Probability Models for Tennis Scoring Systems

Riddle, Lawrence H.

doi:10.2307/2347494

Cited by 23 publications

(14 citation statements)

References 7 publications

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“…Early articles of this nature considered the sports of tennis (Kemeny and Snell, 1960), squash (Wright, 1988) and one-day cricket (Clarke, 1988). Tennis was also the subject of several extended models, including those by Riddle (1988), Sadovskiĭ and Sadovskiĭ (1993) and Spanias and Knottenbelt (2013), and variations specifically aimed at predicting match outcomes using combined player statistics (Barnett and Clarke, 2005) and common-opponent models (Knottenbelt et al, 2012). Other sports analysed by means of discrete-time Markov chains include Australian football (Clarke and Norman, 1998), curling (Kostuk and Willoughby, 1999), badminton (Percy, 2009), table tennis (Pfeiffer et al, 2010) and golf (Maher, 2013).…”

Section: Markov Chainsmentioning

confidence: 99%

Strategy selection and outcome prediction in sport using dynamic learning for stochastic processes

Percy

2015

Journal of the Operational Research Society

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Stochastic processes are natural models for the progression of many individual and team sports. Such models have been applied successfully to select strategies and to predict outcomes in the context of games, tournaments and leagues. This information is useful to participants and gamblers, who often need to make decisions while the sports are in progress. In order to apply these models, much of the published research uses parameters estimated from historical data, thereby ignoring the uncertainty of the parameter values and the most relevant information that arises during competition. In this paper, we investigate candidate stochastic processes for familiar sporting applications that include cricket, football and badminton, reviewing existing models and offering some new suggestions. We then consider how to model parameter uncertainty with prior and posterior distributions, how to update these distributions dynamically during competition and how to use these results to make optimal decisions. Finally, we combine these ideas in a case study aimed at predicting the winners of next year's University Boat Race.

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Section: Markov Chainsmentioning

confidence: 99%

Strategy selection and outcome prediction in sport using dynamic learning for stochastic processes

Percy

2015

Journal of the Operational Research Society

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“…3 Examples are Riddle (1988), Bukiet, Harold and Palacios (1998), and Hirotsu and Wright (2002). 4 Proper utility functions require that utility be increasing in V at a diminishing rate, or that and .…”

Section: A Portfolio Model Of Play Selectionmentioning

confidence: 99%

The Passing Premium Puzzle Revisited

Rockerbie¹

2008

Journal of Quantitative Analysis in Sports

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“…Whereas the scoring of games within a set, sets within a match, and tiebreakers is purely numeric, the scoring within a service-game features nonnumerical terms that originated in France as far back as the 13 th century (Riddle, 1988). A player who has won one, two, and three points has score 15, 30, and 40 respectively (the numbers are thought to be based on the face value of medieval French coins (Liu, 2001)).…”

Section: Scoring a Tennis Matchmentioning

confidence: 99%

“…Liu (2001) used finite Markov chains and results for random walks to derive equivalent formulas. Notable earlier works include Riddle (1988) on probability models for various alternative tiebreaker scoring systems, and Morris (1977) on determining which point is the most important in a tennis match.…”

Section: Introductionmentioning

confidence: 99%

Probability Formulas and Statistical Analysis in Tennis

O’Malley¹

2008

Journal of Quantitative Analysis in Sports

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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.

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Probability Models for Tennis Scoring Systems

Cited by 23 publications

References 7 publications

Strategy selection and outcome prediction in sport using dynamic learning for stochastic processes

Strategy selection and outcome prediction in sport using dynamic learning for stochastic processes

The Passing Premium Puzzle Revisited

Probability Formulas and Statistical Analysis in Tennis

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