# Fair Judging in Figure Skating

I’ll be honest. I don’t like to watch figure skating. Nevertheless, thanks to a blogger at Substandard Analysis, I have a newfound interest in watching or at least paying some attention to the results in Torino.

In an effort of establishing a “fair” judging system, the scoring system for figure skating has been changed. This is in response the the fiasco over biased judging at the last Olympics in Salt Lake City. John Emerson, Assistant Professor of Statistics of Yale University, claims that the new system is in fact less fair than before. Here is Dr. Emerson’s synopsis of the new scoring system:

In place since the 2004 World Championships and in use at the 2006 Olympic Games, the new system awards points for technical elements as well as five program components: skating skills, transition/linking footwork, performance/execution, choreography/composition, and interpretation.

The scores for the technical elements depend on a base value for the level of difficulty of the elements. The twelve judges add or deduct points from this base value, acknowledging the “grade of execution” of the performance of the elements. Program component scores range from 0 to 10, with increments of 0.25, reflecting the overall presentation of the program and quality of the figure skating.

Judging is now anonymous. Nine of twelve judges are selected at random for the Short Program and again for the Free Skate. Scores for each executed element or program component are calculated using a trimmed mean, as in the old system, dropping the maximum and minimum of the nine scores.

Dr. Emerson then proceeds to demonstrate that the random selection process, in the case of a tight competition, can result in more than one possible outcome. The sample data he cites is from the Ladies’ 2006 European Figure Skating Championships. Due to the trimming of the pool of judges by three, there is a possible 220 different outcomes. In the mentioned competition, Dr. Emerson demonstrates that although every one of the 220 possible random choices resulted in the same 1st place finish, there was a wide distribution of outcomes for the other places.

The one thing that Dr. Emerson lacks in his article is a clear interpretation of “fairness.” He claims that the random procedure is less fair due to the fact that he hopes to never hear “a 4th or 5th place finisher give the following interview: ‘I did my best, and I would have won Bronze if all twelve judges’ scores had been included. And if a different panel of 9 judges had been selected, I might have won Gold.’”

As a mathematician I’d like to know a bit more about this new system. For example, “What’s the probability that at least half of the 220 different possible random judge selections give different top 3 rankings than a given control set of selected judges?” If that probability is too high ($$\alpha > 0.05$$), I might interpret that as “unfair”.