Olympic Figure Skating:
Silver and Bronze, or Bronze and Silver?

John Emerson
Assistant Professor of Statistics
Yale University

There are 12 judges for each figure skating event in Torino, Italy. A computer selects 9 at random. I demonstrate the effect of this system using results from the recent Pairs competition. A different selection of 9 judges would have produced slightly different scores, and could have changed the medal standings. For example, about 1/8 of the panels would have awarded Pang and Tong the bronze. My recommendation: use the scores of all 12 judges. Unfortunately for Pang and Tong, this would have awarded the medals in the observed order -- they would still have finished 4th.

The plots show the proportions of rankings (out of 48,400 possible combinations of panels in the Short and Free Skate segments) for each of the top 4 finishers in the Olympic Pairs competition. A draft of a more complete discussion of these results is now available.

I had a first look at the European Championship results in class on Friday, February 10. I then presented my full analysis of the Ladies 2006 European Championships as an example in my introductory statistics lecture on February 13. It started out as a fun example for the students, and it turned into a monster that ate my weekend. I should point out, however, that in no way are the results of past competitions, or the Olympics this week, illegitimate. Rules are rules, and they will be applied fairly to determine the medalists at the Olympics. There are concerns about nationalism and block voting influencing the results. If the elimination of 9 judges at random addresses this concern (and I'm not sure it does), there is still a cost to be paid, by the skaters in close competitions.

Back to Jay's Home Page with links and other information.

Acknowledgement: I just found a page by Katherine Godfrey, PhD, that appears to have been written between in March, 2003, prior to the new rules implemented by the ISU in June, 2004. Godfrey's simulations showed exactly what I have demonstrated with real data, and Godfrey's recommendation agrees with mine: use all the judges. Godfrey's concerns seem to be organized at Skatefair.com, although I have not been able to contact her. I hope my work with real data from major competitions using the newest scoring system helps shed light on this issue.

The data (not for the timid)!

Detailed Olympic Figure Skating Results from the ISU.

Note: I make the following data sets available in Excel format in case anyone is interested in studying the results themselves. All my calculations may be replicated using the following files. Brief documentation is available here.

My cleaned version of the data for the top 8 skaters.
Same thing, but with SOV inserted. This is really what you need to produce scores.