We design, describe and implement a statistical engine to analyze the performance of gymnastics judges with three objectives: (1) provide constructive feedback to judges, executive committees and national federations; (2) assign the best judges to the most important competitions; (3) detect bias and persistent misjudging. Judging a gymnastics routine is a random process, and we model this process using heteroscedastic random variables. The developed marking score scales the difference between the mark of a judge and the true performance level of a gymnast as a function of the intrinsic judging error variability estimated from historical data for each apparatus. This dependence between judging variability and performance quality has never been properly studied. We leverage the intrinsic judging error variability and the marking score to detect outlier marks and study the national bias of judges favoring athletes of the same nationality. We also study ranking scores assessing to what extent judges rate gymnasts in the correct order. Our main observation is that there are significant differences between the best and worst judges, both in terms of accuracy and national bias. The insights from this work have led to recommendations and rule changes at the Fédération Internationale de Gymnastique.

中文翻译：

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评判：评估国际体操评委的准确性和国家偏见

我们设计、描述和实施了一个统计引擎来分析体操裁判的表现，具有三个目标：（1）向裁判、执行委员会和国家联合会提供建设性的反馈；(2) 为最重要的比赛分配最优秀的评委；(3) 发现偏见和持续的误判。判断一个体操套路是一个随机过程，我们使用异方差随机变量对这个过程进行建模。开发的评分分数衡量了裁判的分数和体操运动员的真实表现水平之间的差异，作为根据每个设备的历史数据估计的内在判断误差可变性的函数。这种判断可变性和性能质量之间的依赖关系从未得到过适当的研究。我们利用固有的判断误差可变性和评分分数来检测异常值，并研究有利于同一国籍运动员的裁判的国家偏见。我们还研究了排名分数，以评估评委以正确顺序对体操运动员进行评分的程度。我们的主要观察是，最好和最差的评委在准确性和国家偏见方面存在显着差异。这项工作的见解导致了国际体操联合会的建议和规则变更。在准确性和国家偏见方面。这项工作的见解导致了国际体操联合会的建议和规则变更。在准确性和国家偏见方面。这项工作的见解导致了国际体操联合会的建议和规则变更。