Abstract Soccer is undeniably the most popular sport world-wide and everyone from general managers and coaching staff to fans and media are interested in evaluating players’ performance. Metrics applied successfully in other sports, such as the (adjusted) +/− that allows for division of credit among a basketball team’s players, exhibit several challenges when applied to soccer due to severe co-linearities. Recently, a number of player evaluation metrics have been developed utilizing optical tracking data, but they are based on proprietary data. In this work, our objective is to develop an open framework that can estimate the expected contribution of a soccer player to his team’s winning chances using publicly available data. In particular, using data from (i) approximately 20,000 games from 11 European leagues over eight seasons, and, (ii) player ratings from the FIFA video game, we estimate through a Skellam regression model the importance of every line (attackers, midfielders, defenders and goalkeeping) in winning a soccer game. We consequently translate the model to expected league points added above a replacement player (eLPAR). This model can further be used as a guide for allocating a team’s salary budget to players based on their expected contributions on the pitch. We showcase similar applications using annual salary data from the English Premier League and identify evidence that in our dataset the market appears to under-value defensive line players relative to goalkeepers.
{"title":"A Skellam regression model for quantifying positional value in soccer","authors":"K. Pelechrinis, Wayne L. Winston","doi":"10.1515/JQAS-2019-0122","DOIUrl":"https://doi.org/10.1515/JQAS-2019-0122","url":null,"abstract":"Abstract Soccer is undeniably the most popular sport world-wide and everyone from general managers and coaching staff to fans and media are interested in evaluating players’ performance. Metrics applied successfully in other sports, such as the (adjusted) +/− that allows for division of credit among a basketball team’s players, exhibit several challenges when applied to soccer due to severe co-linearities. Recently, a number of player evaluation metrics have been developed utilizing optical tracking data, but they are based on proprietary data. In this work, our objective is to develop an open framework that can estimate the expected contribution of a soccer player to his team’s winning chances using publicly available data. In particular, using data from (i) approximately 20,000 games from 11 European leagues over eight seasons, and, (ii) player ratings from the FIFA video game, we estimate through a Skellam regression model the importance of every line (attackers, midfielders, defenders and goalkeeping) in winning a soccer game. We consequently translate the model to expected league points added above a replacement player (eLPAR). This model can further be used as a guide for allocating a team’s salary budget to players based on their expected contributions on the pitch. We showcase similar applications using annual salary data from the English Premier League and identify evidence that in our dataset the market appears to under-value defensive line players relative to goalkeepers.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"25 1","pages":"187 - 201"},"PeriodicalIF":0.8,"publicationDate":"2020-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82584379","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 : 2020-11-18DOI: 10.1515/jqas-2020-frontmatter4
{"title":"Frontmatter","authors":"","doi":"10.1515/jqas-2020-frontmatter4","DOIUrl":"https://doi.org/10.1515/jqas-2020-frontmatter4","url":null,"abstract":"","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"37 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81971614","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}
Else Marie Håland, Astrid Salte Wiig, L. M. Hvattum, M. Stålhane
Abstract In association football, a network flow motif describes how distinct players from a team are involved in a passing sequence. The flow motif encodes whether the same players appear several times in a passing sequence, and in which order the players make passes. This information has previously been used to classify the passing style of different teams. In this work, flow motifs are analyzed in terms of their effectiveness in terms of generating shots. Data from four seasons of the Norwegian top division are analyzed, using flow motifs representing subsequences of three passes. The analysis is performed with a generalized additive model (GAM), with a range of explanatory variables included. Findings include that motifs with fewer distinct players are less effective, and that motifs are more likely to lead to shots if the passes in the motif utilize a bigger area of the pitch.
{"title":"Evaluating the effectiveness of different network flow motifs in association football","authors":"Else Marie Håland, Astrid Salte Wiig, L. M. Hvattum, M. Stålhane","doi":"10.1515/jqas-2019-0097","DOIUrl":"https://doi.org/10.1515/jqas-2019-0097","url":null,"abstract":"Abstract In association football, a network flow motif describes how distinct players from a team are involved in a passing sequence. The flow motif encodes whether the same players appear several times in a passing sequence, and in which order the players make passes. This information has previously been used to classify the passing style of different teams. In this work, flow motifs are analyzed in terms of their effectiveness in terms of generating shots. Data from four seasons of the Norwegian top division are analyzed, using flow motifs representing subsequences of three passes. The analysis is performed with a generalized additive model (GAM), with a range of explanatory variables included. Findings include that motifs with fewer distinct players are less effective, and that motifs are more likely to lead to shots if the passes in the motif utilize a bigger area of the pitch.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"44 1","pages":"311 - 323"},"PeriodicalIF":0.8,"publicationDate":"2020-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85743050","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 Examining data for the 10 Olympic Games contested this century, we ask whether confirmation bias exists in judged events. We theorize that if such bias is present, then competitors in judged events should perform closer to predicted than competitors in non-judged events. Among a sample of over 5100 predicted medalists from the 10 Games, we find that, all else equal, the differences between ex-ante conventional wisdom and ex-post observed outcome are larger for competitors in timed events than for competitors in judged events. These results suggest that confirmation bias does potentially exist for judged events at the Olympic Games.
{"title":"Does confirmation bias exist in judged events at the Olympic Games?","authors":"Christiana E. Hilmer, Michael J. Hilmer","doi":"10.1515/jqas-2019-0043","DOIUrl":"https://doi.org/10.1515/jqas-2019-0043","url":null,"abstract":"Abstract Examining data for the 10 Olympic Games contested this century, we ask whether confirmation bias exists in judged events. We theorize that if such bias is present, then competitors in judged events should perform closer to predicted than competitors in non-judged events. Among a sample of over 5100 predicted medalists from the 10 Games, we find that, all else equal, the differences between ex-ante conventional wisdom and ex-post observed outcome are larger for competitors in timed events than for competitors in judged events. These results suggest that confirmation bias does potentially exist for judged events at the Olympic Games.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"26 1","pages":"1 - 10"},"PeriodicalIF":0.8,"publicationDate":"2020-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87258302","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 work we develop a new algorithm for rating of teams (or players) in one-on-one games by exploiting the observed difference of the game-points (such as goals), also known as a margin of victory (MOV). Our objective is to obtain the Elo-style algorithm whose operation is simple to implement and to understand intuitively. This is done in three steps: first, we define the probabilistic model between the teams’ skills and the discretized MOV variable: this generalizes the model underpinning the Elo algorithm, where the MOV variable is discretized into three categories (win/loss/draw). Second, with the formal probabilistic model at hand, the optimization required by the maximum likelihood rule is implemented via stochastic gradient; this yields simple online equations for the rating updates which are identical in their general form to those characteristic of the Elo algorithm: the main difference lies in the way the scores and the expected scores are defined. Third, we propose a simple method to estimate the coefficients of the model, and thus define the operation of the algorithm; it is done in a closed form using the historical data so the algorithm is tailored to the sport of interest and the coefficients defining its operation are determined in entirely transparent manner. The alternative, optimization-based strategy to find the coefficients is also presented. We show numerical examples based on the results of the association football of the English Premier League and the American football of the National Football League.
{"title":"G-Elo: generalization of the Elo algorithm by modeling the discretized margin of victory","authors":"L. Szczecinski","doi":"10.1515/jqas-2020-0115","DOIUrl":"https://doi.org/10.1515/jqas-2020-0115","url":null,"abstract":"Abstract In this work we develop a new algorithm for rating of teams (or players) in one-on-one games by exploiting the observed difference of the game-points (such as goals), also known as a margin of victory (MOV). Our objective is to obtain the Elo-style algorithm whose operation is simple to implement and to understand intuitively. This is done in three steps: first, we define the probabilistic model between the teams’ skills and the discretized MOV variable: this generalizes the model underpinning the Elo algorithm, where the MOV variable is discretized into three categories (win/loss/draw). Second, with the formal probabilistic model at hand, the optimization required by the maximum likelihood rule is implemented via stochastic gradient; this yields simple online equations for the rating updates which are identical in their general form to those characteristic of the Elo algorithm: the main difference lies in the way the scores and the expected scores are defined. Third, we propose a simple method to estimate the coefficients of the model, and thus define the operation of the algorithm; it is done in a closed form using the historical data so the algorithm is tailored to the sport of interest and the coefficients defining its operation are determined in entirely transparent manner. The alternative, optimization-based strategy to find the coefficients is also presented. We show numerical examples based on the results of the association football of the English Premier League and the American football of the National Football League.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":"124 1","pages":"1 - 14"},"PeriodicalIF":0.8,"publicationDate":"2020-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89446626","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 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":"43 1","pages":"107 - 115"},"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":"25 1","pages":"117 - 127"},"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":"27 1","pages":"129 - 143"},"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":"30 1","pages":"29 - 46"},"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":"18 1","pages":"237-254"},"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}
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