Abstract In this work, we deal with the problem of rating in sports, where the skills of the players/teams are inferred from the observed outcomes of the games. Our focus is on the on-line rating algorithms that estimate skills after each new game by exploiting the probabilistic models that (i) relate the skills to the outcome of the game and (ii) describe how the skills evolve in time. We propose a Bayesian approach which may be seen as an approximate Kalman filter and which is generic in the sense that it can be used with any skills-outcome model and can be applied in the individual as well as in the group sports. We show how the well-known Elo, Glicko, and TrueSkill algorithms may be seen as instances of the one-fits-all approach we propose. To clarify the conditions under which the gains of the Bayesian approach over simpler solutions can actually materialize, we critically compare the known and new algorithms by means of numerical examples using synthetic and empirical data.
{"title":"Simplified Kalman filter for on-line rating: one-fits-all approach","authors":"L. Szczecinski, Raphaëlle Tihon","doi":"10.1515/jqas-2021-0061","DOIUrl":"https://doi.org/10.1515/jqas-2021-0061","url":null,"abstract":"Abstract In this work, we deal with the problem of rating in sports, where the skills of the players/teams are inferred from the observed outcomes of the games. Our focus is on the on-line rating algorithms that estimate skills after each new game by exploiting the probabilistic models that (i) relate the skills to the outcome of the game and (ii) describe how the skills evolve in time. We propose a Bayesian approach which may be seen as an approximate Kalman filter and which is generic in the sense that it can be used with any skills-outcome model and can be applied in the individual as well as in the group sports. We show how the well-known Elo, Glicko, and TrueSkill algorithms may be seen as instances of the one-fits-all approach we propose. To clarify the conditions under which the gains of the Bayesian approach over simpler solutions can actually materialize, we critically compare the known and new algorithms by means of numerical examples using synthetic and empirical data.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83750473","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 2019, Eliud Kipchoge ran a sub-two hour marathon wearing Nike’s Alphafly shoes. Despite being the fastest marathon time ever recorded, it wasn’t officially recognized as race conditions were tightly controlled to maximize his success. Besides, Kipchoge’s use of Alphafly shoes was controversial, with some experts claiming that they might have provided an unfair competitive advantage. In this work, we assess the potential influence of advanced footwear technology and the likelihood of a sub-two hour marathon in official races, by studying the evolution of running top performances from 2001 to 2019 for long distances ranging from 10 km to marathon. The analysis is performed using extreme value theory, a field of statistics dealing with analysis of rare events. We find a significant evidence of performance-enhancement effect with a 10% increase of the probability that a new world record for marathon-men discipline is set in 2021. However, results suggest that achieving a sub-two hour marathon in an official race in 2021 is still very unlikely, and exceeds 10% probability only by 2025.
{"title":"Influence of advanced footwear technology on sub-2 hour marathon and other top running performances","authors":"Andreu Arderiu, Raphaël de Fondeville","doi":"10.1515/jqas-2021-0043","DOIUrl":"https://doi.org/10.1515/jqas-2021-0043","url":null,"abstract":"Abstract In 2019, Eliud Kipchoge ran a sub-two hour marathon wearing Nike’s Alphafly shoes. Despite being the fastest marathon time ever recorded, it wasn’t officially recognized as race conditions were tightly controlled to maximize his success. Besides, Kipchoge’s use of Alphafly shoes was controversial, with some experts claiming that they might have provided an unfair competitive advantage. In this work, we assess the potential influence of advanced footwear technology and the likelihood of a sub-two hour marathon in official races, by studying the evolution of running top performances from 2001 to 2019 for long distances ranging from 10 km to marathon. The analysis is performed using extreme value theory, a field of statistics dealing with analysis of rare events. We find a significant evidence of performance-enhancement effect with a 10% increase of the probability that a new world record for marathon-men discipline is set in 2021. However, results suggest that achieving a sub-two hour marathon in an official race in 2021 is still very unlikely, and exceeds 10% probability only by 2025.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77299328","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 With the vast amount of data collected on football and the growth of computing power, many games involving decision choices can be optimized. The underlying rule is the maximization of an expected utility of outcomes and the law of large numbers. The data available allows one to compute with high accuracy the probabilities of outcomes of actions, and the well defined points system in the game allows for a specification of the terminal utilities. With some well established decision theory we can optimize choices for each single play level. A full exposition of the theory and analysis is presented in the paper.
{"title":"A reinforcement learning based approach to play calling in football","authors":"Preston Biro, S. Walker","doi":"10.1515/jqas-2021-0029","DOIUrl":"https://doi.org/10.1515/jqas-2021-0029","url":null,"abstract":"Abstract With the vast amount of data collected on football and the growth of computing power, many games involving decision choices can be optimized. The underlying rule is the maximization of an expected utility of outcomes and the law of large numbers. The data available allows one to compute with high accuracy the probabilities of outcomes of actions, and the well defined points system in the game allows for a specification of the terminal utilities. With some well established decision theory we can optimize choices for each single play level. A full exposition of the theory and analysis is presented in the paper.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78506004","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 : 2021-01-11DOI: 10.1515/jqas-2021-frontmatter1
{"title":"Frontmatter","authors":"","doi":"10.1515/jqas-2021-frontmatter1","DOIUrl":"https://doi.org/10.1515/jqas-2021-frontmatter1","url":null,"abstract":"","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87316480","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 Elo rating system, originally designed for rating chess players, has since become a popular way to estimate competitors’ time-varying skills in many sports. Though the self-correcting Elo algorithm is simple and intuitive, it lacks a probabilistic justification which can make it hard to extend. In this paper, we present a simple connection between approximate Bayesian posterior mode estimation and Elo. We provide a novel justification of the approximations made by linking Elo to steady-state Kalman filtering. Our second key contribution is to observe that the derivation suggests a straightforward procedure for extending Elo. We use the procedure to derive versions of Elo incorporating margins of victory, correlated skills across different playing surfaces, and differing skills by tournament level in tennis. Combining all these extensions results in the most complete version of Elo presented for the sport yet. We evaluate the derived models on two seasons of men’s professional tennis matches (2018 and 2019). The best-performing model was able to predict matches with higher accuracy than both Elo and Glicko (65.8% compared to 63.7 and 63.5%, respectively) and a higher mean log-likelihood (−0.615 compared to −0.632 and −0.633, respectively), demonstrating the proposed model’s ability to improve predictions.
{"title":"How to extend Elo: a Bayesian perspective","authors":"Martin Ingram","doi":"10.1515/JQAS-2020-0066","DOIUrl":"https://doi.org/10.1515/JQAS-2020-0066","url":null,"abstract":"Abstract The Elo rating system, originally designed for rating chess players, has since become a popular way to estimate competitors’ time-varying skills in many sports. Though the self-correcting Elo algorithm is simple and intuitive, it lacks a probabilistic justification which can make it hard to extend. In this paper, we present a simple connection between approximate Bayesian posterior mode estimation and Elo. We provide a novel justification of the approximations made by linking Elo to steady-state Kalman filtering. Our second key contribution is to observe that the derivation suggests a straightforward procedure for extending Elo. We use the procedure to derive versions of Elo incorporating margins of victory, correlated skills across different playing surfaces, and differing skills by tournament level in tennis. Combining all these extensions results in the most complete version of Elo presented for the sport yet. We evaluate the derived models on two seasons of men’s professional tennis matches (2018 and 2019). The best-performing model was able to predict matches with higher accuracy than both Elo and Glicko (65.8% compared to 63.7 and 63.5%, respectively) and a higher mean log-likelihood (−0.615 compared to −0.632 and −0.633, respectively), demonstrating the proposed model’s ability to improve predictions.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90609468","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 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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
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