The Conditional Probability of Winning Games of Tennis

Croucher, John S.

doi:10.1080/02701367.1986.10605384

Cited by 23 publications

(28 citation statements)

References 9 publications

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“…Forexample, for individual sports Kenyon and Schutz (1970) used stochastic models to examine the pattern of outcomes (scores) for golfers over a summer season, and Croucher (1986) analyzed the conditional probability of winning a game of tennis. Others have studied the sequential patterns ofindividual play within a team game; Gilovich, Vallone, and Tversky (1985) investigated streak shooting in the NBA, and Gould (1989) reexamined DiMaggio's famous 5&game hitting streak.…”

Section: Roes: September 1992mentioning

confidence: 99%

Transition Play in Team Performance of Volleyball: A Log-Linear Analysis

Eom¹,

Schutz²

1992

Research Quarterly for Exercise and Sport

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The purpose of this study was to develop and test a method to analyze and evaluate sequential skill performances in a team sport. An on-line computerized system was developed to record and summarize the sequential skill performances in volleyball. Seventy-two sample games from the third Federation of International Volleyball Cup men's competition were videotaped and grouped into two categories according to the final team standing and game outcome. Log-linear procedures were used to investigate the nature and degree of the relationship in the first-order (pass-to-set, set-to-spike) and second-order (pass-to-spike) transition plays. Results showed that there was a significant dependency in both the first-order and second-order transition plays, indicating that the outcome of a skill performance is highly influenced by the quality of a preceding skill performance. In addition, the pattern of the transition plays was stable and consistent, regardless of the classification status: Game Outcome, Team Standing, or Transition Process. The methodology and subsequent results provide valuable aids for a thorough understanding of the characteristics of transition plays in volleyball. In addition, the concept of sequential performance analysis may serve as an example for sport scientists in investigating probabilistic patterns of motor performance.

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Section: Roes: September 1992mentioning

confidence: 99%

Transition Play in Team Performance of Volleyball: A Log-Linear Analysis

Eom¹,

Schutz²

1992

Research Quarterly for Exercise and Sport

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“…and other factors including gender and surface would suggest that the assumption ofindependence may be tenuous in some singles events. The importance of the assumption of independence is that mathematical models of the probability of winning games of tennis (Carter & Crews, 1974;Croucher, 1982;Fischer, 1980;Schutz, 1970) as well as models of importance of points (Croucher, 1986;Morris, 1977) are based on this assumption. The proportion of points won by the winning player during a match ranged from .45 to .62.…”

Section: Discussionmentioning

confidence: 99%

“…Probablistic models relating to tennis points and their importance to the current game have been proposed (Croucher, 1986;Morris, 1977). Morris (1977) assumed that the probability of the server winning a point, p, was independent of the current score.…”

Section: The Most Important Pointsmentioning

confidence: 99%

“…The expected number of times that the score would occur in a game was given by N . Croucher (1986) provided expressions for the conditional probability of winning a game from each game score in terms of the probability of the server winning a point, p, which was assumed to be independent of score within a game. Croucher's model showed that when pwas greater than .5, scores in which the server was trailing ranked highly, whereas when Pwas less than .5, scores in which the server was leading ranked highly.…”

Section: The Most Important Pointsmentioning

confidence: 99%

“…Mathematical models have been developed to determine the importance ofeach score, given the probability of the serving player winning a point Ps (Croucher, 1986;Morris, 1977). Other mathematical models are used to evaluate the accuracy of different scoring systems.…”

Section: Roes: June 2007mentioning

confidence: 99%

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The Most Important Points in Grand Slam Singles Tennis

O’Donoghue

2001

Research Quarterly for Exercise and Sport

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A computerized data management system was used to enter details of points played in 252 tennis matches from the men's and women's singles events of all four Grand Slam tournaments over a 2-year period. A supplementary data analysis system was developed to determine the proportion of points won by each player on serve at each game score from love all to deuce as well as the proportion of games the player went on to win from each score. Analysis of the 43 matches in which both players served at each score from love all to deuce revealed that the proportion of points won by the server was not significantly influenced by score, F(15, 495) = 0.8, p > .05. A further analysis of the 175 matches consisting of at least 100 points revealed that the proportion of points won by the superior player was not significantly influenced by gender, F(1, 165) = 0.1, p > .05, or surface, F(3, 165) = 0.1, p > .05. However, the proportion of points won when serving was significantly greater in men's singles than women's singles, F(1, 165) = 69.7, p < .001, R2 = .30. Surface also had a significant influence on the proportion of points won when serving, F(3, 165) = 8.1, p < .001, R2 = .13, with a significantly greater proportion of points won when serving by both winning and losing players at Wimbledon than at the Australian and French Opens, p < .05. This suggests that gender and surface should be accounted for when determining the importance of points in Grand Slam tennis.

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An Overview of Operations Research in Tennis

Pollard

Meyer

2011

Wiley Encyclopedia of Operations Research and Management Science

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For nearly 100 years, the equipment and the rules of tennis hardly changed. But since the opening of the game to professionals as well as amateurs in 1968, and the expansion of the game worldwide and in the media, scientific and technological developments have created both problems and opportunities for tennis. This article looks at the use and opportunities for operations research and management science methods to analyze the unique tennis scoring system and the optimal strategies and techniques players might employ. It also considers the use of these methods for the optimization of tennis equipment, including court surface and line calling, and coaching while minimizing medical risk. Efficient tournament management and the accuracy of player ranking are also addressed. This article describes how modern developments allow a scientific approach to measuring and categorizing while suggesting that it may be necessary to limit developments in order to maintain the character of the game.

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The Conditional Probability of Winning Games of Tennis

Cited by 23 publications

References 9 publications

Transition Play in Team Performance of Volleyball: A Log-Linear Analysis

Transition Play in Team Performance of Volleyball: A Log-Linear Analysis

The Most Important Points in Grand Slam Singles Tennis

An Overview of Operations Research in Tennis

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