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The strategic jump-the order effect on winning “The Final Three” in long jump competitions 战略性跳跃--在跳远比赛中赢得 "最后三名 "的顺序效应
IF 0.8 Q3 SOCIAL SCIENCES, MATHEMATICAL METHODS Pub Date : 2024-02-20 DOI: 10.1515/jqas-2022-0028
Niklas Karlsson, Anders Lunander
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.
近年来,跳远比赛的比赛规则发生了变化。如今,只有在五次初试中跳得最好的三名运动员才有资格再跳第六次--这种形式被称为 "最后三跳"。在首次实施的 "最后三跳 "中,排名靠前的运动员依次进行最后一跳,从最初试跳中排名第三的运动员开始。在第六次尝试中跳得最远的运动员将赢得比赛,与之前尝试的成绩无关。在本研究中,我们分析了在首次实施的 "决赛三人组 "中,运动员的跳跃顺序对比赛获胜概率的影响。根据 2021 年东京奥运会跳远决赛的估计分布参数,我们推导出决赛的对称子博弈完美均衡,并计算出相应的均衡获胜概率。在建立博弈模型之前,我们还建立了跳远比赛结果的随机模型。我们的研究结果表明,尽管后发优势很小,但仍存在。我们的模型还揭示了在这种比赛形式中,接近跑长度变化小和战略思维的重要性。
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引用次数: 0
Estimating age-dependent performance in paired comparisons competitions: application to snooker 估算成对比较竞赛中与年龄有关的成绩:斯诺克的应用
IF 0.8 Q3 SOCIAL SCIENCES, MATHEMATICAL METHODS Pub Date : 2024-02-01 DOI: 10.1515/jqas-2023-0082
Rose D. Baker, Ian G. McHale
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.
我们首先提出了一个斯诺克比赛结果模型,在该模型中,选手实力随时间变化而确定。其结果使我们能够确定有史以来最伟大的球员,并研究年龄与表现之间的关系。其次,我们提出了一个随机效应模型,利用第一个模型估算出的实力来预测球员的表现,并评估早期承诺的保持程度。罗尼-奥沙利文(Ronnie O'Sullivan)和斯蒂芬-亨德利(Stephen Hendry)是史上最伟大选手的两位候选人。我们发现,他们的巅峰表现出现在 25 岁到 30 岁之间,与其他运动项目的研究结果相比,他们的年龄比预期的要小。除体育运动外,这些研究结果还为有关随年龄变化的表现的一般文献做出了贡献。
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引用次数: 0
Opponent choice in tournaments: winning and shirking 比赛中对手的选择:获胜与逃避
IF 0.8 Q3 SOCIAL SCIENCES, MATHEMATICAL METHODS Pub Date : 2024-01-19 DOI: 10.1515/jqas-2023-0030
Nicholas G. Hall, Zhixin Liu
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.
我们为采用预赛阶段的比赛提出了另一种设计方案,预赛阶段之后是几轮单败淘汰赛。这些比赛的传统 "分组 "设计存在若干缺陷。具体来说,比赛的各种合理成绩标准无法得到满足,棋手的对阵中存在不必要的运气成分,而且存在棋手有动机推卸责任的情况。为了解决所有这些问题,我们允许在单败淘汰赛阶段排名较高的选手在每轮比赛中按顺序选择下一个对手。我们允许每位棋手的排名保持不变,或通过击败排名更高的棋手来提高排名(Guyon, J. 2022."选择你的对手":混合锦标赛的新淘汰赛设计。J. Sports Anal.8: 9-29).我们利用 1991 年至 2017 年期间 2215 场男子职业网球比赛的数据,证明了所得结果的合理性。我们还就配对胜率矩阵中不规则性增加对三个传统绩效指标的影响进行了敏感性分析。最后,我们考虑了个人和团体层面的策略性推卸行为,并展示了我们的对手选择设计如何减轻这种行为。总体而言,与传统的分组设计相比,对手选择设计提供了更高的最佳棋手获胜和两个最佳棋手相遇的概率,并减少了推卸责任行为。
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引用次数: 0
Improving ranking quality and fairness in Swiss-system chess tournaments 提高瑞士系统国际象棋比赛的排名质量和公平性
IF 0.8 Q3 SOCIAL SCIENCES, MATHEMATICAL METHODS Pub Date : 2024-01-18 DOI: 10.1515/jqas-2022-0090
Pascal Sauer, Ágnes Cseh, Pascal Lenzner
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.
国际棋联(FIDE)在瑞士赛制的国际象棋比赛中规定了大量复杂的棋手配对标准,并认可能够计算规定配对的计算机程序。这些手续的目的是确保棋手在比赛中公平配对,并确保最终排名符合棋手的真实实力顺序。我们对国际棋联官方的棋手配对程序提出质疑,并提出了其他配对规则。这些规则可以通过计算精心设计的图形中的最大权重配对来执行。我们通过大量实验证明,采用我们的机制的比赛形式(1)在比赛的各轮中产生更公平的配对,(2)产生的最终排名比国际棋联最先进的配对系统更能反映棋手的真实实力。
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引用次数: 0
Fair world para masters point system for swimming 公平的世界游泳大师积分系统
IF 0.8 Q3 SOCIAL SCIENCES, MATHEMATICAL METHODS Pub Date : 2024-01-18 DOI: 10.1515/jqas-2023-0051
Christoph Bartneck, Elena Moltchanova
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.
公平和包容的竞赛取决于考虑到所有相关因素的计分系统。我们分析了现行的世界残疾人游泳积分系统,发现了一些理论和实践上的弊端。我们提出并测试了一种公平的世界残疾人积分系统,该系统不仅改进了算法,还扩展了算法以适应运动员的年龄。它还提供了一种打破积分并列的方法。这将使残疾人游泳大师首次能够相互公平竞争。我们还开发并发布了一些工具,使赛事组织者能够直接使用公平世界残疾人积分系统。
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引用次数: 0
A multiplicative approach to decathlon scoring based on efficient frontiers 基于高效前沿的十项全能评分乘法
IF 0.8 Q3 SOCIAL SCIENCES, MATHEMATICAL METHODS Pub Date : 2024-01-10 DOI: 10.1515/jqas-2022-0012
Manuel Schütz, Chris Tofallis
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.
十项全能比赛由十个项目组成,这些项目的得分经汇总后确定最终排名。我们开发的十项全能评分方法比现有的标准表(IAAF1984)简单得多,因为影响总排名的参数只有 9 个而不是 30 个。我们首先确定那些处于帕累托效率前沿的运动员,即那些不受其他任何人支配的运动员。然后,我们剔除这些前沿运动员,再次挑选所有未被支配的运动员,以获得第二个支配组/帕累托前沿,并对 1986 年至 2020 年的十项全能数据重复这一过程。然后,每个组都以其十个中位数成绩为特征。因此,从最后一组到最高一组的进步可以被视为一条从最低成绩中位数到最高成绩中位数的进步之路。每个事件都应具有相同的重要性,因此我们对数据进行归一化处理,使进步路径尽可能遵循十维超立方的空间对角线。此外,对基准的任何调整都不会改变任何实际的十项全能成绩,因此不会出现任何不必要的排名颠倒。这样一来,如果需要引入新的标枪类型来缩小范围,就可以在将来顺利调整这些表格。我们将当前 7000 分至 9000 分之间的成绩归一化,使其与我们的积分表保持在同一范围内。
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引用次数: 0
Equity, diversity, and inclusion in sports analytics 体育分析中的公平性、多样性和包容性
IF 0.8 Q3 SOCIAL SCIENCES, MATHEMATICAL METHODS Pub Date : 2024-01-09 DOI: 10.1515/jqas-2022-0025
Craig Fernandes, Jason D. Vescovi, Richard Norman, Cheri L. Bradish, Nathan Taback, Timothy C. Y. Chan
This paper presents a landmark study of equity, diversity and inclusion (EDI) in the field of sports analytics. We developed a survey that examined personal and job-related demographics, as well as individual perceptions and experiences about EDI in the workplace. We sent the survey to individuals in the five major North American professional leagues, representatives from the Olympic and Paralympic Committees in Canada and the U.S., the NCAA Division I programs, companies in sports tech/analytics, and university research groups. Our findings indicate the presence of a clear dominant group in sports analytics identifying as: young (72.0 %), White (69.5 %), heterosexual (89.7 %) and male (82.0 %). Within professional sports, males in management positions earned roughly $30,000 (27 %) more on average compared to females. A smaller but equally alarming pay gap of $17,000 (14 %) was found between White and racialized management personnel. Of concern, females were nearly five times as likely to experience discrimination and twice as likely to have considered leaving their job due to isolation or feeling unwelcome. While they had similar levels of agreement regarding fair processes for rewards and compensation, females “strongly agreed” less often than males regarding equitable support, equitable workload, having a voice, and being taken seriously. Over one third (36.3 %) of females indicated that they “strongly agreed” that they must work harder than others to be valued equally, compared to 9.8 % of males. We conclude the paper with concrete recommendations that could be considered to create a more equitable, diverse and inclusive environment for individuals working within the sports analytics sector.
本文介绍了对体育分析领域的公平、多样性和包容性(EDI)进行的一项具有里程碑意义的研究。我们制定了一项调查,研究个人和工作相关的人口统计数据,以及个人对工作场所 EDI 的看法和经验。我们向北美五大职业联盟的个人、加拿大和美国奥林匹克委员会和残奥委员会的代表、美国国家大学生体育协会一级项目、体育科技/分析领域的公司以及大学研究小组发送了调查问卷。我们的研究结果表明,在体育分析领域存在一个明显的主导群体,他们的特征是:年轻(72.0%)、白人(69.5%)、异性恋(89.7%)和男性(82.0%)。在职业体育界,担任管理职位的男性平均收入比女性高出约 3 万美元(27%)。白人和种族化管理人员之间的薪酬差距较小,但同样令人担忧,差距为 1.7 万美元(14%)。值得关注的是,女性遭受歧视的可能性几乎是男性的五倍,由于孤立无援或感觉不受欢迎而考虑离职的可能性是男性的两倍。虽然她们对公平的奖励和补偿程序的认同程度相似,但女性对公平的支持、公平的工作量、有发言权和受到重视的 "强烈认同 "程度低于男性。超过三分之一(36.3%)的女性表示,她们 "非常同意 "自己必须比别人付出更多努力才能得到同等重视,而男性的这一比例仅为 9.8%。在本文的最后,我们提出了一些具体建议,以便为在体育分析领域工作的个人创造一个更加公平、多元化和包容的环境。
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引用次数: 0
Contributions of Carl Morris in sports analytics, a memorium 纪念卡尔-莫里斯在体育分析方面的贡献
IF 0.8 Q3 SOCIAL SCIENCES, MATHEMATICAL METHODS Pub Date : 2024-01-05 DOI: 10.1515/jqas-2023-0092
Jim Albert
Carl Morris 1938–2023 was well-known for his pioneering research in Bayesian multiparameter inference and prediction. Morris was also known for his development of statistical thinking and methodology in sports. This paper provides an overview of Morris’ contributions in sports. This includes Morris’ experience in sports as a youth, summaries of some of Morris’ best-known contributions using sports data, his influence working with students, and some of Morris’ thinking about the interplay of statistics and sports.
卡尔-莫里斯(Carl Morris)1938-2023 年,因其在贝叶斯多参数推理和预测方面的开创性研究而闻名于世。莫里斯还因其在体育领域的统计思想和方法论的发展而闻名。本文概述了莫里斯在体育领域的贡献。其中包括莫里斯年轻时的体育经历、莫里斯利用体育数据做出的一些最著名贡献的摘要、他对学生工作的影响以及莫里斯对统计与体育相互作用的一些思考。
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引用次数: 0
Miss it like Messi: Extracting value from off-target shots in soccer 像梅西一样错失良机:从足球的脱靶射门中提取价值
IF 0.8 Q3 SOCIAL SCIENCES, MATHEMATICAL METHODS Pub Date : 2024-01-01 DOI: 10.1515/jqas-2022-0107
Ethan Baron, Nathan Sandholtz, Devin Pleuler, Timothy C. Y. Chan
Measuring soccer shooting skill is a challenging analytics problem due to the scarcity and highly contextual nature of scoring events. The introduction of more advanced data surrounding soccer shots has given rise to model-based metrics which better cope with these challenges. Specifically, metrics such as expected goals added, goals above expectation, and post-shot expected goals all use advanced data to offer an improvement over the classical conversion rate. However, all metrics developed to date assign a value of zero to off-target shots, which account for almost two-thirds of all shots, since these shots have no probability of scoring. We posit that there is non-negligible shooting skill signal contained in the trajectories of off-target shots and propose two shooting skill metrics that incorporate the signal contained in off-target shots. Specifically, we develop a player-specific generative model for shot trajectories based on a mixture of truncated bivariate Gaussian distributions. We use this generative model to compute metrics that allow us to attach non-zero value to off-target shots. We demonstrate that our proposed metrics are more stable than current state-of-the-art metrics and have increased predictive power.
由于得分事件的稀缺性和高度情境性,衡量足球射门技能是一个具有挑战性的分析问题。围绕足球射门的更先进数据的引入,催生了基于模型的指标,从而更好地应对了这些挑战。具体来说,预期进球数、超预期进球数和射门后预期进球数等指标都是利用先进数据来改进传统的转换率。然而,迄今为止开发的所有指标都将占所有射门近三分之二的脱靶射门赋值为零,因为这些射门没有得分的可能性。我们认为,脱靶射门的轨迹中包含了不可忽略的射门技巧信号,并提出了两种包含脱靶射门信号的射门技巧指标。具体来说,我们基于截断双变量高斯分布的混合物,为投篮轨迹建立了一个球员特定的生成模型。我们利用这一生成模型计算出指标,从而为偏离目标的击球赋予非零值。我们证明,我们提出的指标比目前最先进的指标更稳定,而且预测能力更强。
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引用次数: 0
On the design of international match calendar: the effect of “FIFA reserved dates” on European football matches’ outcomes 论国际比赛日历的设计:“国际足联保留日期”对欧洲足球比赛结果的影响
IF 0.8 Q3 SOCIAL SCIENCES, MATHEMATICAL METHODS Pub Date : 2023-11-28 DOI: 10.1515/jqas-2022-0041
Levi Pérez
Every season, the international football calendar contains periods reserved for a series of so-called special matches including international friendly or official matches played by national teams. All these periods are called “FIFA reserved dates” in the calendar and generally cause domestic competitions to shut down for some days. Such interruptions of leagues might generate different effects or externalities on the performance of players, clubs or even on the competition itself. While a number of studies focus on the effect of players’ absence on teams performance, this paper contributes to the literature by specifically evaluating the effect of the “FIFA reserved dates” on football outcomes. Using data for four seasons from the “big five” European leagues, I find evidence that the outcomes distribution in those matches played after a “FIFA reserved date” becomes more balanced, thus increasing the uncertainty of outcome. The results of this paper contribute to the ongoing debate about the management and design of the international match calendar.
每个赛季,国际足球日历上都有一系列所谓的特殊比赛,包括国际友谊赛或国家队的正式比赛。所有这些时期在日历上被称为“国际足联保留日”,通常会导致国内比赛关闭几天。联赛的中断可能会对球员、俱乐部甚至比赛本身的表现产生不同的影响或外部性。虽然许多研究关注的是球员缺勤对球队表现的影响,但本文通过具体评估“FIFA保留日期”对足球结果的影响,为文献做出了贡献。使用欧洲五大联赛四个赛季的数据,我发现在“国际足联保留日期”之后进行的比赛的结果分布变得更加平衡,从而增加了结果的不确定性。本文的研究结果有助于对国际比赛日程管理和设计的持续争论。
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引用次数: 0
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Journal of Quantitative Analysis in Sports
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