Abstract It is often the goal of sports analysts, coaches, and fans to predict athlete performance over time. Models such as Bradley–Terry and Plackett–Luce measure athlete skill based on results of competitions over time, but have limited predictive strength without making assumptions about the nature of the evolution of athletic skill. Growth curves are often applied in the context of sports to predict future ability, but these curves are too simple to account for complex career trajectories. We propose a non-linear, mixed-effects trajectory to model the ratings as a function of time and other athlete-specific covariates. The mixture of trajectories allows for flexibility in the estimated shape of career trajectories between athletes as well as between sports. We use the fitted trajectories to make predictions of an athlete’s career trajectory through a model of how athlete performance progresses over time in a multi-competitor scenario as an extension to the Plackett–Luce model. We show how this model is useful for predicting the outcome of women’s luge races, as well as show how we can use the model to compare athletes to one another by clustering career trajectories.
{"title":"Plackett–Luce modeling with trajectory models for measuring athlete strength","authors":"Katy McKeough, Mark Glickman","doi":"10.1515/jqas-2021-0034","DOIUrl":"https://doi.org/10.1515/jqas-2021-0034","url":null,"abstract":"Abstract It is often the goal of sports analysts, coaches, and fans to predict athlete performance over time. Models such as Bradley–Terry and Plackett–Luce measure athlete skill based on results of competitions over time, but have limited predictive strength without making assumptions about the nature of the evolution of athletic skill. Growth curves are often applied in the context of sports to predict future ability, but these curves are too simple to account for complex career trajectories. We propose a non-linear, mixed-effects trajectory to model the ratings as a function of time and other athlete-specific covariates. The mixture of trajectories allows for flexibility in the estimated shape of career trajectories between athletes as well as between sports. We use the fitted trajectories to make predictions of an athlete’s career trajectory through a model of how athlete performance progresses over time in a multi-competitor scenario as an extension to the Plackett–Luce model. We show how this model is useful for predicting the outcome of women’s luge races, as well as show how we can use the model to compare athletes to one another by clustering career trajectories.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"50 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135161172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We introduce a three-step framework to determine at which pitches Major League batters should swing. Unlike traditional plate discipline metrics, which implicitly assume that all batters should always swing at (resp. take) pitches inside (resp. outside) the strike zone, our approach explicitly accounts not only for the players and umpires involved in the pitch but also in-game contextual information like the number of outs, the count, baserunners, and score. We first fit flexible Bayesian nonparametric models to estimate (i) the probability that the pitch is called a strike if the batter takes the pitch; (ii) the probability that the batter makes contact if he swings; and (iii) the number of runs the batting team is expected to score following each pitch outcome (e.g. swing and miss, take a called strike, etc.). We then combine these intermediate estimates to determine whether swinging increases the batting team’s run expectancy. Our approach enables natural uncertainty propagation so that we can not only determine the optimal swing/take decision but also quantify our confidence in that decision. We illustrate our framework using a case study of pitches faced by Mike Trout in 2019.
{"title":"Evaluating plate discipline in Major League Baseball with Bayesian Additive Regression Trees","authors":"Ryan Yee, Sameer K. Deshpande","doi":"10.1515/jqas-2023-0048","DOIUrl":"https://doi.org/10.1515/jqas-2023-0048","url":null,"abstract":"Abstract We introduce a three-step framework to determine at which pitches Major League batters should swing. Unlike traditional plate discipline metrics, which implicitly assume that all batters should always swing at (resp. take) pitches inside (resp. outside) the strike zone, our approach explicitly accounts not only for the players and umpires involved in the pitch but also in-game contextual information like the number of outs, the count, baserunners, and score. We first fit flexible Bayesian nonparametric models to estimate (i) the probability that the pitch is called a strike if the batter takes the pitch; (ii) the probability that the batter makes contact if he swings; and (iii) the number of runs the batting team is expected to score following each pitch outcome (e.g. swing and miss, take a called strike, etc.). We then combine these intermediate estimates to determine whether swinging increases the batting team’s run expectancy. Our approach enables natural uncertainty propagation so that we can not only determine the optimal swing/take decision but also quantify our confidence in that decision. We illustrate our framework using a case study of pitches faced by Mike Trout in 2019.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136264248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-31DOI: 10.1515/jqas-2023-frontmatter3
{"title":"Frontmatter","authors":"","doi":"10.1515/jqas-2023-frontmatter3","DOIUrl":"https://doi.org/10.1515/jqas-2023-frontmatter3","url":null,"abstract":"","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135890803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We analyze the impact of psychological pressure on performance with over 5500 handball penalties thrown in either the decisive stage or the rest of the game during matches of the 2019/2020 season in the first three German handball leagues. Contrary to the choking under pressure phenomenon, most of the analyzed players perform best when it matters the most. The positive effect of pressure on performance is highest when the score is even or when the thrower’s team is trailing. We control for gender and psychological traits assessed with a survey. In our sample, female players score with a higher probability than male players. The positive impact of pressure is not significantly higher for female players.
{"title":"Performing best when it matters the most: evidence from professional handball","authors":"Christoph Bühren, Marvin Gabriel","doi":"10.1515/jqas-2022-0070","DOIUrl":"https://doi.org/10.1515/jqas-2022-0070","url":null,"abstract":"Abstract We analyze the impact of psychological pressure on performance with over 5500 handball penalties thrown in either the decisive stage or the rest of the game during matches of the 2019/2020 season in the first three German handball leagues. Contrary to the choking under pressure phenomenon, most of the analyzed players perform best when it matters the most. The positive effect of pressure on performance is highest when the score is even or when the thrower’s team is trailing. We control for gender and psychological traits assessed with a survey. In our sample, female players score with a higher probability than male players. The positive impact of pressure is not significantly higher for female players.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74265293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Mindset can shape sports performance, but these effects can be difficult to detect empirically. We use data from high school sprinters to explore mindset effects on 100 m finishing times and find that headwinds hamper performance more than can be attributed to the physics of wind resistance alone. These (implied) psychological effects of wind on sprint times are stronger for girls than for boys. Having established the presence of mindset-based slack in physical performance, we then test whether sprint times changed in the wake of Matthew Boling’s record-breaking sprint in 2019 that, after going viral on social media, potentially boosted self-efficacy among high school sprinters. Using 2018 and 2019 high school track meets in California, we observe notable changes in average sprinter performance for certain types of athletes in specific wind conditions after Boling’s race that did not occur in the previous season. These results control for many observable variables, correct for multiple hypothesis testing, and use entropy balancing weights to ensure statistical comparability between the two years. We detect differences in this ‘Boling effect’ based on the predicted racial composition of teams and the predicted race of athletes, which is relevant given the racial angle of coverage of the record-setting run. We posit vicarious self-efficacy as a plausible explanation for these difference-in-differences patterns. Pronounced heterogeneity in these results demonstrates some of the complexities and nuances of mindset effects even in settings where performance is easily quantified. Subtle contextual and salience cues appear to mediate the impact of vicarious self-efficacy beliefs on performance.
{"title":"Feeling fast? Beliefs and performance among high school sprinters","authors":"Travis J. Lybbert, Geyi Zheng","doi":"10.1515/jqas-2022-0084","DOIUrl":"https://doi.org/10.1515/jqas-2022-0084","url":null,"abstract":"Abstract Mindset can shape sports performance, but these effects can be difficult to detect empirically. We use data from high school sprinters to explore mindset effects on 100 m finishing times and find that headwinds hamper performance more than can be attributed to the physics of wind resistance alone. These (implied) psychological effects of wind on sprint times are stronger for girls than for boys. Having established the presence of mindset-based slack in physical performance, we then test whether sprint times changed in the wake of Matthew Boling’s record-breaking sprint in 2019 that, after going viral on social media, potentially boosted self-efficacy among high school sprinters. Using 2018 and 2019 high school track meets in California, we observe notable changes in average sprinter performance for certain types of athletes in specific wind conditions after Boling’s race that did not occur in the previous season. These results control for many observable variables, correct for multiple hypothesis testing, and use entropy balancing weights to ensure statistical comparability between the two years. We detect differences in this ‘Boling effect’ based on the predicted racial composition of teams and the predicted race of athletes, which is relevant given the racial angle of coverage of the record-setting run. We posit vicarious self-efficacy as a plausible explanation for these difference-in-differences patterns. Pronounced heterogeneity in these results demonstrates some of the complexities and nuances of mindset effects even in settings where performance is easily quantified. Subtle contextual and salience cues appear to mediate the impact of vicarious self-efficacy beliefs on performance.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"72 1","pages":"153 - 170"},"PeriodicalIF":0.8,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77406362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In recent years, the game of football has made a shift towards being more quantitative. With the advent of charting and tracking data, player evaluation is able to be studied from several different angles. In this paper, we build and refine two novel metrics: Bite Distance Under Expected (BDUE) and Ground Covered Over Expected (GCOE) for the evaluation of linebackers in the National Football League (NFL). Here, we show that these metrics are heavily correlated with each other, which demonstrates the trade-off linebackers have to make between being aggressive against the run and being effective when the opposing offense is using play-action. We also show that these metrics are more stable than those in the public space. Finally, we show how these metrics measure deception by opposing offenses.
{"title":"Investigating trade-offs made by American football linebackers using tracking data","authors":"Eric Eager, Tej Seth","doi":"10.1515/jqas-2022-0091","DOIUrl":"https://doi.org/10.1515/jqas-2022-0091","url":null,"abstract":"Abstract In recent years, the game of football has made a shift towards being more quantitative. With the advent of charting and tracking data, player evaluation is able to be studied from several different angles. In this paper, we build and refine two novel metrics: Bite Distance Under Expected (BDUE) and Ground Covered Over Expected (GCOE) for the evaluation of linebackers in the National Football League (NFL). Here, we show that these metrics are heavily correlated with each other, which demonstrates the trade-off linebackers have to make between being aggressive against the run and being effective when the opposing offense is using play-action. We also show that these metrics are more stable than those in the public space. Finally, we show how these metrics measure deception by opposing offenses.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"25 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91186959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this study we analyse data from world cup cross-country skiing sprint elimination tournaments for men and women in 2015–2020. Instead of being assigned a quarterfinal according to a seeding scheme, prequalified athletes choose themselves in sequential order in which of the five quarterfinals to compete. Due to a time constraint on the day the competition is held, the recovery time between the elimination heats varies. This implies a clear advantage for the athlete to race in an early rather than in a late quarterfinal to maximize the probability of reaching the podium. The purpose of the paper is to analyse the athletes’ choices facing the trade-off between recovery time and expected degree of competition when choosing in which quarterfinal to compete. We find empirical support for the prediction that higher ranked athletes from the qualification round prefer to compete in early quarterfinals, despite facing expected harder competition. Nevertheless, our results also suggest that athletes underestimate the value of choosing an early quarterfinal. In addition, we propose a seeding scheme capturing the fundamental disparity across quarterfinals using the estimates from alogistic regression model.
{"title":"Choosing opponents in skiing sprint elimination tournaments","authors":"Anders Lunander, N. Karlsson","doi":"10.1515/jqas-2021-0027","DOIUrl":"https://doi.org/10.1515/jqas-2021-0027","url":null,"abstract":"Abstract In this study we analyse data from world cup cross-country skiing sprint elimination tournaments for men and women in 2015–2020. Instead of being assigned a quarterfinal according to a seeding scheme, prequalified athletes choose themselves in sequential order in which of the five quarterfinals to compete. Due to a time constraint on the day the competition is held, the recovery time between the elimination heats varies. This implies a clear advantage for the athlete to race in an early rather than in a late quarterfinal to maximize the probability of reaching the podium. The purpose of the paper is to analyse the athletes’ choices facing the trade-off between recovery time and expected degree of competition when choosing in which quarterfinal to compete. We find empirical support for the prediction that higher ranked athletes from the qualification round prefer to compete in early quarterfinals, despite facing expected harder competition. Nevertheless, our results also suggest that athletes underestimate the value of choosing an early quarterfinal. In addition, we propose a seeding scheme capturing the fundamental disparity across quarterfinals using the estimates from alogistic regression model.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"52 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81344647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We introduce a non-standard generalization of the Elo rating system for competitions involving two or more participants. The new system can be understood as an online estimation algorithm for the parameters of a Plackett–Luce model which can be used to make probabilistic forecasts for the results of future competitions. The system’s distinguishing feature is the way it treats competitions as sequences of elimination-type rounds that sequentially identify the worst competitors rather than sequences of selection-type rounds that identify the best. The significance of this important modelling choice is discussed and its consequences are explored. Finally, our generalized Elo system’s predictive power is demonstrated using data from Formula One racing.
{"title":"Generalizing the Elo rating system for multiplayer games and races: why endurance is better than speed","authors":"B. Powell","doi":"10.1515/jqas-2023-0004","DOIUrl":"https://doi.org/10.1515/jqas-2023-0004","url":null,"abstract":"Abstract We introduce a non-standard generalization of the Elo rating system for competitions involving two or more participants. The new system can be understood as an online estimation algorithm for the parameters of a Plackett–Luce model which can be used to make probabilistic forecasts for the results of future competitions. The system’s distinguishing feature is the way it treats competitions as sequences of elimination-type rounds that sequentially identify the worst competitors rather than sequences of selection-type rounds that identify the best. The significance of this important modelling choice is discussed and its consequences are explored. Finally, our generalized Elo system’s predictive power is demonstrated using data from Formula One racing.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"16 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73313384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The FIFA Men’s World Cup tournament is the most popular sporting event in the world. Scholars have identified several flaws in the organization of the World Cup causing competitive imbalance. We empirically assess competitive imbalance between groups for the World Cup tournaments from 1954 through 2022. We average the Elo ratings of a team’s opponents in the group stage to calculate their group opponents rating. In every World Cup, the range in group opponents rating exceeds 118 Elo rating points – the difference between an average participant and an average semifinalist. Using logistic regression, we find that for an average participant in a 32-team World Cup, an increase in group opponents rating of only 88 Elo rating points can reduce the probability of reaching the quarterfinal from 0.174 to 0.081, which is a decrease of more than 50 %. None of the five seeding systems used by FIFA during 1954–2022 lessened the negative impact of group opponents rating on the probability of reaching the quarterfinal. We close with seven policy recommendations to restore competitive balance at the World Cup.
{"title":"The evolution of seeding systems and the impact of imbalanced groups in FIFA Men’s World Cup tournaments 1954–2022","authors":"Michael A. Lapré, Elizabeth M. Palazzolo","doi":"10.1515/jqas-2022-0087","DOIUrl":"https://doi.org/10.1515/jqas-2022-0087","url":null,"abstract":"Abstract The FIFA Men’s World Cup tournament is the most popular sporting event in the world. Scholars have identified several flaws in the organization of the World Cup causing competitive imbalance. We empirically assess competitive imbalance between groups for the World Cup tournaments from 1954 through 2022. We average the Elo ratings of a team’s opponents in the group stage to calculate their group opponents rating. In every World Cup, the range in group opponents rating exceeds 118 Elo rating points – the difference between an average participant and an average semifinalist. Using logistic regression, we find that for an average participant in a 32-team World Cup, an increase in group opponents rating of only 88 Elo rating points can reduce the probability of reaching the quarterfinal from 0.174 to 0.081, which is a decrease of more than 50 %. None of the five seeding systems used by FIFA during 1954–2022 lessened the negative impact of group opponents rating on the probability of reaching the quarterfinal. We close with seven policy recommendations to restore competitive balance at the World Cup.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"36 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82602215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-01DOI: 10.1515/jqas-2023-frontmatter2
{"title":"Frontmatter","authors":"","doi":"10.1515/jqas-2023-frontmatter2","DOIUrl":"https://doi.org/10.1515/jqas-2023-frontmatter2","url":null,"abstract":"","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135937894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：