Abstract This paper explores defensive play in soccer. The analysis is predicated on the assumption that the area of the convex hull formed by the players on a team provides a proxy for defensive style where small areas coincide with a greater defensive focus. With the availability of tracking data, the massive dataset considered in this paper consists of areas of convex hulls, related covariates and shots taken during matches. Whereas the pre-processing of the data is an exercise in data science, the statistical analysis is carried out using linear models. The resultant messages are nuanced but the primary message suggests that an extreme defensive style (defined by a small convex hull) is negatively associated with generating shots.
{"title":"Parking the bus","authors":"Tianyu Guan, Jiguo Cao, T. Swartz","doi":"10.1515/jqas-2021-0059","DOIUrl":"https://doi.org/10.1515/jqas-2021-0059","url":null,"abstract":"Abstract This paper explores defensive play in soccer. The analysis is predicated on the assumption that the area of the convex hull formed by the players on a team provides a proxy for defensive style where small areas coincide with a greater defensive focus. With the availability of tracking data, the massive dataset considered in this paper consists of areas of convex hulls, related covariates and shots taken during matches. Whereas the pre-processing of the data is an exercise in data science, the statistical analysis is carried out using linear models. The resultant messages are nuanced but the primary message suggests that an extreme defensive style (defined by a small convex hull) is negatively associated with generating shots.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"16 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77141524","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 Summary statistics of football matches such as final score, possession and percentage of completed passes are not satisfyingly informative about style of play seen on the pitch. In this sense, networks and graphs are able to quantify how teams play differently from each others. We study the distribution of triad census, i.e., the distribution of local structures in networks and we show how it is possible to characterize passing networks of football teams. We describe the triadic structure and analyse its distribution under some specific probabilistic assumptions, introducing, in this context, some tests to verify the presence of specific triadic patterns in football data. We firstly run an omnibus test against random structure to asses whether observed triadic distribution deviates from randomness. Then, we redesign the Dirichlet-Multinomial test to recognize different triadic behaviours after choosing some reference patterns. The proposed tests are applied to a real dataset regarding 288 matches in the Group Stage of UEFA Champions League among three consecutive seasons.
{"title":"Testing styles of play using triad census distribution: an application to men’s football","authors":"Lucio Palazzo, Riccardo Ievoli, G. Ragozini","doi":"10.1515/jqas-2022-0010","DOIUrl":"https://doi.org/10.1515/jqas-2022-0010","url":null,"abstract":"Abstract Summary statistics of football matches such as final score, possession and percentage of completed passes are not satisfyingly informative about style of play seen on the pitch. In this sense, networks and graphs are able to quantify how teams play differently from each others. We study the distribution of triad census, i.e., the distribution of local structures in networks and we show how it is possible to characterize passing networks of football teams. We describe the triadic structure and analyse its distribution under some specific probabilistic assumptions, introducing, in this context, some tests to verify the presence of specific triadic patterns in football data. We firstly run an omnibus test against random structure to asses whether observed triadic distribution deviates from randomness. Then, we redesign the Dirichlet-Multinomial test to recognize different triadic behaviours after choosing some reference patterns. The proposed tests are applied to a real dataset regarding 288 matches in the Group Stage of UEFA Champions League among three consecutive seasons.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"76 1","pages":"125 - 151"},"PeriodicalIF":0.8,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90681418","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}
Susan E. Martonosi, Martin Gonzalez, Nicolas Oshiro
Abstract NBA team managers and owners try to acquire high-performing players. An important consideration in these decisions is how well the new players will perform in combination with their teammates. Our objective is to identify elite five-person lineups, which we define as those having a positive plus-minus per minute (PMM). Using individual player order statistics, our model can identify an elite lineup even if the five players in the lineup have never played together, which can inform player acquisition decisions, salary negotiations, and real-time coaching decisions. We combine seven classification tools into a unanimous consent classifier (all-or-nothing classifier, or ANC) in which a lineup is predicted to be elite only if all seven classifiers predict it to be elite. In this way, we achieve high positive predictive value (i.e., precision), the likelihood that a lineup classified as elite will indeed have a positive PMM. We train and test the model on individual player and lineup data from the 2017–18 season and use the model to predict the performance of lineups drawn from all 30 NBA teams’ 2018–19 regular season rosters. Although the ANC is conservative and misses some high-performing lineups, it achieves high precision and recommends positionally balanced lineups.
{"title":"Predicting elite NBA lineups using individual player order statistics","authors":"Susan E. Martonosi, Martin Gonzalez, Nicolas Oshiro","doi":"10.1515/jqas-2022-0039","DOIUrl":"https://doi.org/10.1515/jqas-2022-0039","url":null,"abstract":"Abstract NBA team managers and owners try to acquire high-performing players. An important consideration in these decisions is how well the new players will perform in combination with their teammates. Our objective is to identify elite five-person lineups, which we define as those having a positive plus-minus per minute (PMM). Using individual player order statistics, our model can identify an elite lineup even if the five players in the lineup have never played together, which can inform player acquisition decisions, salary negotiations, and real-time coaching decisions. We combine seven classification tools into a unanimous consent classifier (all-or-nothing classifier, or ANC) in which a lineup is predicted to be elite only if all seven classifiers predict it to be elite. In this way, we achieve high positive predictive value (i.e., precision), the likelihood that a lineup classified as elite will indeed have a positive PMM. We train and test the model on individual player and lineup data from the 2017–18 season and use the model to predict the performance of lineups drawn from all 30 NBA teams’ 2018–19 regular season rosters. Although the ANC is conservative and misses some high-performing lineups, it achieves high precision and recommends positionally balanced lineups.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"26 1","pages":"51 - 71"},"PeriodicalIF":0.8,"publicationDate":"2023-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91148150","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 : 2023-03-01DOI: 10.1515/jqas-2023-frontmatter1
{"title":"Frontmatter","authors":"","doi":"10.1515/jqas-2023-frontmatter1","DOIUrl":"https://doi.org/10.1515/jqas-2023-frontmatter1","url":null,"abstract":"","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136389894","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 Modern and post-modern portfolio theory were devised by Harry Markowitz (among others) for purposes of allocating some monetary resources among a number of financial assets so as to strike a suitable balance between risk and expected return. The problem it addresses bears a considerable resemblance to one encountered in making “moneyline” bets on the outcomes of contests in sports like American football. In distributing some allotted funds among a number of such bets, it may be desired to account for the risk. By introducing suitable modifications, the procedures employed in modern and post-modern portfolio theory for the allocation of resources among financial assets can be adapted for use in the distribution of funds among multiple bets. As in the case of financial assets, the most appropriate measures of risk are ones like the semi-deviation or semi-variance that penalize only negative or below-target returns. The various procedures are illustrated and compared by applying them retrospectively to moneyline bets on the outcomes of the college football “bowl” games from the 2020 season.
{"title":"Modern and post-modern portfolio theory as applied to moneyline betting","authors":"D. Harville","doi":"10.1515/jqas-2021-0107","DOIUrl":"https://doi.org/10.1515/jqas-2021-0107","url":null,"abstract":"Abstract Modern and post-modern portfolio theory were devised by Harry Markowitz (among others) for purposes of allocating some monetary resources among a number of financial assets so as to strike a suitable balance between risk and expected return. The problem it addresses bears a considerable resemblance to one encountered in making “moneyline” bets on the outcomes of contests in sports like American football. In distributing some allotted funds among a number of such bets, it may be desired to account for the risk. By introducing suitable modifications, the procedures employed in modern and post-modern portfolio theory for the allocation of resources among financial assets can be adapted for use in the distribution of funds among multiple bets. As in the case of financial assets, the most appropriate measures of risk are ones like the semi-deviation or semi-variance that penalize only negative or below-target returns. The various procedures are illustrated and compared by applying them retrospectively to moneyline bets on the outcomes of the college football “bowl” games from the 2020 season.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"7 1","pages":"73 - 89"},"PeriodicalIF":0.8,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78600023","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 present a mathematical modeling framework for roster construction of a Major League Soccer (MLS) expansion team. The model seeks to construct the best squad feasible under league salary rules, while balancing present value, potential value, and future cap flexibility. Player acquisition decisions, as well as allocation of salary, targeted allocation money (TAM), general allocation money (GAM), and designated player slots, are determined simultaneously by a mixed-integer programming model. We demonstrate the model’s functionality in constructing a hypothetical expansion roster and propose a number of extensions.
{"title":"A roster construction decision tool for MLS expansion teams","authors":"Zachary J. Smith, J. Bickel","doi":"10.1515/jqas-2021-0041","DOIUrl":"https://doi.org/10.1515/jqas-2021-0041","url":null,"abstract":"Abstract We present a mathematical modeling framework for roster construction of a Major League Soccer (MLS) expansion team. The model seeks to construct the best squad feasible under league salary rules, while balancing present value, potential value, and future cap flexibility. Player acquisition decisions, as well as allocation of salary, targeted allocation money (TAM), general allocation money (GAM), and designated player slots, are determined simultaneously by a mixed-integer programming model. We demonstrate the model’s functionality in constructing a hypothetical expansion roster and propose a number of extensions.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"33 1","pages":"1 - 14"},"PeriodicalIF":0.8,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87977853","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 ATP finals is the concluding tournament of the tennis season since its initiation over 50 years ago. It features the 8 best players of that year and is often considered to be the most prestigious event in the sport other than the 4 grand slams. Unlike any other professional tennis tournament, it includes a round-robin stage where all players in a group compete against each other, making it a unique testbed for examining performance under forgiving conditions, where losing does not immediately result in elimination. Analysis of the distribution of final group standings in the ATP Finals for singles from 1972 to 2021 reveals a surprising pattern, where one of the possible and seemingly likely outcomes almost never materializes. The present study uses a model-free, optimization approach to account for this distinctive phenomenon by calculating what match winning probabilities between players in a group can lead to the observed distribution. Results show that the only way to explain the empirical findings is through a “paradoxical” balance of power where the best player in a group shows a vulnerability against the weakest player. We discuss the possible mechanisms underlying this result and their implications for match prediction, bettors, and tournament organization.
{"title":"A peculiar phenomenon and its potential explanation in the ATP tennis tour finals for singles","authors":"Itamar Lerner","doi":"10.1515/jqas-2022-0043","DOIUrl":"https://doi.org/10.1515/jqas-2022-0043","url":null,"abstract":"Abstract The ATP finals is the concluding tournament of the tennis season since its initiation over 50 years ago. It features the 8 best players of that year and is often considered to be the most prestigious event in the sport other than the 4 grand slams. Unlike any other professional tennis tournament, it includes a round-robin stage where all players in a group compete against each other, making it a unique testbed for examining performance under forgiving conditions, where losing does not immediately result in elimination. Analysis of the distribution of final group standings in the ATP Finals for singles from 1972 to 2021 reveals a surprising pattern, where one of the possible and seemingly likely outcomes almost never materializes. The present study uses a model-free, optimization approach to account for this distinctive phenomenon by calculating what match winning probabilities between players in a group can lead to the observed distribution. Results show that the only way to explain the empirical findings is through a “paradoxical” balance of power where the best player in a group shows a vulnerability against the weakest player. We discuss the possible mechanisms underlying this result and their implications for match prediction, bettors, and tournament organization.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"147 1","pages":"27 - 36"},"PeriodicalIF":0.8,"publicationDate":"2023-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72385703","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 This paper examines how the Kelly criterion, a strategy for maximizing the expected log-growth of capital through informed betting, can be applied to non-mutually exclusive bets. These are bets where there is no one-to-one correspondence between the bets and the possible outcomes of the game. This type of situation is common in horse racing, where multiple types of bets are available for a single race. The paper begins by providing a theoretical overview of the Kelly betting strategy and then discusses how it can be extended to non-mutually exclusive bets. A new formulation of the fractional Kelly strategy, which involves betting a fixed fraction of the amount suggested by the Kelly criterion, is also presented for this type of scenario.
{"title":"Kelly criterion and fractional Kelly strategy for non-mutually exclusive bets","authors":"Benjamin P. Jacot, Paul V. Mochkovitch","doi":"10.1515/jqas-2020-0122","DOIUrl":"https://doi.org/10.1515/jqas-2020-0122","url":null,"abstract":"Abstract This paper examines how the Kelly criterion, a strategy for maximizing the expected log-growth of capital through informed betting, can be applied to non-mutually exclusive bets. These are bets where there is no one-to-one correspondence between the bets and the possible outcomes of the game. This type of situation is common in horse racing, where multiple types of bets are available for a single race. The paper begins by providing a theoretical overview of the Kelly betting strategy and then discusses how it can be extended to non-mutually exclusive bets. A new formulation of the fractional Kelly strategy, which involves betting a fixed fraction of the amount suggested by the Kelly criterion, is also presented for this type of scenario.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"69 1","pages":"37 - 42"},"PeriodicalIF":0.8,"publicationDate":"2023-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75650977","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 existence (or not) of the hot hand in sport continues to attract the attention of economists and psychologists. The paper presents analysis to test the belief prevalent in golfing circles that golfers go in and out of form quickly, while ‘class’ remains relatively constant. By going in and out of form, the golfer is effectively experiencing a longer-run hot hand: one can speculate that periods of confidence breed good performance. To test for the existence of ‘form’, we present a new application of the Ornstein–Uhlenbeck model and use it to identify both a golfer’s class and form when modelling golf scores. The findings suggest that short-term form does exist in golf and that this hot hand lasts for about four weeks.
{"title":"‘Form is temporary, class is permanent’: identifying a longer-term hot hand in golf","authors":"R. Baker, Ian G. McHale","doi":"10.1515/jqas-2022-0051","DOIUrl":"https://doi.org/10.1515/jqas-2022-0051","url":null,"abstract":"Abstract The existence (or not) of the hot hand in sport continues to attract the attention of economists and psychologists. The paper presents analysis to test the belief prevalent in golfing circles that golfers go in and out of form quickly, while ‘class’ remains relatively constant. By going in and out of form, the golfer is effectively experiencing a longer-run hot hand: one can speculate that periods of confidence breed good performance. To test for the existence of ‘form’, we present a new application of the Ornstein–Uhlenbeck model and use it to identify both a golfer’s class and form when modelling golf scores. The findings suggest that short-term form does exist in golf and that this hot hand lasts for about four weeks.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"15 1","pages":"241 - 251"},"PeriodicalIF":0.8,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86453532","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 Statistical analysis in competitive sport is an important tool for developing strategy and seeking competitive advantages. However, for complex team sports such as Australian Rules Football, major limitations occur when using possession event data for game analysis. First, focusing on counting possession events does not capture the impact of off-the-ball actions such as ground positioning of other players. Second, it is difficult to determine the extent that an event is due to either team’s relative proficiency or skill. Third, there is limited possession event data available from each match and modelling efforts often have low statistical power. Here we reinterpret event data into positional systems and utilise pairwise performance metrics to understand the relative team proficiency in each of these states. These metrics can then be used to construct transition probabilities between states for future games, and ultimately, absorbing probabilities of goal states. Our approach effectively predicts match outcomes using team ratings for forward, midfield and defensive systems and is sufficiently interpretable to support strategic decision-making by coaching departments in the Australian Football League (AFL).
{"title":"Modelling Australian Rules Football as spatial systems with pairwise comparisons","authors":"Anton Andreacchio, N. Bean, Lewis Mitchell","doi":"10.1515/jqas-2021-0035","DOIUrl":"https://doi.org/10.1515/jqas-2021-0035","url":null,"abstract":"Abstract Statistical analysis in competitive sport is an important tool for developing strategy and seeking competitive advantages. However, for complex team sports such as Australian Rules Football, major limitations occur when using possession event data for game analysis. First, focusing on counting possession events does not capture the impact of off-the-ball actions such as ground positioning of other players. Second, it is difficult to determine the extent that an event is due to either team’s relative proficiency or skill. Third, there is limited possession event data available from each match and modelling efforts often have low statistical power. Here we reinterpret event data into positional systems and utilise pairwise performance metrics to understand the relative team proficiency in each of these states. These metrics can then be used to construct transition probabilities between states for future games, and ultimately, absorbing probabilities of goal states. Our approach effectively predicts match outcomes using team ratings for forward, midfield and defensive systems and is sufficiently interpretable to support strategic decision-making by coaching departments in the Australian Football League (AFL).","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"32 1","pages":"215 - 226"},"PeriodicalIF":0.8,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72969644","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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