C. Avinash, DiPietro Loretta, Young Heather, Elmi Angelo
In assessments of sports-related injury severity, time loss (TL) is measured as a count of days lost to injury and analyzed using ordinal cut points. This approach ignores various athlete and event-specific factors that determine the severity of an injury. We present a conceptual framework for modeling this outcome using univariate random effects count or survival regression. Using a sample of US collegiate soccer-related injury observations, we fit random effects Poisson and Weibull Regression models to perform “severity-adjusted” evaluations of TL, and use our models to make inferences regarding the recovery process. Injury site, injury mechanism and injury history emerged as the strongest predictors in our sample. In comparing random and fixed effects models, we noted that the incorporation of the random effect attenuated associations between most observed covariates and TL, and model fit statistics revealed that the random effects models (AICPoisson = 51875.20; AICWeibull-AFT = 51113.00) improved model fit over the fixed effects models (AICPoisson = 160695.20; AICWeibull-AFT = 53179.00). Our analyses serve as a useful starting point for modeling how TL may actually occur when a player is injured, and suggest that random effects or frailty based approaches can help isolate the effect of potential determinants of TL.
{"title":"Modeling time loss from sports-related injuries using random effects models: an illustration using soccer-related injury observations","authors":"C. Avinash, DiPietro Loretta, Young Heather, Elmi Angelo","doi":"10.1515/JQAS-2019-0030","DOIUrl":"https://doi.org/10.1515/JQAS-2019-0030","url":null,"abstract":"In assessments of sports-related injury severity, time loss (TL) is measured as a count of days lost to injury and analyzed using ordinal cut points. This approach ignores various athlete and event-specific factors that determine the severity of an injury. We present a conceptual framework for modeling this outcome using univariate random effects count or survival regression. Using a sample of US collegiate soccer-related injury observations, we fit random effects Poisson and Weibull Regression models to perform “severity-adjusted” evaluations of TL, and use our models to make inferences regarding the recovery process. Injury site, injury mechanism and injury history emerged as the strongest predictors in our sample. In comparing random and fixed effects models, we noted that the incorporation of the random effect attenuated associations between most observed covariates and TL, and model fit statistics revealed that the random effects models (AICPoisson = 51875.20; AICWeibull-AFT = 51113.00) improved model fit over the fixed effects models (AICPoisson = 160695.20; AICWeibull-AFT = 53179.00). Our analyses serve as a useful starting point for modeling how TL may actually occur when a player is injured, and suggest that random effects or frailty based approaches can help isolate the effect of potential determinants of TL.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"15 1","pages":"221-235"},"PeriodicalIF":0.8,"publicationDate":"2020-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82611389","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 Vast data on eSports should be easily accessible but often is not. League of Legends (LoL) only has rudimentary statistics such as levels, items, gold, and deaths. We present a new way to capture more useful data. We track every champion’s location multiple times every second. We track every ability cast and attack made, all damages caused and avoided, vision, health, mana, and cooldowns. We track continuously, invisibly, remotely, and live. Using a combination of computer vision, dynamic client hooks, machine learning, visualization, logistic regression, large-scale cloud computing, and fast and frugal trees, we generate this new high-frequency data on millions of ranked LoL games, calibrate an in-game win probability model, develop enhanced definitions for standard metrics, introduce dozens more advanced metrics, automate player improvement analysis, and apply a new player-evaluation framework on the basic and advanced stats. How much does an individual contribute to a team’s performance? We find that individual actions conditioned on changes to estimated win probability correlate almost perfectly to team performance: regular kills and deaths do not nearly explain as much as smart kills and worthless deaths. Our approach offers applications for other eSports and traditional sports. All the code is open-sourced.
{"title":"Smart kills and worthless deaths: eSports analytics for League of Legends","authors":"Philip Z. Maymin","doi":"10.1515/jqas-2019-0096","DOIUrl":"https://doi.org/10.1515/jqas-2019-0096","url":null,"abstract":"Abstract Vast data on eSports should be easily accessible but often is not. League of Legends (LoL) only has rudimentary statistics such as levels, items, gold, and deaths. We present a new way to capture more useful data. We track every champion’s location multiple times every second. We track every ability cast and attack made, all damages caused and avoided, vision, health, mana, and cooldowns. We track continuously, invisibly, remotely, and live. Using a combination of computer vision, dynamic client hooks, machine learning, visualization, logistic regression, large-scale cloud computing, and fast and frugal trees, we generate this new high-frequency data on millions of ranked LoL games, calibrate an in-game win probability model, develop enhanced definitions for standard metrics, introduce dozens more advanced metrics, automate player improvement analysis, and apply a new player-evaluation framework on the basic and advanced stats. How much does an individual contribute to a team’s performance? We find that individual actions conditioned on changes to estimated win probability correlate almost perfectly to team performance: regular kills and deaths do not nearly explain as much as smart kills and worthless deaths. Our approach offers applications for other eSports and traditional sports. All the code is open-sourced.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"19 3 1","pages":"11 - 27"},"PeriodicalIF":0.8,"publicationDate":"2020-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83284203","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 paper, we investigate the correlation between the main physical characteristics of eight variants of football and hockey (such as field size, goal size, player velocity, ball velocity, player density, and game duration) and the resulting average numbers of goals scored per game. To do so, the Pi-theorem in physics is extended to sport science and a non-dimensional parameter of interest is defined. It is based on the ratio between the duration of the game and the order of magnitude of the time needed to cross the midfield, which depends on the average velocity of the ball and the players, the player density and the size of the goals. An excellent correlation is found between the proposed parameter and the average number of goals scored per game during recent international competitions. Using the derived correlation, the effect of any modification of the main characteristics of football and hockey (and their variants) on the scoring pace can be assessed. For instance, it can be predicted that decreasing the length of football fields by 20 m would raise the average number of goals scored to 3.6 (±0.6) per game, versus the 2.6 goals scored during the most recent men’s World Cup.
{"title":"The influence of field size, goal size and number of players on the average number of goals scored per game in variants of football and hockey: the Pi-theorem applied to team sports","authors":"J. Blondeau","doi":"10.1515/JQAS-2020-0009","DOIUrl":"https://doi.org/10.1515/JQAS-2020-0009","url":null,"abstract":"Abstract In this paper, we investigate the correlation between the main physical characteristics of eight variants of football and hockey (such as field size, goal size, player velocity, ball velocity, player density, and game duration) and the resulting average numbers of goals scored per game. To do so, the Pi-theorem in physics is extended to sport science and a non-dimensional parameter of interest is defined. It is based on the ratio between the duration of the game and the order of magnitude of the time needed to cross the midfield, which depends on the average velocity of the ball and the players, the player density and the size of the goals. An excellent correlation is found between the proposed parameter and the average number of goals scored per game during recent international competitions. Using the derived correlation, the effect of any modification of the main characteristics of football and hockey (and their variants) on the scoring pace can be assessed. For instance, it can be predicted that decreasing the length of football fields by 20 m would raise the average number of goals scored to 3.6 (±0.6) per game, versus the 2.6 goals scored during the most recent men’s World Cup.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"46 1","pages":"145 - 154"},"PeriodicalIF":0.8,"publicationDate":"2020-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74968437","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}
Elizabeth L. Bouzarth, B. Grannan, John M Harris, A. Hartley, K. Hutson, E. Morton
Abstract Defensive repositioning strategies (shifts) have become more prevalent in Major League Baseball in recent years. In 2018, batters faced some form of the shift in 34% of their plate appearances (Sawchik, Travis. 2019. “Don’t Worry, MLB–Hitters Are Killing The Shift On Their Own.” FiveThirtyEight, January 17, 2019. Also available at fivethirtyeight.com/features/dont-worry-mlb-hitters-are-killing-the-shift-on-their-own/). Most teams use a shift that overloads one side of the infield and adjusts the positioning of the outfield. In this work we describe a mathematical approach to the positioning of players over the entire field of play without the limitations of traditional positions or current methods of shifting. The model uses historical data for individual batters, and it leaves open the possibility of fewer than four infielders. The model also incorporates risk penalties for positioning players too far from areas of the field in which extra-base hits are more likely. This work is meant to serve as a decision-making tool for coaches and managers to best use their defensive assets. Our simulations show that an optimal positioning with three infielders lowered predicted batting average on balls in play (BABIP) by 5.9% for right-handers and by 10.3% for left-handers on average when compared to a standard four-infielder placement of players.
{"title":"Swing shift: a mathematical approach to defensive positioning in baseball","authors":"Elizabeth L. Bouzarth, B. Grannan, John M Harris, A. Hartley, K. Hutson, E. Morton","doi":"10.1515/jqas-2020-0027","DOIUrl":"https://doi.org/10.1515/jqas-2020-0027","url":null,"abstract":"Abstract Defensive repositioning strategies (shifts) have become more prevalent in Major League Baseball in recent years. In 2018, batters faced some form of the shift in 34% of their plate appearances (Sawchik, Travis. 2019. “Don’t Worry, MLB–Hitters Are Killing The Shift On Their Own.” FiveThirtyEight, January 17, 2019. Also available at fivethirtyeight.com/features/dont-worry-mlb-hitters-are-killing-the-shift-on-their-own/). Most teams use a shift that overloads one side of the infield and adjusts the positioning of the outfield. In this work we describe a mathematical approach to the positioning of players over the entire field of play without the limitations of traditional positions or current methods of shifting. The model uses historical data for individual batters, and it leaves open the possibility of fewer than four infielders. The model also incorporates risk penalties for positioning players too far from areas of the field in which extra-base hits are more likely. This work is meant to serve as a decision-making tool for coaches and managers to best use their defensive assets. Our simulations show that an optimal positioning with three infielders lowered predicted batting average on balls in play (BABIP) by 5.9% for right-handers and by 10.3% for left-handers on average when compared to a standard four-infielder placement of players.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"1942 1","pages":"47 - 55"},"PeriodicalIF":0.8,"publicationDate":"2020-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91187229","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 action of crossing the ball in soccer has a long history as an effective tactic for producing goals. Lately, the benefit of crossing the ball has come under question, and alternative strategies have been suggested. This paper utilizes player tracking data to explore crossing at a deeper level. First, we investigate the spatio-temporal conditions that lead to crossing. Then we introduce an intended target model that investigates crossing success. Finally, a contextual analysis is provided that assesses the benefits of crossing in various situations. The analysis is based on causal inference techniques and suggests that crossing remains an effective tactic in particular contexts.
{"title":"A contextual analysis of crossing the ball in soccer","authors":"Lucas Y. Wu, Aaron Danielson, X. J. Hu, T. Swartz","doi":"10.1515/jqas-2020-0060","DOIUrl":"https://doi.org/10.1515/jqas-2020-0060","url":null,"abstract":"Abstract The action of crossing the ball in soccer has a long history as an effective tactic for producing goals. Lately, the benefit of crossing the ball has come under question, and alternative strategies have been suggested. This paper utilizes player tracking data to explore crossing at a deeper level. First, we investigate the spatio-temporal conditions that lead to crossing. Then we introduce an intended target model that investigates crossing success. Finally, a contextual analysis is provided that assesses the benefits of crossing in various situations. The analysis is based on causal inference techniques and suggests that crossing remains an effective tactic in particular contexts.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"36 1","pages":"57 - 66"},"PeriodicalIF":0.8,"publicationDate":"2020-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85154465","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 investigates the fouling time distribution of players in the National Basketball Association. A Bayesian analysis is presented based on the assumption that fouling time distributions follow a gamma distribution. Various insights are obtained including the observation that players accumulate fouls at a rate that increases with the current number of fouls. We demonstrate possible ways to incorporate the fouling time distributions to provide decision support to coaches in the management of playing time.
{"title":"Foul accumulation in the NBA","authors":"Dani Chu","doi":"10.1515/jqas-2019-0119","DOIUrl":"https://doi.org/10.1515/jqas-2019-0119","url":null,"abstract":"Abstract This paper investigates the fouling time distribution of players in the National Basketball Association. A Bayesian analysis is presented based on the assumption that fouling time distributions follow a gamma distribution. Various insights are obtained including the observation that players accumulate fouls at a rate that increases with the current number of fouls. We demonstrate possible ways to incorporate the fouling time distributions to provide decision support to coaches in the management of playing time.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"10 1","pages":"301 - 309"},"PeriodicalIF":0.8,"publicationDate":"2020-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87587976","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 : 2020-09-01DOI: 10.1515/jqas-2020-frontmatter3
{"title":"Frontmatter","authors":"","doi":"10.1515/jqas-2020-frontmatter3","DOIUrl":"https://doi.org/10.1515/jqas-2020-frontmatter3","url":null,"abstract":"","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"3 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85251101","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}
Daniele Gambarelli, G. Gambarelli, Dries R. Goossens
{"title":"Corrigendum to: Offensive or defensive play in soccer: a game-theoretical approach","authors":"Daniele Gambarelli, G. Gambarelli, Dries R. Goossens","doi":"10.1515/jqas-2020-0080","DOIUrl":"https://doi.org/10.1515/jqas-2020-0080","url":null,"abstract":"","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"46 1","pages":"343 - 343"},"PeriodicalIF":0.8,"publicationDate":"2020-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76920080","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 recently concluded 2019 World Swimming Championships was another major swimming competition that witnessed some great progresses achieved by human athletes in many events. However, some world records created 10 years ago back in the era of high-tech swimsuits remained untouched. With the advancements in technical skills and training methods in the past decade, the inability to break those world records is a strong indication that records with the swimsuit bonus cannot reflect the real progressions achieved by human athletes in history. Many swimming professionals and enthusiasts are eager to know a measure of the real world records had the high-tech swimsuits never been allowed. This paper attempts to restore the real world records in Men’s swimming without high-tech swimsuits by integrating various advanced methods in probabilistic modeling and optimization. Through the modeling and separation of swimsuit bias, natural improvement, and athletes’ intrinsic performance, the result of this paper provides the optimal estimates and the 95% confidence intervals for the real world records. The proposed methodology can also be applied to a variety of similar studies with multi-factor considerations.
{"title":"Restoring the real world records in Men’s swimming without high-tech swimsuits","authors":"Zhenyu Gao, Yixing Li, Zhengxin Wang","doi":"10.1515/jqas-2019-0087","DOIUrl":"https://doi.org/10.1515/jqas-2019-0087","url":null,"abstract":"Abstract The recently concluded 2019 World Swimming Championships was another major swimming competition that witnessed some great progresses achieved by human athletes in many events. However, some world records created 10 years ago back in the era of high-tech swimsuits remained untouched. With the advancements in technical skills and training methods in the past decade, the inability to break those world records is a strong indication that records with the swimsuit bonus cannot reflect the real progressions achieved by human athletes in history. Many swimming professionals and enthusiasts are eager to know a measure of the real world records had the high-tech swimsuits never been allowed. This paper attempts to restore the real world records in Men’s swimming without high-tech swimsuits by integrating various advanced methods in probabilistic modeling and optimization. Through the modeling and separation of swimsuit bias, natural improvement, and athletes’ intrinsic performance, the result of this paper provides the optimal estimates and the 95% confidence intervals for the real world records. The proposed methodology can also be applied to a variety of similar studies with multi-factor considerations.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"216 1","pages":"291 - 300"},"PeriodicalIF":0.8,"publicationDate":"2020-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91388380","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 Analytics and professional sports have become linked over the past several years, but little attention has been paid to the growing field of esports within the sports analytics community. We seek to apply an Adjusted Plus Minus (APM) model, an accepted analytic approach used in traditional sports like hockey and basketball, to one particular esports game: Defense of the Ancients 2 (Dota 2). As with traditional sports, we show how APM metrics developed with Bayesian hierarchical regression can be used to quantify individual player contributions to their teams and, ultimately, use this player-level information to predict game outcomes. In particular, we first provide evidence that gold can be used as a continuous proxy for wins to evaluate a team’s performance, and then use a Bayesian APM model to estimate how players contribute to their team’s gold differential. We demonstrate that this APM model outperforms models based on common team-level statistics (often referred to as “box score statistics”). Beyond the specifics of our modeling approach, this paper serves as an example of the potential utility of applying analytical methodologies from traditional sports analytics to esports.
在过去的几年里，分析学和职业体育联系在一起，但在体育分析界，很少有人关注电子竞技领域的发展。我们试图将调整正负(APM)模型应用于一款特定的电子竞技游戏:《Defense of the Ancients 2》(Dota 2)，这是一种传统体育项目(如曲棍球和篮球)中使用的公认分析方法。与传统体育项目一样，我们展示了如何使用贝叶斯层次回归开发APM指标来量化个人玩家对团队的贡献，并最终使用这些玩家级别的信息来预测游戏结果。特别是，我们首先提供了证据，证明金牌数可以作为衡量球队表现的连续指标，然后使用贝叶斯APM模型来估计球员对球队金牌数差异的贡献。我们证明了这个APM模型优于基于普通团队级别统计(通常称为“框得分统计”)的模型。除了我们的建模方法的细节之外，本文还作为将传统体育分析的分析方法应用于电子竞技的潜在效用的一个例子。
{"title":"A Bayesian adjusted plus-minus analysis for the esport Dota 2","authors":"Nicholas J. Clark, Brian Macdonald, Ian Kloo","doi":"10.1515/jqas-2019-0103","DOIUrl":"https://doi.org/10.1515/jqas-2019-0103","url":null,"abstract":"Abstract Analytics and professional sports have become linked over the past several years, but little attention has been paid to the growing field of esports within the sports analytics community. We seek to apply an Adjusted Plus Minus (APM) model, an accepted analytic approach used in traditional sports like hockey and basketball, to one particular esports game: Defense of the Ancients 2 (Dota 2). As with traditional sports, we show how APM metrics developed with Bayesian hierarchical regression can be used to quantify individual player contributions to their teams and, ultimately, use this player-level information to predict game outcomes. In particular, we first provide evidence that gold can be used as a continuous proxy for wins to evaluate a team’s performance, and then use a Bayesian APM model to estimate how players contribute to their team’s gold differential. We demonstrate that this APM model outperforms models based on common team-level statistics (often referred to as “box score statistics”). Beyond the specifics of our modeling approach, this paper serves as an example of the potential utility of applying analytical methodologies from traditional sports analytics to esports.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"28 1","pages":"325 - 341"},"PeriodicalIF":0.8,"publicationDate":"2020-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86655099","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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