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Does the New Way
Of Judging Skating
Actually Add Up?

February 15, 2006; Page A13

Perhaps it was a incomplete toe loop that cost Pang Qing and Tong Jian a medal in Monday's pairs figure-skating competition. Perhaps a weak death spiral or a wobbly landing.

But it might well have been a computer, so one statistician postulates.

Ms. Pang and Mr. Tong, who skated an energetic program to the strains of "Phantom of the Opera," placed fourth and missed the podium by 24 hundredths of a point, trailing countrymen Shen Xue and Zhao Hongbo 186.91 to 186.67.

It could have come out another way. Under figure skating's new scoring rubric, 12 judges mark the competition, then a computer randomly picks only nine of them to feed into the algorithm that decides the outcomes. The other three are dropped.

Which ones aren't counted can make a difference.

Working from a full set of score data released Monday by the International Skating Union, Yale University statistician John W. Emerson calculates that 12% of the possible choices of judges would have given Ms. Pang and Mr. Tong a bronze, instead of leaving them out of the medals. Bronze medalists Ms. Shen and Mr. Zhao could have finished as high as silver (4% of the possible arrangements) or as low as fourth (12%) had the computer picked a different set of scores.

In other words, the silver and bronze medals depended on the computerized equivalent of a roll of the dice. Russians Maxim Marinin and Tatiana Totmianina, who skated to gold, were so dominant they came out on top in all possible choices.

"This is a real problem," Mr. Emerson says. "It's a crapshoot."

Devra Pitt Getaz, a spokeswoman for the International Skating Union, the sport's governing body, said that the random choices of judges "may affect to a small degree the overall score" but called Mr. Emerson's analysis "misleading." She noted that under the old system judges were also randomly selected to mark events -- though no scores were dropped -- and defended the new system as less subject to judges' whims. The random procedure, she said, is intended to deter corruption, since no one knows whether a judge's score will count.

The new scoring system ostensibly was designed to make scoring less subjective. Skaters are judged on two programs with scores added for a final tally. One element of the new system takes some of the judging out of the judges' hands by ceding the compilation of technical marks to a five-person committee of technocrats; they watch the skaters' programs and punch in points into a computer each time a skater successful completes an element.

The panel of 12 judges, all anonymous, simultaneously score factors such as choreography and artistic merit. A computer picks nine of the 12 judges for each program. There are 220 possible ways to select nine judges out of 12, so there are a total of 220 times 220, or 48,400 possible judge combinations for the final score.

Shortly after the score sheets -- which include all 12 judges' marks -- were posted Monday, Mr. Emerson set to work on the data. His computer chewed through all 48,400 combinations for every skater. It wrapped up in the wee hours of the morning.

Mr. Emerson, who describes himself as "not a figure-skating fanatic," began his number-crunching odyssey last week, while hunting around for data to use in his introductory statistics class. He came across the score sheets for the 2006 European women's championship. In the short program -- the first of the competition's two parts -- only 84 hundredths of a point separated second from fifth place.

Mr. Emerson found that any of them could have landed in any of those four positions, depending on which judges the computer discarded. By luck, Swiss skater Sarah Meier, for instance, was third -- but more than half of the possible combinations would have put her fourth or fifth. Russian Irina Slutskaya, the eventual champion, was first in all of the possible panels.

The margins of victory widened after the second part of the program, and randomness wasn't a factor in the overall finishing order.

Still, Mr. Emerson says the ambiguity of the short-program standings made him wonder about the Olympics. "Maybe it's going to be a clear ordering," he said. "Maybe not."

The women skate next week.

--Barry Newman in Turin contributed to this article.

Write to Charles Forelle at

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