Probability of Winning at Tennis I. Theory and Data

  title={Probability of Winning at Tennis I. Theory and Data},
  author={P. Newton and J. Keller},
  journal={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
Rule of Tangent for Win-By-Two Games
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
  • M. Sim, D. Choi
  • 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
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On the winning probabilities and mean durations of volleyball
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
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
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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


An Analysis of the Game of Tennis
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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
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
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
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?
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
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