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Judging a gymnastics routine is a noisy process, and the performance ofjudges varies widely. In collaboration with the F\'ed\'eration Internationalede Gymnastique (FIG) and Longines, we are designing and implementing animproved statistical engine to analyze the performance of gymnastics judgesduring and after major competitions like the Olympic Games and the WorldChampionships. The engine, called the Judge Evaluation Program (JEP), has threeobjectives: (1) provide constructive feedback to judges, executive committeesand national federations; (2) assign the best judges to the most importantcompetitions; (3) detect bias and outright cheating.  Using data from international gymnastics competitions held during the2013-2016 Olympic cycle, we first develop a marking score evaluating theaccuracy of the marks given by gymnastics judges. Judging a gymnastics routineis a random process, and we can model this process very accurately usingheteroscedastic random variables. The marking score scales the differencebetween the mark of a judge and the theoretical performance of a gymnast as afunction of the standard deviation of the judging error estimated from data foreach apparatus. This dependence between judging variability and performancequality has never been properly studied. We then study ranking scores assessingto what extent judges rate gymnasts in the correct order, and explain why weultimately chose not to implement them. We also study outlier detection topinpoint gymnasts who were poorly evaluated by judges. Finally, we discussinteresting observations and discoveries that led to recommendations and rulechanges at the FIG.

Judging the Judges: Evaluating the Performance of International Gymnastics Judges