand
Monte Carlo Tennis | SIAM Review | Vol. 48, No. 4 | Society for Industrial and Applied Mathematics
• 2006
The probability of winning a game, set, match, or single elimination tournament in tennis is computed using Monte Carlo simulations based on each player’s probability of winning a point on serve,Expand
Monte Carlo Tennis: A Stochastic Markov Chain Model
• 2009
We develop a stochastic Markov chain model to obtain the probability density function (pdf) for a player to win a match in tennis. By analyzing both individual player and 'field' data (all playersExpand
Probability of winning and match length in Tiebreak Ten tennis
• Computer Science
• 2019
ABSTRACT New formats of tennis have been developed to make matches more exciting and unpredictable than the traditional format of the game. The purpose of the current investigation was to compare theExpand
A common-opponent stochastic model for predicting the outcome of professional tennis matches
• Computer Science, Mathematics
• Comput. Math. Appl.
• 2012
A hierarchical Markov model is presented which yields a pre-play estimate of the probability of each player winning a professional singles tennis match and provides a fair basis of comparison between players by analysing match statistics for opponents that both players have encountered in the past. Expand
The probability of winning break points in Grand Slam men's singles tennis
• Mathematics
• 2012
Abstract The probability of winning games of tennis has been modelled in terms of the probability of the server winning an individual point. These models are based on the assumptions of stationarityExpand

#### References

SHOWING 1-10 OF 30 REFERENCES
An Analysis of the Game of Tennis
• Psychology
• 1974
The popularity of the game of tennis as a spectator sport was demonstrated recently by the "Match of the Century" between Billy Jean King and Bobby Riggs. As with other sports, the rules by whichExpand
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 ofExpand
The effect of new balls in tennis: four years at Wimbledon
• Mathematics
• 1999
We analyse two often-heard hypotheses concerning tennis-balls. The first is: are new balls an advantage to the server? They are not (at least not at Wimbledon). However, they do affect the way thatExpand
Are Points in Tennis Independent and Identically Distributed? Evidence From a Dynamic Binary Panel Data Model
• Mathematics, Medicine
• 2001
It is shown that points are neither independent nor identically distributed: winning the previous point has a positive effect on winning the current point, and at “important” points it is more difficult for the server to win the point than at less important points. Expand
The final set in a tennis match: Four years at Wimbledon
• Mathematics
• 1999
We consider the 'final' (deciding) set in a tennis match. We examine whether it is true that the chances for both players to win the match are equal at the beginning of the final set, even thoughExpand
Symmetric Sequential Analysis: The Efficiencies of Sports Scoring Systems (With Particular Reference to Those of Tennis)
SUMMARY Bernoulli-type models are adopted for the sequence of contested points between two players (or teams). In bipoints, there are two types of point- "A serving" and "B serving"-necessary for aExpand
Heavy Defeats in Tennis: Psychological Momentum or Random Effect?
• Computer Science
• 1997
If PM is a factor, the authors are talking about a true dependcncy structure for the probability of winning a set, not merely an updated estimate of an unchanging probability based on additional data. Expand
Optimal strategy at decision points in singles squash.
• J. Renick
• Computer Science, Medicine
• Research quarterly
• 1976
The optimal Strategy at decision points in the singles game of squash played by North American rules is specific to the scoring system and, the tie point at which the decision must be made, providing the best possibility of winning a game. Expand
Comparison of Scoring Systems in Two-Sided Competitions
• J. Kingston
• Computer Science, Mathematics
• J. Comb. Theory, Ser. A
• 1976
It is shown that the probability of winning is independent of whether the two contestants alternate this advantage or whether the contestant who wins a part of the competition is permitted to have this advantage for the next part. Expand
Games of Two Players
• Computer Science
• 1971
Probability models on games involving two opposing players or teams are discussed with particular emphasis on the relative probability of a server in a play, and several comments and suggestions are made regarding their game rules. Expand