Plus-minus is a widely used performance metric in sports. Players with high plus-minus ratings are often considered more efficient than others. While numerous plus-minus models have emerged since the introduction of adjusted plus-minus in 2004, most of these metrics focus on evaluating player performance at the individual level. In the present study, we follow the plus-minus framework and adopt a hierarchical Bayesian linear model to estimate plus-minus at the position level in the NBA from 2015–16 to 2021–22. Results show that players with versatile offensive skills and big players who defend the paint area are the most valuable offensive and defensive contributors respectively. We also find that the gaps in offensive plus-minus between offensive position groups have decreased over time. Overall, our analysis offers valuable information regarding average positional values in the NBA, allowing more objective player comparisons within position groups. We also show improved prediction accuracy in player plus-minus when factoring in player positions.
正负值是体育运动中广泛使用的一项成绩指标。正负值高的球员通常被认为比其他球员更有效率。自 2004 年引入调整正负值以来，出现了许多正负值模型，但这些指标大多侧重于评估球员个人层面的表现。在本研究中，我们遵循正负值框架，采用分层贝叶斯线性模型来估算 2015-16 至 2021-22 年 NBA 球员在位置层面的正负值。结果显示，进攻技能全面的球员和防守油漆区的大个球员分别是最有价值的进攻和防守贡献者。我们还发现，随着时间的推移，进攻位置组之间的进攻正负值差距有所缩小。总体而言，我们的分析提供了有关 NBA 平均位置价值的宝贵信息，使位置组内的球员比较更加客观。我们还显示，在考虑球员位置因素时，对球员正负值的预测准确性有所提高。
{"title":"Estimating positional plus-minus in the NBA","authors":"Hua Gong, Su Chen","doi":"10.1515/jqas-2022-0120","DOIUrl":"https://doi.org/10.1515/jqas-2022-0120","url":null,"abstract":"\u0000 Plus-minus is a widely used performance metric in sports. Players with high plus-minus ratings are often considered more efficient than others. While numerous plus-minus models have emerged since the introduction of adjusted plus-minus in 2004, most of these metrics focus on evaluating player performance at the individual level. In the present study, we follow the plus-minus framework and adopt a hierarchical Bayesian linear model to estimate plus-minus at the position level in the NBA from 2015–16 to 2021–22. Results show that players with versatile offensive skills and big players who defend the paint area are the most valuable offensive and defensive contributors respectively. We also find that the gaps in offensive plus-minus between offensive position groups have decreased over time. Overall, our analysis offers valuable information regarding average positional values in the NBA, allowing more objective player comparisons within position groups. We also show improved prediction accuracy in player plus-minus when factoring in player positions.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140658304","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}
The COVID-19 pandemic has led to a global shutdown of sporting activities. While professional sports competitions restarted in mid-2020, spectators were usually not allowed. This paper investigates the effect of absent fans and reduced social pressure on performance in professional darts – a setting where individual player performances can be well observed. Considering almost five years of tournament data, we use Bayesian multilevel models to investigate potential heterogeneity across players concerning reduced social pressure. For our analysis, we consider the two main performance measures in darts: the three-dart average and the checkout performance. Our results indicate that the effect of reduced social pressure on performance varies substantially across players. We further find experienced players to be less affected by social pressure compared to relatively inexperienced players.
{"title":"No cheering in the background? Individual performance in professional darts during COVID-19","authors":"Finn Spilker, Marius Ötting","doi":"10.1515/jqas-2022-0036","DOIUrl":"https://doi.org/10.1515/jqas-2022-0036","url":null,"abstract":"The COVID-19 pandemic has led to a global shutdown of sporting activities. While professional sports competitions restarted in mid-2020, spectators were usually not allowed. This paper investigates the effect of absent fans and reduced social pressure on performance in professional darts – a setting where individual player performances can be well observed. Considering almost five years of tournament data, we use Bayesian multilevel models to investigate potential heterogeneity across players concerning reduced social pressure. For our analysis, we consider the two main performance measures in darts: the three-dart average and the checkout performance. Our results indicate that the effect of reduced social pressure on performance varies substantially across players. We further find experienced players to be less affected by social pressure compared to relatively inexperienced players.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140582580","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}
Viktor Wolf, Ralf Lanwehr, Marcel Bieschke, Daniel Leyhr
Prior clustering approaches of soccer players have employed a variety of methods based on various data categories, but none of them have focused on clustering by career paths characterized through a time series analysis of yearly performance quality. Therefore, this study aims to propose a methodology how a career path can be represented as a time series of a player’s seasonal qualities and then be clustered with players that have a similar career path. The underlying data focuses on soccer players from the five largest European soccer nations (Big-5). This allows for the identification of different types of career paths of players and the investigation of significant disparities between career paths among the Big-5 nations. In line with our proposed methodological approach, we identified and interpreted 13 different clusters of player career paths. These range from the cluster with the highest player quality scores to the pattern comprising players with the weakest scores. Further, the detected clusters show significant differences regarding variables of soccer players’ early career phase in adolescence (e.g., age of debut in professional soccer, years spent in a youth academy). The presented approach might represent a first step for stakeholders in soccer to get an objective insight in players’ career by utilizing mainly freely available data sources.
{"title":"Career path clustering of elite soccer players among European Big-5 nations utilizing Dynamic Time Warping","authors":"Viktor Wolf, Ralf Lanwehr, Marcel Bieschke, Daniel Leyhr","doi":"10.1515/jqas-2023-0080","DOIUrl":"https://doi.org/10.1515/jqas-2023-0080","url":null,"abstract":"Prior clustering approaches of soccer players have employed a variety of methods based on various data categories, but none of them have focused on clustering by career paths characterized through a time series analysis of yearly performance quality. Therefore, this study aims to propose a methodology how a career path can be represented as a time series of a player’s seasonal qualities and then be clustered with players that have a similar career path. The underlying data focuses on soccer players from the five largest European soccer nations (Big-5). This allows for the identification of different types of career paths of players and the investigation of significant disparities between career paths among the Big-5 nations. In line with our proposed methodological approach, we identified and interpreted 13 different clusters of player career paths. These range from the cluster with the highest player quality scores to the pattern comprising players with the weakest scores. Further, the detected clusters show significant differences regarding variables of soccer players’ early career phase in adolescence (e.g., age of debut in professional soccer, years spent in a youth academy). The presented approach might represent a first step for stakeholders in soccer to get an objective insight in players’ career by utilizing mainly freely available data sources.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140582579","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}
Jonathan Arsenault, Margaret Cunniff, Eric Tulsky, James Richard Forbes
Special teams (i.e. power play and penalty kill) situations play an outsized role in determining the outcome of ice hockey games. Yet, quantitative methods for characterizing special teams tactics are limited. This work focuses on team structure and player deployment during in-zone special teams possessions. Leveraging player and puck tracking data from the National Hockey League (NHL), a framework is developed for describing player positioning during 5-on-4 power play and 4-on-5 penalty kill possessions. More specifically, player roles are defined directly from the player tracking data using non-negative matrix factorization, and every player is allocated a unique role at every frame of tracking data by solving a linear assignment problem. Team formations naturally arise through the combination of roles occupied in a frame. Roles that vary on a per-frame basis allow for a fine-grained analysis of team structure. This property of the roles-based representation is used to group together similar power play possessions using latent Dirichlet allocation, a topic modelling technique. The concept of assignments, which remain constant over an entire possession, is also introduced. Assignments provide a more stable measure of player positioning, which may be preferable when assessing deployment over longer periods of time.
{"title":"Spatial roles in hockey special teams","authors":"Jonathan Arsenault, Margaret Cunniff, Eric Tulsky, James Richard Forbes","doi":"10.1515/jqas-2023-0019","DOIUrl":"https://doi.org/10.1515/jqas-2023-0019","url":null,"abstract":"Special teams (i.e. power play and penalty kill) situations play an outsized role in determining the outcome of ice hockey games. Yet, quantitative methods for characterizing special teams tactics are limited. This work focuses on team structure and player deployment during in-zone special teams possessions. Leveraging player and puck tracking data from the National Hockey League (NHL), a framework is developed for describing player positioning during 5-on-4 power play and 4-on-5 penalty kill possessions. More specifically, player roles are defined directly from the player tracking data using non-negative matrix factorization, and every player is allocated a unique role at every frame of tracking data by solving a linear assignment problem. Team formations naturally arise through the combination of roles occupied in a frame. Roles that vary on a per-frame basis allow for a fine-grained analysis of team structure. This property of the roles-based representation is used to group together similar power play possessions using latent Dirichlet allocation, a topic modelling technique. The concept of assignments, which remain constant over an entire possession, is also introduced. Assignments provide a more stable measure of player positioning, which may be preferable when assessing deployment over longer periods of time.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140582583","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}
The tournament rules for long jump competitions have changed in recent years. Today, only the three athletes with the best jumps from the five initial attempts are qualified to make an additional sixth jump – a format called The Final Three. In the first implemented version of The Final Three, the top athletes sequentially make one final jump, starting with the athlete ranked third place from the initial attempts. The athlete with the longest jump in this sixth attempt wins the competition, irrespective of achieved results in previous attempts. In this study, we analyze the effect of the athletes’ jump order on the probability of winning the competition within this first implemented version of The Final Three. We derive the final’s symmetric subgame perfect equilibrium and compute the corresponding equilibrium winning probabilities, given estimated distributional parameters from the Olympic long jumping final in Tokyo 2021. The modeling of the game is preceded by a development of a stochastic model for the outcome in long jumping. Our results indicate a last mover advantage, albeit small. Our model also reveals the importance of having a low variation in the approach run length and thinking strategically in this tournament format.
{"title":"The strategic jump-the order effect on winning “The Final Three” in long jump competitions","authors":"Niklas Karlsson, Anders Lunander","doi":"10.1515/jqas-2022-0028","DOIUrl":"https://doi.org/10.1515/jqas-2022-0028","url":null,"abstract":"The tournament rules for long jump competitions have changed in recent years. Today, only the three athletes with the best jumps from the five initial attempts are qualified to make an additional sixth jump – a format called The Final Three. In the first implemented version of The Final Three, the top athletes sequentially make one final jump, starting with the athlete ranked third place from the initial attempts. The athlete with the longest jump in this sixth attempt wins the competition, irrespective of achieved results in previous attempts. In this study, we analyze the effect of the athletes’ jump order on the probability of winning the competition within this first implemented version of The Final Three. We derive the final’s symmetric subgame perfect equilibrium and compute the corresponding equilibrium winning probabilities, given estimated distributional parameters from the Olympic long jumping final in Tokyo 2021. The modeling of the game is preceded by a development of a stochastic model for the outcome in long jumping. Our results indicate a last mover advantage, albeit small. Our model also reveals the importance of having a low variation in the approach run length and thinking strategically in this tournament format.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139928138","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}
We first present a model for the outcome of snooker matches in which player strengths are allowed to vary deterministically with time. The results allow us to identify the greatest players of all time, and to examine the relationship between age and performance. Second, we present a random effects model which uses the estimated strengths from our first model, to forecast player performance, and to assess the extent to which early promise has been maintained. Ronnie O’Sullivan and Stephen Hendry are the two candidates for the title of the greatest of all time. We find that peak performance occurs between the ages of 25 and 30, younger than would be expected when compared to findings in other sports. Outside sport, these findings contribute to the general literature on variation of performance with age.
{"title":"Estimating age-dependent performance in paired comparisons competitions: application to snooker","authors":"Rose D. Baker, Ian G. McHale","doi":"10.1515/jqas-2023-0082","DOIUrl":"https://doi.org/10.1515/jqas-2023-0082","url":null,"abstract":"We first present a model for the outcome of snooker matches in which player strengths are allowed to vary deterministically with time. The results allow us to identify the greatest players of all time, and to examine the relationship between age and performance. Second, we present a random effects model which uses the estimated strengths from our first model, to forecast player performance, and to assess the extent to which early promise has been maintained. Ronnie O’Sullivan and Stephen Hendry are the two candidates for the title of the greatest of all time. We find that peak performance occurs between the ages of 25 and 30, younger than would be expected when compared to findings in other sports. Outside sport, these findings contribute to the general literature on variation of performance with age.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139678519","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}
We propose an alternative design for tournaments that use a preliminary stage, followed by several rounds of single elimination play. The conventional “bracket” design of these tournaments suffers from several deficiencies. Specifically, various reasonable performance criteria for the tournament are not satisfied, there is an unnecessary element of luck in the matchups of players, and there are situations where players have an incentive to shirk. To address all these issues, we allow higher ranked players at the single elimination stage to choose their next opponent sequentially at each round. We allow each player’s ranking either to remain static, or to improve by beating a higher ranked player (Guyon, J. 2022. “Choose your opponent”: a new knockout design for hybrid tournaments. J. Sports Anal. 8: 9–29). Using data from 2215 men’s professional tennis tournaments from 1991 to 2017, we demonstrate the reasonableness of the results obtained. We also perform sensitivity analysis for the effect of increasing irregularity in the pairwise win probability matrix on three traditional performance measures. Finally, we consider strategic shirking behavior at both the individual and group levels, and show how our opponent choice design can mitigate such behavior. Overall, the opponent choice design provides higher probabilities that the best player wins and also that the two best players meet, and reduces shirking, compared to the conventional bracket design.
{"title":"Opponent choice in tournaments: winning and shirking","authors":"Nicholas G. Hall, Zhixin Liu","doi":"10.1515/jqas-2023-0030","DOIUrl":"https://doi.org/10.1515/jqas-2023-0030","url":null,"abstract":"We propose an alternative design for tournaments that use a preliminary stage, followed by several rounds of single elimination play. The conventional “bracket” design of these tournaments suffers from several deficiencies. Specifically, various reasonable performance criteria for the tournament are not satisfied, there is an unnecessary element of luck in the matchups of players, and there are situations where players have an incentive to shirk. To address all these issues, we allow higher ranked players at the single elimination stage to choose their next opponent sequentially at each round. We allow each player’s ranking either to remain static, or to improve by beating a higher ranked player (Guyon, J. 2022. “Choose your opponent”: a new knockout design for hybrid tournaments. <jats:italic>J. Sports</jats:italic> Anal<jats:italic>.</jats:italic> 8: 9–29). Using data from 2215 men’s professional tennis tournaments from 1991 to 2017, we demonstrate the reasonableness of the results obtained. We also perform sensitivity analysis for the effect of increasing irregularity in the pairwise win probability matrix on three traditional performance measures. Finally, we consider strategic shirking behavior at both the individual and group levels, and show how our opponent choice design can mitigate such behavior. Overall, the opponent choice design provides higher probabilities that the best player wins and also that the two best players meet, and reduces shirking, compared to the conventional bracket design.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139515811","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}
The International Chess Federation (FIDE) imposes a voluminous and complex set of player pairing criteria in Swiss-system chess tournaments and endorses computer programs that are able to calculate the prescribed pairings. The purpose of these formalities is to ensure that players are paired fairly during the tournament and that the final ranking corresponds to the players’ true strength order. We contest the official FIDE player pairing routine by presenting alternative pairing rules. These can be enforced by computing maximum weight matchings in a carefully designed graph. We demonstrate by extensive experiments that a tournament format using our mechanism (1) yields fairer pairings in the rounds of the tournament and (2) produces a final ranking that reflects the players’ true strengths better than the state-of-the-art FIDE pairing system.
{"title":"Improving ranking quality and fairness in Swiss-system chess tournaments","authors":"Pascal Sauer, Ágnes Cseh, Pascal Lenzner","doi":"10.1515/jqas-2022-0090","DOIUrl":"https://doi.org/10.1515/jqas-2022-0090","url":null,"abstract":"The International Chess Federation (FIDE) imposes a voluminous and complex set of player pairing criteria in Swiss-system chess tournaments and endorses computer programs that are able to calculate the prescribed pairings. The purpose of these formalities is to ensure that players are paired fairly during the tournament and that the final ranking corresponds to the players’ true strength order. We contest the official FIDE player pairing routine by presenting alternative pairing rules. These can be enforced by computing maximum weight matchings in a carefully designed graph. We demonstrate by extensive experiments that a tournament format using our mechanism (1) yields fairer pairings in the rounds of the tournament and (2) produces a final ranking that reflects the players’ true strengths better than the state-of-the-art FIDE pairing system.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139515636","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}
A fair and inclusive competition depends on a scoring system that takes all relevant factors into account. We analysed the current World Para Point System for swimming and identified several theoretical and practical disadvantages. We propose and test a Fair World Para Point System that not only improves the algorithm, but also extends it to accommodate for the age of the athlete. It also provides a method to break point ties. This will enable para masters swimmers for the first time to compete fairly with each other. We also develop and publish tools that enable event organisers to directly use the Fair World Para Point System.
{"title":"Fair world para masters point system for swimming","authors":"Christoph Bartneck, Elena Moltchanova","doi":"10.1515/jqas-2023-0051","DOIUrl":"https://doi.org/10.1515/jqas-2023-0051","url":null,"abstract":"A fair and inclusive competition depends on a scoring system that takes all relevant factors into account. We analysed the current World Para Point System for swimming and identified several theoretical and practical disadvantages. We propose and test a Fair World Para Point System that not only improves the algorithm, but also extends it to accommodate for the age of the athlete. It also provides a method to break point ties. This will enable para masters swimmers for the first time to compete fairly with each other. We also develop and publish tools that enable event organisers to directly use the Fair World Para Point System.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139515809","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}
The decathlon consists of ten events with scores which are then aggregated to determine the final ranking. We develop a decathlon scoring method which is far simpler than the existing standard (IAAF1984) tables, as there are only 9 parameters instead of 30 which have an impact on the overall rank. We first identify athletes who are on the Pareto-efficient frontier i.e. those who are not dominated by anyone else. We then remove these frontier athletes and again pick all non-dominated athletes to obtain a second dominating group/Pareto frontier and iterate this procedure for the decathlon data from 1986 to 2020. Each of these groups are then characterized by their set of ten median performances. Improving from the last to the top group can then be seen as a path of progress, leading from the lowest to the highest set of median performances. Every event should have the same importance, so we normalize the data such that the path of progress follows as much as possible a space diagonal of a ten dimensional hypercube. Furthermore, any adjustment of a benchmark does not change any actual decathlon performance, hence there cannot be any unwanted rank reversals. This allows a smooth adjustment of these tables in the future, if for instance a new type of javelin needs to be introduced to reduce the range. We normalize such that current performances between 7000 and 9000 points still fall into the same range with our point tables.
{"title":"A multiplicative approach to decathlon scoring based on efficient frontiers","authors":"Manuel Schütz, Chris Tofallis","doi":"10.1515/jqas-2022-0012","DOIUrl":"https://doi.org/10.1515/jqas-2022-0012","url":null,"abstract":"The decathlon consists of ten events with scores which are then aggregated to determine the final ranking. We develop a decathlon scoring method which is far simpler than the existing standard (IAAF1984) tables, as there are only 9 parameters instead of 30 which have an impact on the overall rank. We first identify athletes who are on the Pareto-efficient frontier i.e. those who are not dominated by anyone else. We then remove these frontier athletes and again pick all non-dominated athletes to obtain a second dominating group/Pareto frontier and iterate this procedure for the decathlon data from 1986 to 2020. Each of these groups are then characterized by their set of ten median performances. Improving from the last to the top group can then be seen as a path of progress, leading from the lowest to the highest set of median performances. Every event should have the same importance, so we normalize the data such that the path of progress follows as much as possible a space diagonal of a ten dimensional hypercube. Furthermore, any adjustment of a benchmark does not change any actual decathlon performance, hence there cannot be any unwanted rank reversals. This allows a smooth adjustment of these tables in the future, if for instance a new type of javelin needs to be introduced to reduce the range. We normalize such that current performances between 7000 and 9000 points still fall into the same range with our point tables.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139420563","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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