I was interested to learn today that in spite of the fact that the American gymnast Nastia Liukin and the Chinese gymnast He Kexin both posted scores of 16.725 for their uneven bars performances in the Beijing Olympics, He was awarded the gold medal whereas Liukin received the silver medal. Apparently ties were allowed in Olympic gymnastics until 2000; in such cases, both athletes would be awarded the same medal type. However, since 2000, the International Olympic Committee (IOC) has adopted so-called “tiebreaker” rules conceived of by the International Gymnastics Federation (FIG) which effectively penalize the athlete who receives the least consistent, or most highly variable set of scores across 6 judges.
The technical details concerning the actual algorithm used by FIG are provided here. For starters, the highest and lowest scores provided by 6 judges are tossed out so the “execution” score is based upon the average of the remaining four scores. Effectively, the data are “winsorized”, presumably for the purpose of discounting the effects of overly generous and overly miserly judges. Once this calculation has been made, then the first tie-break calculation requires throwing out the highest and lowest deductions from a perfect”execution score of 10 and then averaging the remaining four deductions. If there is a tie after the first tie-break (as there was in this case), then the rules call for a second tie-break in which the highest remaining deduction is thrown out, leaving a total of 3 of the original 6 deductions to averaged. When this calculation was performed, He had an average deduction of .933 versus Liukin’s .966. Liukin lost primarily because after the second pass, she had a higher average deduction among the remaining three judges. He won because her average deduction from 10 by the 3 remaining judges was lower than it was for Liukin.