Abstract: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 mat… Show more
“…However, this method does not allow for the distinction or impact (in itself) of being the home or away team, and further complicates the interpretation of the analysis with one variable for each team. Other data structure examples include the use of only "differentials" (HT minus AT for all variables), given the suggestion that this adequately captures the impact of each variable (O'Malley, 2008); this method has been used in various sporting investigations (Delen, Cogdell, & Kasap, 2012;Robertson, Back, & Bartlett, 2016). However, this approach does not allow for the absolute nature of each factor to be explicitly investigated, nor does it allow the use of categorical variables for which no advantage can be assigned (e.g.…”
In Australian football (AF), few studies have assessed combinations of pre- game factors and their relation to game outcomes (win/loss) in multivariable analyses. Further, previous research has mostly been confined to association-based linear approaches and post-game prediction, with limited assessment of predictive machine learning (ML) models in a pre-game setting. Therefore, our aim was to use ML techniques to predict game outcomes and produce a hierarchy of important (win/loss) variables. A total of 152 variables (79 absolute and 73 differentials) were used from the 2013–2018 Australian Football League (AFL) seasons. Various ML models were trained (cross-validation) on the 2013–2017 seasons with the–2018 season used as an independent test set. Model performance varied (66.5-73.3% test set accuracy), although the best model (glmnet – 73.3%) rivalled bookmaker predictions in the same period (70.9%). The glmnet model revealed measures of team quality (a player-based rating and a team-based) in their relative form as the most important variables for prediction. Models that contained in-built feature selection or could model non-linear relationships generally performed better. These findings show that AFL game outcomes can be predicted using ML methods and provide a hierarchy of predictors that maximize the chance of winning.
“…However, this method does not allow for the distinction or impact (in itself) of being the home or away team, and further complicates the interpretation of the analysis with one variable for each team. Other data structure examples include the use of only "differentials" (HT minus AT for all variables), given the suggestion that this adequately captures the impact of each variable (O'Malley, 2008); this method has been used in various sporting investigations (Delen, Cogdell, & Kasap, 2012;Robertson, Back, & Bartlett, 2016). However, this approach does not allow for the absolute nature of each factor to be explicitly investigated, nor does it allow the use of categorical variables for which no advantage can be assigned (e.g.…”
In Australian football (AF), few studies have assessed combinations of pre- game factors and their relation to game outcomes (win/loss) in multivariable analyses. Further, previous research has mostly been confined to association-based linear approaches and post-game prediction, with limited assessment of predictive machine learning (ML) models in a pre-game setting. Therefore, our aim was to use ML techniques to predict game outcomes and produce a hierarchy of important (win/loss) variables. A total of 152 variables (79 absolute and 73 differentials) were used from the 2013–2018 Australian Football League (AFL) seasons. Various ML models were trained (cross-validation) on the 2013–2017 seasons with the–2018 season used as an independent test set. Model performance varied (66.5-73.3% test set accuracy), although the best model (glmnet – 73.3%) rivalled bookmaker predictions in the same period (70.9%). The glmnet model revealed measures of team quality (a player-based rating and a team-based) in their relative form as the most important variables for prediction. Models that contained in-built feature selection or could model non-linear relationships generally performed better. These findings show that AFL game outcomes can be predicted using ML methods and provide a hierarchy of predictors that maximize the chance of winning.
“…In the Markov chain method, we rely on the explicit structure of the data-generating process in tennis. In tennis, points are linked to games, games to sets, and sets to matches; thus, a match can be modeled as a binary Markov chain (Newton & Aslam, 2009;O'Malley, 2008). 5…”
This paper empirically examines how suspense and surprise explain demand for entertainment. We use the Wimbledon Championships tennis tournament as a natural laboratory.This setting allows us to both operationalize suspense and surprise using the audience's belief about the final outcome of the match and observe of the demand for live entertainment using JEL Classification: D83, L82, L83
“…The O'Malley tennis formulae 2,3 allow us to calculate the probability that a particular player wins a game , a set, or the whole match , given only the two players’ probabilities of winning a point on serve (which are assumed to be fixed throughout the match).For instance, the O'Malley formula for the probability of the server winning a game (starting at 0–0) iswhere p is the server's point‐win probability. As an illustration, if p = 0.63, then G ( p ) is approximately 0.795; if p = 0.66, then G ( p ) is approximately 0.846.O'Malley's set‐win and match‐win formulae are much more complicated to write down than the game‐win formula above, but they follow the same underlying principle: namely, the only inputs required for the calculation are the two players’ point‐win probabilities.…”
Section: Setting the Scenementioning
confidence: 99%
“…The O'Malley tennis formulae 2,3 allow us to calculate the probability that a particular player wins a game , a set, or the whole match , given only the two players’ probabilities of winning a point on serve (which are assumed to be fixed throughout the match).…”
Section: Setting the Scenementioning
confidence: 99%
“…What is the best way to go about computing these match‐win probabilities? Rather than build up the calculation completely from scratch, the tidiest approach is to apply the celebrated “tennis formulae” published in 2008 by O'Malley (see box above) 2 . By feeding the values of p A and p B into the relevant O'Malley formulae, we can determine not only the players’ win probabilities at the start of the match, but their win probabilities in every possible match scenario.…”
Are some professional tennis players really taking “backhanders” to throw matches? Tim Paulden explains how spotting anomalous movements in the betting markets can help shine a light into the murky world of tennis match‐fixing
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
