Abstract Spatial point processes have been successfully used to model the relative efficiency of shot locations for each player in professional basketball games. Those analyses were possible because each player makes enough baskets to reliably fit a point process model. Goals in hockey are rare enough that a point process cannot be fit to each player’s goal locations, so novel techniques are needed to obtain measures of shot efficiency for each player. A Log-Gaussian Cox Process (LGCP) is used to model all shot locations, including goals, of each NHL player who took at least 500 shots during the 2011–2018 seasons. Each player’s LGCP surface is treated as an image and these images are then used in an unsupervised statistical learning algorithm that decomposes the pictures into a linear combination of spatial basis functions. The coefficients of these basis functions are shown to be a very useful tool to compare players. To incorporate goals, the locations of all shots that resulted in a goal are treated as a “perfect player” and used in the same algorithm (goals are further split into perfect forwards, perfect centres and perfect defence). These perfect players are compared to other players as a measure of shot efficiency. This analysis provides a map of common shooting locations, identifies regions with the most goals relative to the number of shots and demonstrates how each player’s shot location differs from scoring locations.
{"title":"Algorithmically deconstructing shot locations as a method for shot quality in hockey","authors":"Devan G. Becker, D. Woolford, C. Dean","doi":"10.1515/jqas-2020-0012","DOIUrl":"https://doi.org/10.1515/jqas-2020-0012","url":null,"abstract":"Abstract Spatial point processes have been successfully used to model the relative efficiency of shot locations for each player in professional basketball games. Those analyses were possible because each player makes enough baskets to reliably fit a point process model. Goals in hockey are rare enough that a point process cannot be fit to each player’s goal locations, so novel techniques are needed to obtain measures of shot efficiency for each player. A Log-Gaussian Cox Process (LGCP) is used to model all shot locations, including goals, of each NHL player who took at least 500 shots during the 2011–2018 seasons. Each player’s LGCP surface is treated as an image and these images are then used in an unsupervised statistical learning algorithm that decomposes the pictures into a linear combination of spatial basis functions. The coefficients of these basis functions are shown to be a very useful tool to compare players. To incorporate goals, the locations of all shots that resulted in a goal are treated as a “perfect player” and used in the same algorithm (goals are further split into perfect forwards, perfect centres and perfect defence). These perfect players are compared to other players as a measure of shot efficiency. This analysis provides a map of common shooting locations, identifies regions with the most goals relative to the number of shots and demonstrates how each player’s shot location differs from scoring locations.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82534789","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}
Stephen Devlin, T. Treloar, Molly Creagar, S. Cassels
Abstract We introduce a simple and natural iterative version of the well-known and widely studied Markov rating method. We show that this iterative Markov method converges to the usual global Markov rating, and shares a close relationship with the well-known Elo rating. Together with recent results on the relationship between the global Markov method and the maximum likelihood estimate of the rating vector in the Bradley–Terry (BT) model, we connect and explore the global and iterative Markov, Elo, and Bradley–Terry ratings on real and simulated data.
{"title":"An iterative Markov rating method","authors":"Stephen Devlin, T. Treloar, Molly Creagar, S. Cassels","doi":"10.1515/jqas-2019-0070","DOIUrl":"https://doi.org/10.1515/jqas-2019-0070","url":null,"abstract":"Abstract We introduce a simple and natural iterative version of the well-known and widely studied Markov rating method. We show that this iterative Markov method converges to the usual global Markov rating, and shares a close relationship with the well-known Elo rating. Together with recent results on the relationship between the global Markov method and the maximum likelihood estimate of the rating vector in the Bradley–Terry (BT) model, we connect and explore the global and iterative Markov, Elo, and Bradley–Terry ratings on real and simulated data.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89543112","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 Trail running is an endurance sport in which athletes face severe physical challenges. Due to the growing number of participants, the organization of limited staff, equipment, and medical support in these races now plays a key role. Monitoring runner’s performance is a difficult task that requires knowledge of the terrain and of the runner’s ability. In the past, choices were solely based on the organizers’ experience without reliance on data. However, this approach is neither scalable nor transferable. Instead, we propose a firm statistical methodology to perform this task, both before and during the race. Our proposed framework, Trail Running Assessment of Performance (TRAP), studies (1) the assessment of the runner’s ability to reach the next checkpoint, (2) the prediction of the runner’s expected passage time at the next checkpoint, and (3) corresponding prediction intervals for the passage time. We apply our methodology, using the race history of runners from the International Trail Running Association (ITRA) along with checkpoint and terrain-level information, to the “holy grail” of ultra-trail running, the Ultra-Trail du Mont-Blanc (UTMB) race, demonstrating the predictive power of our methodology.
{"title":"TRAP: a predictive framework for the Assessment of Performance in Trail Running","authors":"Riccardo Fogliato, N. L. Oliveira, Ronald Yurko","doi":"10.1515/JQAS-2020-0013","DOIUrl":"https://doi.org/10.1515/JQAS-2020-0013","url":null,"abstract":"Abstract Trail running is an endurance sport in which athletes face severe physical challenges. Due to the growing number of participants, the organization of limited staff, equipment, and medical support in these races now plays a key role. Monitoring runner’s performance is a difficult task that requires knowledge of the terrain and of the runner’s ability. In the past, choices were solely based on the organizers’ experience without reliance on data. However, this approach is neither scalable nor transferable. Instead, we propose a firm statistical methodology to perform this task, both before and during the race. Our proposed framework, Trail Running Assessment of Performance (TRAP), studies (1) the assessment of the runner’s ability to reach the next checkpoint, (2) the prediction of the runner’s expected passage time at the next checkpoint, and (3) corresponding prediction intervals for the passage time. We apply our methodology, using the race history of runners from the International Trail Running Association (ITRA) along with checkpoint and terrain-level information, to the “holy grail” of ultra-trail running, the Ultra-Trail du Mont-Blanc (UTMB) race, demonstrating the predictive power of our methodology.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73494087","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 order to make comparisons of competitive balance across sports leagues, we need to take into account how different season lengths influence observed measures of balance. We develop the first measures of competitive balance that are invariant to season length. The most commonly used measure, the ASD/ISD or Noll-Scully ratio, is biased. It artificially inflates the imbalance for leagues with long seasons (e.g., MLB) compared to those with short seasons (e.g., NFL). We provide a general model of competition that leads to unbiased variance estimates. The result is a new ordering across leagues: the NFL goes from having the most balance to being tied for the least, while MLB becomes the sport with the most balance. Our model also provides insight into competitive balance at the game level. We shift attention from team-level to game-level measures as these are more directly related to the predictability of a representative contest. Finally, we measure competitive balance at the season level. We do so by looking at the predictability of the final rankings as seen from the start of the season. Here the NBA stands out for having the most predictable results and hence the lowest full-season competitive balance.
{"title":"Measuring competitive balance in sports","authors":"Matthew Doria, B. Nalebuff","doi":"10.1515/jqas-2020-0006","DOIUrl":"https://doi.org/10.1515/jqas-2020-0006","url":null,"abstract":"Abstract In order to make comparisons of competitive balance across sports leagues, we need to take into account how different season lengths influence observed measures of balance. We develop the first measures of competitive balance that are invariant to season length. The most commonly used measure, the ASD/ISD or Noll-Scully ratio, is biased. It artificially inflates the imbalance for leagues with long seasons (e.g., MLB) compared to those with short seasons (e.g., NFL). We provide a general model of competition that leads to unbiased variance estimates. The result is a new ordering across leagues: the NFL goes from having the most balance to being tied for the least, while MLB becomes the sport with the most balance. Our model also provides insight into competitive balance at the game level. We shift attention from team-level to game-level measures as these are more directly related to the predictability of a representative contest. Finally, we measure competitive balance at the season level. We do so by looking at the predictability of the final rankings as seen from the start of the season. Here the NBA stands out for having the most predictable results and hence the lowest full-season competitive balance.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85137780","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}
Drawing on the golf-related example of regression to the mean as presented by Kahneman in his best-selling book, Thinking Fast and Slow, this study shows how the regression-to-the-mean phenomenon is revealed in first- and second-round scoring in 11 different golfer populations, ranging from golfers with the highest level of skill (professional golfers on the PGA TOUR) to amateur groups of much lower skill. Using the mathematics of truncated normal distributions, the study introduces a new method for estimating the mix between variation in scoring due to differences in player skill and that due to luck. Estimates of the skill/luck mix are very close to those obtained using the regression-based methodology of Morrison and are nearly identical to those implied by fixed effects regression models where fixed player and round effects are estimated simultaneously. The study also sheds light on the “paradox of skill,” originally suggested by Gould and developed further by Mauboussin, as it relates to golf by showing that luck plays a more important role in determining player scores in higher-skilled golfer groups compared with lower-skilled groups.
Kahneman在他的畅销书《思考快与慢》(Thinking Fast and Slow)中提出了与高尔夫相关的回归均值的例子，这项研究显示了回归均值现象是如何在11个不同的高尔夫球手群体的第一轮和第二轮得分中揭示出来的，这些人群包括技术水平最高的高尔夫球手(PGA巡回赛的职业高尔夫球手)和技术水平低得多的业余群体。利用截断正态分布的数学，该研究引入了一种新方法来估计由于玩家技能差异和运气差异而导致的得分变化之间的混合。技能/运气组合的估计值与使用Morrison基于回归的方法所获得的估计值非常接近，并且与固定效果回归模型所暗示的估计值几乎相同，其中固定玩家和回合效果是同时估计的。这项研究还揭示了“技能悖论”，这个悖论最初由古尔德提出，后来由莫布森进一步发展，因为它与高尔夫球有关，表明在决定高技能高尔夫球手群体的得分方面，运气起着比低技能群体更重要的作用。
{"title":"The relative roles of skill and luck within 11 different golfer populations","authors":"Richard J. Rendleman","doi":"10.1515/JQAS-2019-0028","DOIUrl":"https://doi.org/10.1515/JQAS-2019-0028","url":null,"abstract":"Drawing on the golf-related example of regression to the mean as presented by Kahneman in his best-selling book, Thinking Fast and Slow, this study shows how the regression-to-the-mean phenomenon is revealed in first- and second-round scoring in 11 different golfer populations, ranging from golfers with the highest level of skill (professional golfers on the PGA TOUR) to amateur groups of much lower skill. Using the mathematics of truncated normal distributions, the study introduces a new method for estimating the mix between variation in scoring due to differences in player skill and that due to luck. Estimates of the skill/luck mix are very close to those obtained using the regression-based methodology of Morrison and are nearly identical to those implied by fixed effects regression models where fixed player and round effects are estimated simultaneously. The study also sheds light on the “paradox of skill,” originally suggested by Gould and developed further by Mauboussin, as it relates to golf by showing that luck plays a more important role in determining player scores in higher-skilled golfer groups compared with lower-skilled groups.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77994278","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}
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":null,"pages":null},"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 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":null,"pages":null},"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}
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":null,"pages":null},"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}
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":null,"pages":null},"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":null,"pages":null},"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}
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