Incentives in Best of N Contests: Quasi-Simpson’s Paradox in Tennis

Wright, Benjamin; Rodenberg, Ryan M.; Sackmann, Jeff

doi:10.1080/24748668.2013.11868689

Cited by 11 publications

(12 citation statements)

References 2 publications

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“…Figure 11(b) shows that for the full range of probabilities of Player A winning a point on serve from 0.6 to 1.0, the probability of Player A winning the match is lower in Fast4 tennis than in traditional tennis. One of the explanations for the greater chance of an upset in Fast4 tennis is the greater chance of Simpson's Paradox matches (Wright et al, 2013) where one player wins the match despite winning a minority of the points in the match. Consider a traditional best of 5 sets match where a player wins 0-6, 0-6, 7-6, 7-6, 7-6 where each game they lose is lost to love (0-4), each game that is won requires one deuce (5-3) and the three tiebreakers are won 7-5.…”

Section: Discussionmentioning

confidence: 99%

“…It is possible that superior players can win Simpson's Paradox matches against inferior opponents. However, Simpson's Paradox matches are more likely to be upsets than matches won by the superior player (Wright et al, 2013). Fast4 tennis can involve Simpson's Paradox matches where matches can be won with an even lower percentage of points than in traditional tennis.…”

Section: Discussionmentioning

confidence: 99%

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Probabilistic models comparing Fast4 and traditional tennis

Simmonds

O’Donoghue

2018

International Journal of Computer Science in Sport

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Tennis matches are hierarchies made up of sets containing games which, in turn, contain points. Traditional tennis games and tiebreakers could theoretically be infinite in length because a player needs to be at least 2 points ahead of the opponent to win. Fast4 tennis is a newer format of tennis that has been used at a number of levels of the sport including professional tennis where it has been used in Next Generation Finals events since 2017. The purpose of the current investigation is to compare the traditional tennis format to Fast4 tennis in terms of the probability of different players winning matches and the duration of matches. Probabilistic models of Fast4 tennis games and tiebreakers were developed. These models allowed the probability of winning games and tiebreakers to be compared between the two formats of tennis for a range of probabilities of players winning points. The models were then used within a series of simulations to determine the probability of winning sets and matches as well as the durations of games, tiebreakers, sets and matches in the two formats. Each component of the two formats of tennis was simulated 100,000 times revealing a reduced impact of serve, greater chance of upsets and shorter matches in Fast 4 tennis than in traditional tennis. The probability of players of differing abilities winning matches as well as the duration of tennis matches should be considered by those making decisions on the format of matches to be applied in tennis tournaments as well as by those preparing to compete in such tournaments.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Probabilistic models comparing Fast4 and traditional tennis

Simmonds

O’Donoghue

2018

International Journal of Computer Science in Sport

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“…The asymmetric importance in points has also drawn academic attention. Wright, Rodenberg, and Sackmann (2013) report that 5% of matches are won by players who won fewer points than their opponents in the Association of Tennis Professionals (ATP) World Tour and Grand Slams between 1991. Varshney (2014 analyzes the rather scarce critical points that largely determine the winners of matches.…”

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confidence: 99%

Relationship Between Parent and Child Physical Activity Using Novel Acceleration Metrics

Donnelly

Buchan

McLellan

et al. 2020

Research Quarterly for Exercise and Sport

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Purpose: This study builds a stochastic model of a discrete-time Markov chain (DTMC) that fits well with a dataset of professional playing records. Methods: The point-by-point dataset of Men's single matches played in the Association of Tennis Professionals (ATP) tour from 2011 to 2015 is analyzed. A long-debated assumption on the iid-ness in the point winning probability of the server is statistically tested. A DTMC model is then developed to analyze the dataset further. Results: The statistical test results indicate that the identicality of point winning probabilities is not a valid assumption. For example, the server's point winning probability from scores 40:0, 30:15, 15:30, and 0:40 are significantly different. On the other hand, the independence is a generally valid assumption except for 40:15 where who won the previous point influences the point winning probability. Game winning probabilities and the importance of each point in winning a game are analyzed using the DTMC model by court surfaces and player groups of the different levels of serve effectiveness. Conclusion: Extensive empirical validation concludes unsealed debates over the stochastic models for tennis. The presented results reveal interesting properties in professional tennis matches.

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“…

Due to its unique scoring system, in tennis it is possible to win a match with fewer points or fewer games than the opponent. This scoring quirk has been called Quasi-Simpson paradox (QSP) and has been analyzed by Wright et al (2013) for the years 1990-2011. This work follows up that of Wright et al (2013) and extends it in that: i) the QSP is studied for different, and more recent, years (2012-2017), allowing a time comparison; ii) QSP is considered with respect to games as well as to points; iii) it considers both men and women; iv) the significance of the results is verified by means of statistical tests; v) it analyzes also the difference of won points, between the winner and the loser, when QSP occurs; vi) QSP is studied also through Monte Carlo simulations allowing to analyze QSP excluding any possible players' strategy.

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confidence: 99%

Winning tennis matches with fewer points or games than the opponent

Lisi

Grigoletto

Canesso

2019

JSA

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Due to its unique scoring system, in tennis it is possible to win a match with fewer points or fewer games than the opponent. This scoring quirk has been called Quasi-Simpson paradox (QSP) and has been analyzed by Wright et al. (2013) for the years 1990-2011. This work follows up that of Wright et al. (2013) and extends it in that: i) the QSP is studied for different, and more recent, years (2012-2017), allowing a time comparison; ii) QSP is considered with respect to games as well as to points; iii) it considers both men and women; iv) the significance of the results is verified by means of statistical tests; v) it analyzes also the difference of won points, between the winner and the loser, when QSP occurs; vi) QSP is studied also through Monte Carlo simulations allowing to analyze QSP excluding any possible players' strategy. The simulative approach allows us to solve the seeming "Federer paradox".

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Incentives in Best of N Contests: Quasi-Simpson’s Paradox in Tennis

Cited by 11 publications

References 2 publications

Probabilistic models comparing Fast4 and traditional tennis

Probabilistic models comparing Fast4 and traditional tennis

Relationship Between Parent and Child Physical Activity Using Novel Acceleration Metrics

Winning tennis matches with fewer points or games than the opponent

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