Craig Fernandes, Jason D. Vescovi, Richard Norman, Cheri L. Bradish, Nathan Taback, Timothy C. Y. Chan
This paper presents a landmark study of equity, diversity and inclusion (EDI) in the field of sports analytics. We developed a survey that examined personal and job-related demographics, as well as individual perceptions and experiences about EDI in the workplace. We sent the survey to individuals in the five major North American professional leagues, representatives from the Olympic and Paralympic Committees in Canada and the U.S., the NCAA Division I programs, companies in sports tech/analytics, and university research groups. Our findings indicate the presence of a clear dominant group in sports analytics identifying as: young (72.0 %), White (69.5 %), heterosexual (89.7 %) and male (82.0 %). Within professional sports, males in management positions earned roughly $30,000 (27 %) more on average compared to females. A smaller but equally alarming pay gap of $17,000 (14 %) was found between White and racialized management personnel. Of concern, females were nearly five times as likely to experience discrimination and twice as likely to have considered leaving their job due to isolation or feeling unwelcome. While they had similar levels of agreement regarding fair processes for rewards and compensation, females “strongly agreed” less often than males regarding equitable support, equitable workload, having a voice, and being taken seriously. Over one third (36.3 %) of females indicated that they “strongly agreed” that they must work harder than others to be valued equally, compared to 9.8 % of males. We conclude the paper with concrete recommendations that could be considered to create a more equitable, diverse and inclusive environment for individuals working within the sports analytics sector.
{"title":"Equity, diversity, and inclusion in sports analytics","authors":"Craig Fernandes, Jason D. Vescovi, Richard Norman, Cheri L. Bradish, Nathan Taback, Timothy C. Y. Chan","doi":"10.1515/jqas-2022-0025","DOIUrl":"https://doi.org/10.1515/jqas-2022-0025","url":null,"abstract":"This paper presents a landmark study of equity, diversity and inclusion (EDI) in the field of sports analytics. We developed a survey that examined personal and job-related demographics, as well as individual perceptions and experiences about EDI in the workplace. We sent the survey to individuals in the five major North American professional leagues, representatives from the Olympic and Paralympic Committees in Canada and the U.S., the NCAA Division I programs, companies in sports tech/analytics, and university research groups. Our findings indicate the presence of a clear dominant group in sports analytics identifying as: young (72.0 %), White (69.5 %), heterosexual (89.7 %) and male (82.0 %). Within professional sports, males in management positions earned roughly $30,000 (27 %) more on average compared to females. A smaller but equally alarming pay gap of $17,000 (14 %) was found between White and racialized management personnel. Of concern, females were nearly five times as likely to experience discrimination and twice as likely to have considered leaving their job due to isolation or feeling unwelcome. While they had similar levels of agreement regarding fair processes for rewards and compensation, females “strongly agreed” less often than males regarding equitable support, equitable workload, having a voice, and being taken seriously. Over one third (36.3 %) of females indicated that they “strongly agreed” that they must work harder than others to be valued equally, compared to 9.8 % of males. We conclude the paper with concrete recommendations that could be considered to create a more equitable, diverse and inclusive environment for individuals working within the sports analytics sector.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139408042","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}
Carl Morris 1938–2023 was well-known for his pioneering research in Bayesian multiparameter inference and prediction. Morris was also known for his development of statistical thinking and methodology in sports. This paper provides an overview of Morris’ contributions in sports. This includes Morris’ experience in sports as a youth, summaries of some of Morris’ best-known contributions using sports data, his influence working with students, and some of Morris’ thinking about the interplay of statistics and sports.
{"title":"Contributions of Carl Morris in sports analytics, a memorium","authors":"Jim Albert","doi":"10.1515/jqas-2023-0092","DOIUrl":"https://doi.org/10.1515/jqas-2023-0092","url":null,"abstract":"Carl Morris 1938–2023 was well-known for his pioneering research in Bayesian multiparameter inference and prediction. Morris was also known for his development of statistical thinking and methodology in sports. This paper provides an overview of Morris’ contributions in sports. This includes Morris’ experience in sports as a youth, summaries of some of Morris’ best-known contributions using sports data, his influence working with students, and some of Morris’ thinking about the interplay of statistics and sports.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139375743","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}
Ethan Baron, Nathan Sandholtz, Devin Pleuler, Timothy C. Y. Chan
Measuring soccer shooting skill is a challenging analytics problem due to the scarcity and highly contextual nature of scoring events. The introduction of more advanced data surrounding soccer shots has given rise to model-based metrics which better cope with these challenges. Specifically, metrics such as expected goals added, goals above expectation, and post-shot expected goals all use advanced data to offer an improvement over the classical conversion rate. However, all metrics developed to date assign a value of zero to off-target shots, which account for almost two-thirds of all shots, since these shots have no probability of scoring. We posit that there is non-negligible shooting skill signal contained in the trajectories of off-target shots and propose two shooting skill metrics that incorporate the signal contained in off-target shots. Specifically, we develop a player-specific generative model for shot trajectories based on a mixture of truncated bivariate Gaussian distributions. We use this generative model to compute metrics that allow us to attach non-zero value to off-target shots. We demonstrate that our proposed metrics are more stable than current state-of-the-art metrics and have increased predictive power.
{"title":"Miss it like Messi: Extracting value from off-target shots in soccer","authors":"Ethan Baron, Nathan Sandholtz, Devin Pleuler, Timothy C. Y. Chan","doi":"10.1515/jqas-2022-0107","DOIUrl":"https://doi.org/10.1515/jqas-2022-0107","url":null,"abstract":"Measuring soccer shooting skill is a challenging analytics problem due to the scarcity and highly contextual nature of scoring events. The introduction of more advanced data surrounding soccer shots has given rise to model-based metrics which better cope with these challenges. Specifically, metrics such as expected goals added, goals above expectation, and post-shot expected goals all use advanced data to offer an improvement over the classical conversion rate. However, all metrics developed to date assign a value of zero to off-target shots, which account for almost two-thirds of all shots, since these shots have no probability of scoring. We posit that there is non-negligible shooting skill signal contained in the trajectories of off-target shots and propose two shooting skill metrics that incorporate the signal contained in off-target shots. Specifically, we develop a player-specific generative model for shot trajectories based on a mixture of truncated bivariate Gaussian distributions. We use this generative model to compute metrics that allow us to attach non-zero value to off-target shots. We demonstrate that our proposed metrics are more stable than current state-of-the-art metrics and have increased predictive power.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139072175","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}
Every season, the international football calendar contains periods reserved for a series of so-called special matches including international friendly or official matches played by national teams. All these periods are called “FIFA reserved dates” in the calendar and generally cause domestic competitions to shut down for some days. Such interruptions of leagues might generate different effects or externalities on the performance of players, clubs or even on the competition itself. While a number of studies focus on the effect of players’ absence on teams performance, this paper contributes to the literature by specifically evaluating the effect of the “FIFA reserved dates” on football outcomes. Using data for four seasons from the “big five” European leagues, I find evidence that the outcomes distribution in those matches played after a “FIFA reserved date” becomes more balanced, thus increasing the uncertainty of outcome. The results of this paper contribute to the ongoing debate about the management and design of the international match calendar.
{"title":"On the design of international match calendar: the effect of “FIFA reserved dates” on European football matches’ outcomes","authors":"Levi Pérez","doi":"10.1515/jqas-2022-0041","DOIUrl":"https://doi.org/10.1515/jqas-2022-0041","url":null,"abstract":"Every season, the international football calendar contains periods reserved for a series of so-called special matches including international friendly or official matches played by national teams. All these periods are called “FIFA reserved dates” in the calendar and generally cause domestic competitions to shut down for some days. Such interruptions of leagues might generate different effects or externalities on the performance of players, clubs or even on the competition itself. While a number of studies focus on the effect of players’ absence on teams performance, this paper contributes to the literature by specifically evaluating the effect of the “FIFA reserved dates” on football outcomes. Using data for four seasons from the “big five” European leagues, I find evidence that the outcomes distribution in those matches played after a “FIFA reserved date” becomes more balanced, thus increasing the uncertainty of outcome. The results of this paper contribute to the ongoing debate about the management and design of the international match calendar.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138518601","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 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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
Pub Date : 2023-07-25eCollection Date: 2023-12-01DOI: 10.1515/jqas-2022-0021
Erik-Jan van Kesteren, Tom Bergkamp
Successful performance in Formula One is determined by combination of both the driver's skill and race-car constructor advantage. This makes key performance questions in the sport difficult to answer. For example, who is the best Formula One driver, which is the best constructor, and what is their relative contribution to success? In this paper, we answer these questions based on data from the hybrid era in Formula One (2014-2021 seasons). We present a novel Bayesian multilevel rank-ordered logit regression method to model individual race finishing positions. We show that our modelling approach describes our data well, which allows for precise inferences about driver skill and constructor advantage. We conclude that Hamilton and Verstappen are the best drivers in the hybrid era, the top-three teams (Mercedes, Ferrari, and Red Bull) clearly outperform other constructors, and approximately 88 % of the variance in race results is explained by the constructor. We argue that this modelling approach may prove useful for sports beyond Formula One, as it creates performance ratings for independent components contributing to success.
{"title":"Bayesian analysis of Formula One race results: disentangling driver skill and constructor advantage.","authors":"Erik-Jan van Kesteren, Tom Bergkamp","doi":"10.1515/jqas-2022-0021","DOIUrl":"10.1515/jqas-2022-0021","url":null,"abstract":"<p><p>Successful performance in Formula One is determined by combination of both the driver's skill and race-car constructor advantage. This makes key performance questions in the sport difficult to answer. For example, who is the best Formula One driver, which is the best constructor, and what is their relative contribution to success? In this paper, we answer these questions based on data from the hybrid era in Formula One (2014-2021 seasons). We present a novel Bayesian multilevel rank-ordered logit regression method to model individual race finishing positions. We show that our modelling approach describes our data well, which allows for precise inferences about driver skill and constructor advantage. We conclude that Hamilton and Verstappen are the best drivers in the hybrid era, the top-three teams (Mercedes, Ferrari, and Red Bull) clearly outperform other constructors, and approximately 88 % of the variance in race results is explained by the constructor. We argue that this modelling approach may prove useful for sports beyond Formula One, as it creates performance ratings for independent components contributing to success.</p>","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10660124/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80267767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","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":null,"pages":null},"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":null,"pages":null},"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}
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