Abstract Recent measurement technologies enable us to analyze baseball at higher levels of complexity. There are, however, still many unclear points around pitching strategy. There are two elements that make it difficult to measure the effect of a pitching strategy. First, most public datasets do not include location data where the catcher demands a ball, which is essential information to obtain the battery’s intent. Second, there are many confounders associated with pitching/batting results when evaluating pitching strategy. We here clarify the effect of pitching attempts to a specific location, e.g., inside or outside. We employ a causal inference framework called stratified analysis using a propensity score to evaluate the effects while removing the effect of confounding factors. We use a pitch-by-pitch dataset of Japanese professional baseball games held in 2014–2019, which includes location data where the catcher demands a ball. The results reveal that an outside pitching attempt is more effective than an inside one to minimize allowed run average. In addition, the stratified analysis shows that the outside pitching attempt is effective regardless of the magnitude of the estimated batter’s ability, and the proportion of pitched inside for pitcher/batter. Our analysis provides practical insights into selecting a pitching strategy to minimize allowed runs.
{"title":"Pitching strategy evaluation via stratified analysis using propensity score","authors":"Hiroshi Nakahara, K. Takeda, Keisuke Fujii","doi":"10.1515/jqas-2021-0060","DOIUrl":"https://doi.org/10.1515/jqas-2021-0060","url":null,"abstract":"Abstract Recent measurement technologies enable us to analyze baseball at higher levels of complexity. There are, however, still many unclear points around pitching strategy. There are two elements that make it difficult to measure the effect of a pitching strategy. First, most public datasets do not include location data where the catcher demands a ball, which is essential information to obtain the battery’s intent. Second, there are many confounders associated with pitching/batting results when evaluating pitching strategy. We here clarify the effect of pitching attempts to a specific location, e.g., inside or outside. We employ a causal inference framework called stratified analysis using a propensity score to evaluate the effects while removing the effect of confounding factors. We use a pitch-by-pitch dataset of Japanese professional baseball games held in 2014–2019, which includes location data where the catcher demands a ball. The results reveal that an outside pitching attempt is more effective than an inside one to minimize allowed run average. In addition, the stratified analysis shows that the outside pitching attempt is effective regardless of the magnitude of the estimated batter’s ability, and the proportion of pitched inside for pitcher/batter. Our analysis provides practical insights into selecting a pitching strategy to minimize allowed runs.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83392430","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}
N. Carter, A. Harrison, Amar Iyengar, M. Lanham, Scott T. Nestler, Dave Schrader, Amir Zadeh
Abstract In NCAA Division III Wrestling, the question arose how to assign schools to regions in a way that optimizes fairness for individual wrestlers aspiring to the national tournament. The problem fell within cluster analysis but no known clustering algorithms supported its complex and interrelated set of needs. We created several bespoke clustering algorithms based on various heuristics (balanced optimization, weighted spatial clustering, and weighted optimization rectangles) for finding an optimal assignment, and tested each against the generic technique of genetic algorithms. While each of our algorithms had different strengths, the genetic algorithm achieved the highest value on our objective function, including when comparing it to the region assignments that preceded our work. This paper therefore demonstrates a technique that can be used to solve a broad category of clustering problems that arise in athletics, particularly any sport in which athletes compete individually but are assigned to regions as a team.
{"title":"Clustering algorithms to increase fairness in collegiate wrestling","authors":"N. Carter, A. Harrison, Amar Iyengar, M. Lanham, Scott T. Nestler, Dave Schrader, Amir Zadeh","doi":"10.1515/jqas-2020-0101","DOIUrl":"https://doi.org/10.1515/jqas-2020-0101","url":null,"abstract":"Abstract In NCAA Division III Wrestling, the question arose how to assign schools to regions in a way that optimizes fairness for individual wrestlers aspiring to the national tournament. The problem fell within cluster analysis but no known clustering algorithms supported its complex and interrelated set of needs. We created several bespoke clustering algorithms based on various heuristics (balanced optimization, weighted spatial clustering, and weighted optimization rectangles) for finding an optimal assignment, and tested each against the generic technique of genetic algorithms. While each of our algorithms had different strengths, the genetic algorithm achieved the highest value on our objective function, including when comparing it to the region assignments that preceded our work. This paper therefore demonstrates a technique that can be used to solve a broad category of clustering problems that arise in athletics, particularly any sport in which athletes compete individually but are assigned to regions as a team.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74351693","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 Former NBA all-star forward Rasheed Wallace popularized the catchphrase “Ball Don’t Lie.” Rasheed would often shout this after an opponent missed a free throw. It was used by Rasheed to illustrate the mental impact on a free throw shooter from knowing the foul was questionable and its impact on likelihood of converting the ensuing free throw. The tendency to miss free throws associated with questionable foul calls—or the propensity for the ball to miss—would be followed by Rasheed’s “Ball Don’t Lie!” exclamation. This paper aims to test whether the ball was less likely to go through the hoop during free throws following questionable foul calls. We use a proxy to identify the questionableness of a foul call, one that Rasheed Wallace was very familiar with—whenever the original shooting foul was immediately followed by a technical foul. This proxy is meant to capture player and coach reactions to a shooting foul call. If the call was bad, or questionable, we expect more outrage from the team the foul was called on, which tends to draw technical fouls. Our findings do not support Rasheed’s prediction; the propensity to make a shooting foul free throw does not appear to change after a technical. In fact, using a subset of our data period under which the NBA changed technical foul rules to target complaining about foul calls, we find a small increase in free throw percentage after a technical foul call.
{"title":"Does the ball lie? Testing the Rasheed Wallace hypothesis","authors":"B. Meehan, Javier E. Portillo, Corey Jenkins","doi":"10.1515/jqas-2020-0020","DOIUrl":"https://doi.org/10.1515/jqas-2020-0020","url":null,"abstract":"Abstract Former NBA all-star forward Rasheed Wallace popularized the catchphrase “Ball Don’t Lie.” Rasheed would often shout this after an opponent missed a free throw. It was used by Rasheed to illustrate the mental impact on a free throw shooter from knowing the foul was questionable and its impact on likelihood of converting the ensuing free throw. The tendency to miss free throws associated with questionable foul calls—or the propensity for the ball to miss—would be followed by Rasheed’s “Ball Don’t Lie!” exclamation. This paper aims to test whether the ball was less likely to go through the hoop during free throws following questionable foul calls. We use a proxy to identify the questionableness of a foul call, one that Rasheed Wallace was very familiar with—whenever the original shooting foul was immediately followed by a technical foul. This proxy is meant to capture player and coach reactions to a shooting foul call. If the call was bad, or questionable, we expect more outrage from the team the foul was called on, which tends to draw technical fouls. Our findings do not support Rasheed’s prediction; the propensity to make a shooting foul free throw does not appear to change after a technical. In fact, using a subset of our data period under which the NBA changed technical foul rules to target complaining about foul calls, we find a small increase in free throw percentage after a technical foul call.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90925597","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 Choosing the right defensive corner-strategy is a crucial task for each coach in professional football (soccer). Although corners are repeatable and static situations, due to their low conversion rates, several studies in literature failed to find useable insights about the efficiency of various corner strategies. Our work aims to fill this gap. We hand-label the role of each defensive player from 213 corners in 33 matches, where we then employ an augmentation strategy to increase the number of data points. By combining a convolutional neural network with a long short-term memory neural network, we are able to detect the defensive strategy of each player based on positional data. We identify which of seven well-established roles a defensive player conducted (player-marking, zonal-marking, placed for counterattack, back-space, short defender, near-post, and far-post). The model achieves an overall weighted accuracy of 89.3%, and in the case of player-marking, we are able to accurately detect which offensive player the defender is marking 80.8% of the time. The performance of the model is evaluated against a rule-based baseline model, as well as by an inter-labeller accuracy. We demonstrate that rules can also be used to support the labelling process and serve as a baseline for weak supervision approaches. We show three concrete use-cases on how this approach can support a more informed and fact-based decision making process.
{"title":"Individual role classification for players defending corners in football (soccer)","authors":"Pascal Bauer, Gabriel Anzer, J. Smith","doi":"10.1515/jqas-2022-0003","DOIUrl":"https://doi.org/10.1515/jqas-2022-0003","url":null,"abstract":"Abstract Choosing the right defensive corner-strategy is a crucial task for each coach in professional football (soccer). Although corners are repeatable and static situations, due to their low conversion rates, several studies in literature failed to find useable insights about the efficiency of various corner strategies. Our work aims to fill this gap. We hand-label the role of each defensive player from 213 corners in 33 matches, where we then employ an augmentation strategy to increase the number of data points. By combining a convolutional neural network with a long short-term memory neural network, we are able to detect the defensive strategy of each player based on positional data. We identify which of seven well-established roles a defensive player conducted (player-marking, zonal-marking, placed for counterattack, back-space, short defender, near-post, and far-post). The model achieves an overall weighted accuracy of 89.3%, and in the case of player-marking, we are able to accurately detect which offensive player the defender is marking 80.8% of the time. The performance of the model is evaluated against a rule-based baseline model, as well as by an inter-labeller accuracy. We demonstrate that rules can also be used to support the labelling process and serve as a baseline for weak supervision approaches. We show three concrete use-cases on how this approach can support a more informed and fact-based decision making process.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82466879","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 Two new Bayesian methods for estimating and predicting in-game home team win probabilities in Division I NCAA men’s college basketball are proposed. The first method has a prior that adjusts as a function of lead differential and time elapsed. The second is an adjusted version of the first, where the adjustment is a linear combination of the Bayesian estimator with a time-weighted pregame win probability. The proposed methods are compared to existing methods, showing the new methods are competitive with or outperform existing methods for both estimation and prediction. The utility is illustrated via an application to the 2012/2013 through the 2019/2020 NCAA Division I Men’s Basketball seasons.
{"title":"Bayesian estimation of in-game home team win probability for college basketball","authors":"Jason Maddox, Ryan Sides, Jane L. Harvill","doi":"10.1515/jqas-2021-0086","DOIUrl":"https://doi.org/10.1515/jqas-2021-0086","url":null,"abstract":"Abstract Two new Bayesian methods for estimating and predicting in-game home team win probabilities in Division I NCAA men’s college basketball are proposed. The first method has a prior that adjusts as a function of lead differential and time elapsed. The second is an adjusted version of the first, where the adjustment is a linear combination of the Bayesian estimator with a time-weighted pregame win probability. The proposed methods are compared to existing methods, showing the new methods are competitive with or outperform existing methods for both estimation and prediction. The utility is illustrated via an application to the 2012/2013 through the 2019/2020 NCAA Division I Men’s Basketball seasons.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79075522","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 analyse football (soccer) player performance data with mixed type variables from the 2014-15 season of eight European major leagues. We cluster these data based on a tailor-made dissimilarity measure. In order to decide between the many available clustering methods and to choose an appropriate number of clusters, we use the approach by Akhanli and Hennig (2020. “Comparing Clusterings and Numbers of Clusters by Aggregation of Calibrated Clustering Validity Indexes.” Statistics and Computing 30 (5): 1523–44). This is based on several validation criteria that refer to different desirable characteristics of a clustering. These characteristics are chosen based on the aim of clustering, and this allows to define a suitable validation index as weighted average of calibrated individual indexes measuring the desirable features. We derive two different clusterings. The first one is a partition of the data set into major groups of essentially different players, which can be used for the analysis of a team’s composition. The second one divides the data set into many small clusters (with 10 players on average), which can be used for finding players with a very similar profile to a given player. It is discussed in depth what characteristics are desirable for these clusterings. Weighting the criteria for the second clustering is informed by a survey of football experts.
{"title":"Clustering of football players based on performance data and aggregated clustering validity indexes","authors":"Serhat Emre Akhanli, C. Hennig","doi":"10.1515/jqas-2022-0037","DOIUrl":"https://doi.org/10.1515/jqas-2022-0037","url":null,"abstract":"Abstract We analyse football (soccer) player performance data with mixed type variables from the 2014-15 season of eight European major leagues. We cluster these data based on a tailor-made dissimilarity measure. In order to decide between the many available clustering methods and to choose an appropriate number of clusters, we use the approach by Akhanli and Hennig (2020. “Comparing Clusterings and Numbers of Clusters by Aggregation of Calibrated Clustering Validity Indexes.” Statistics and Computing 30 (5): 1523–44). This is based on several validation criteria that refer to different desirable characteristics of a clustering. These characteristics are chosen based on the aim of clustering, and this allows to define a suitable validation index as weighted average of calibrated individual indexes measuring the desirable features. We derive two different clusterings. The first one is a partition of the data set into major groups of essentially different players, which can be used for the analysis of a team’s composition. The second one divides the data set into many small clusters (with 10 players on average), which can be used for finding players with a very similar profile to a given player. It is discussed in depth what characteristics are desirable for these clusterings. Weighting the criteria for the second clustering is informed by a survey of football experts.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87941458","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 Sports analysis has gained paramount importance for coaches, scouts, and fans. Recently, computer vision researchers have taken on the challenge of collecting the necessary data by proposing several methods of automatic player and ball tracking. Building on the gathered tracking data, data miners are able to perform quantitative analysis on the performance of players and teams. With this survey, our goal is to provide a basic understanding for quantitative data analysts about the process of creating the input data and the characteristics thereof. Thus, we summarize the recent methods of optical tracking by providing a comprehensive taxonomy of conventional and deep learning methods, separately. Moreover, we discuss the preprocessing steps of tracking, the most common challenges in this domain, and the application of tracking data to sports teams. Finally, we compare the methods by their cost and limitations, and conclude the work by highlighting potential future research directions.
{"title":"Optical tracking in team sports","authors":"Pegah Rahimian, László Toka","doi":"10.1515/jqas-2020-0088","DOIUrl":"https://doi.org/10.1515/jqas-2020-0088","url":null,"abstract":"Abstract Sports analysis has gained paramount importance for coaches, scouts, and fans. Recently, computer vision researchers have taken on the challenge of collecting the necessary data by proposing several methods of automatic player and ball tracking. Building on the gathered tracking data, data miners are able to perform quantitative analysis on the performance of players and teams. With this survey, our goal is to provide a basic understanding for quantitative data analysts about the process of creating the input data and the characteristics thereof. Thus, we summarize the recent methods of optical tracking by providing a comprehensive taxonomy of conventional and deep learning methods, separately. Moreover, we discuss the preprocessing steps of tracking, the most common challenges in this domain, and the application of tracking data to sports teams. Finally, we compare the methods by their cost and limitations, and conclude the work by highlighting potential future research directions.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84821423","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 Elo rating system contains a coefficient called the K-factor which governs the amount of change to the updated ratings and is often determined by empirical or heuristic means. Theoretical studies on the K-factor have been sparse and not much is known about the pertinent factors that impact its appropriate values in applications. This paper has two main goals: to present a new formulation of the K-factor that is optimal with respect to the mean-squared-error (MSE) criterion in a round-robin tournament setting and to investigate the effects of the relevant variables, including the number of tournament participants n, on the optimal K-factor (based on the model-averaged MSE). It is found that n and the variability of the deviation between the true rating and the pre-tournament rating have a strong influence on the optimal K-factor. Comparisons between the MSE-optimal K-factor and the K-factors from Elo and from the US Chess Federation as a function of n are also provided. Although the results are applicable to other sports in similar settings, the study focuses on chess and makes use of the rating data and the K-factor values from the chess world.
{"title":"MSE-optimal K-factor of the Elo rating system for round-robin tournament","authors":"Victor S. Chan","doi":"10.1515/jqas-2021-0079","DOIUrl":"https://doi.org/10.1515/jqas-2021-0079","url":null,"abstract":"Abstract The Elo rating system contains a coefficient called the K-factor which governs the amount of change to the updated ratings and is often determined by empirical or heuristic means. Theoretical studies on the K-factor have been sparse and not much is known about the pertinent factors that impact its appropriate values in applications. This paper has two main goals: to present a new formulation of the K-factor that is optimal with respect to the mean-squared-error (MSE) criterion in a round-robin tournament setting and to investigate the effects of the relevant variables, including the number of tournament participants n, on the optimal K-factor (based on the model-averaged MSE). It is found that n and the variability of the deviation between the true rating and the pre-tournament rating have a strong influence on the optimal K-factor. Comparisons between the MSE-optimal K-factor and the K-factors from Elo and from the US Chess Federation as a function of n are also provided. Although the results are applicable to other sports in similar settings, the study focuses on chess and makes use of the rating data and the K-factor values from the chess world.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76581251","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 Evaluation of individuals in a team sport setting is inherently difficult. The level of play of one individual is fundamentally tied to the level of play of the teammates. One way to think about evaluation of individuals is to ‘insert’ the posterior distribution of the parameter that measures individual play into an ‘average’ team, and see how the probability of success (or failure) changes. Using a Bayesian hierarchical logistic model, we can estimate both the average contribution to success of various positions, and the individual contribution of all the players in that position. In this paper, we use data from the 2018 World Championships in Volleyball to model both the position played and the players within each position. Using both the posterior distributions for the mean performance of the different positions, and the posterior distributions for the individual players, we can then estimate the change in the number of points scored for a team with a change from an average player to the individual under consideration. We compute both the points scored above average per set (PAAPS) and the points scored above average per 100 touches (PP100) for 168 men and 168 women playing five different positions. Contributions of the various position groups and of individual players within each position are evaluated and compared.
{"title":"Evaluating the performance of elite level volleyball players","authors":"G. Fellingham","doi":"10.1515/jqas-2021-0056","DOIUrl":"https://doi.org/10.1515/jqas-2021-0056","url":null,"abstract":"Abstract Evaluation of individuals in a team sport setting is inherently difficult. The level of play of one individual is fundamentally tied to the level of play of the teammates. One way to think about evaluation of individuals is to ‘insert’ the posterior distribution of the parameter that measures individual play into an ‘average’ team, and see how the probability of success (or failure) changes. Using a Bayesian hierarchical logistic model, we can estimate both the average contribution to success of various positions, and the individual contribution of all the players in that position. In this paper, we use data from the 2018 World Championships in Volleyball to model both the position played and the players within each position. Using both the posterior distributions for the mean performance of the different positions, and the posterior distributions for the individual players, we can then estimate the change in the number of points scored for a team with a change from an average player to the individual under consideration. We compute both the points scored above average per set (PAAPS) and the points scored above average per 100 touches (PP100) for 168 men and 168 women playing five different positions. Contributions of the various position groups and of individual players within each position are evaluated and compared.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89615955","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 : 2021-11-26DOI: 10.1515/jqas-2021-frontmatter4
{"title":"Frontmatter","authors":"","doi":"10.1515/jqas-2021-frontmatter4","DOIUrl":"https://doi.org/10.1515/jqas-2021-frontmatter4","url":null,"abstract":"","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90362442","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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