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 the odds of winning points and games in tennis when serving from deuce. We place this result in the more general setting of a gambler’s ruin problem and also propose a performance measure to quantify the serving and receiving skill of one player relative to another. Then we extend the analysis to table tennis and volleyball. These latter games are similar to tennis in that the winner must obtain a certain minimum score while leading by two points, but they differ in their determination of which player serves a given rally and in whether a point is awarded to the receiver for winning a rally. We quantify the impact of these differences on the outcomes of games, assuming that the probability for a player to win a single point does not change during a game. We also apply a Markov chain analysis to arrive at our earlier results for tennis and to calculate the expected length of a game after reaching deuce. Finally, we develop the idea of “equivalent games” so that the analysis can be carried out using only the probability of winning a point (that is, without regard for the question of which player is serving).
©2012 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
Articles in the same Issue
- Letter from the Editor
- The Next Step
- Article
- A Hierarchical Bayesian Variable Selection Approach to Major League Baseball Hitting Metrics
- Ups and Downs: Team Performance in Best-of-Seven Playoff Series
- The Penalty Shot/Optional Minor Choice in Ice Hockey
- Using Local Correlation to Explain Success in Baseball
- Exploring Competition Performance in Decathlon Using Semi-Parametric Latent Variable Models
- Going for the Green: A Simulation Study of Qualifying Success Probabilities in Professional Golf
- Rule of Tangent for Win-By-Two Games
- Effect of Differences in Kicking Legs, Kick Directions, and Kick Skill on Kicking Accuracy in Soccer Players
- The Methodology of Officially Recognized International Sports Rating Systems
- Scoring Strategies for the Underdog: A General, Quantitative Method for Determining Optimal Sports Strategies
- Using Tree Ensembles to Analyze National Baseball Hall of Fame Voting Patterns: An Application to Discrimination in BBWAA Voting
- An Estimate of How Hitting, Pitching, Fielding, and Basestealing Impact Team Winning Percentages in Baseball
Articles in the same Issue
- Letter from the Editor
- The Next Step
- Article
- A Hierarchical Bayesian Variable Selection Approach to Major League Baseball Hitting Metrics
- Ups and Downs: Team Performance in Best-of-Seven Playoff Series
- The Penalty Shot/Optional Minor Choice in Ice Hockey
- Using Local Correlation to Explain Success in Baseball
- Exploring Competition Performance in Decathlon Using Semi-Parametric Latent Variable Models
- Going for the Green: A Simulation Study of Qualifying Success Probabilities in Professional Golf
- Rule of Tangent for Win-By-Two Games
- Effect of Differences in Kicking Legs, Kick Directions, and Kick Skill on Kicking Accuracy in Soccer Players
- The Methodology of Officially Recognized International Sports Rating Systems
- Scoring Strategies for the Underdog: A General, Quantitative Method for Determining Optimal Sports Strategies
- Using Tree Ensembles to Analyze National Baseball Hall of Fame Voting Patterns: An Application to Discrimination in BBWAA Voting
- An Estimate of How Hitting, Pitching, Fielding, and Basestealing Impact Team Winning Percentages in Baseball
