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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
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