### 8.18.2008

## The vagaries of gymnastics scoring, part the second

After examining these articles from SI and from USA gymnastics, and taking a look at an official gymnastics scoresheet, I am forced to conclude that gymnastics officials are completely innumerate.

As you may know by now, a gymnastics score for a given routine is given by adding the difficulty score to an execution score. The difficulty score is determined by one offical scorer, while the execution score is obtained by a panel of six judges. Each judge submits a score, and the middle four of the six scores are averaged to yield the official execution score.

However, since scoring resolution only goes down to 1/40ths of a point, ties are bound to come up now and then. For the individual event finals, gymnastics has put together a completely arbitrary and unnecessarily complicated scheme for breaking ties.

The first tiebreaker goes to whoever has the higher average execution score. Kind of arbitrary, but simple enough.

The second tiebreaker goes to whoever has the lower average deduction among the four relevant execution judges. However, as far as I can tell from looking at the official scoresheet, execution score is defined to be 10.0 minus deductions, so this second criterion is completely redundant.

(EDIT: This article from AP also seems to subsume the first two criteria into one; it seems more likely now that only one of these two equivalent criteria is actually written into the rules.)

The third tiebreaker is determined by taking the lowest three deductions among the four relevant execution judges and giving the tiebreaker to whoever has the lower average deduction. Given that the first tiebreaker is in effect, this is equivalent to simply tossing out the fifth-highest execution score.

Clearly, this tiebreaking scheme is wholly unnatural and arbitrary (why eliminate the fifth-highest score instead of the second-highest?) If one isn't overly worried about corrupt or incompetent judges, then averaging all six execution scores makes more sense (which would actually give He the gold). But given that the high and low execution scores are discarded and the average of the remaining four execution scores is the same, awarding two gold medals makes more sense than awarding a tiebreaker based on discarding additional information about the scores in an arbitrary manner.

As you may know by now, a gymnastics score for a given routine is given by adding the difficulty score to an execution score. The difficulty score is determined by one offical scorer, while the execution score is obtained by a panel of six judges. Each judge submits a score, and the middle four of the six scores are averaged to yield the official execution score.

However, since scoring resolution only goes down to 1/40ths of a point, ties are bound to come up now and then. For the individual event finals, gymnastics has put together a completely arbitrary and unnecessarily complicated scheme for breaking ties.

The first tiebreaker goes to whoever has the higher average execution score. Kind of arbitrary, but simple enough.

The second tiebreaker goes to whoever has the lower average deduction among the four relevant execution judges. However, as far as I can tell from looking at the official scoresheet, execution score is defined to be 10.0 minus deductions, so this second criterion is completely redundant.

(EDIT: This article from AP also seems to subsume the first two criteria into one; it seems more likely now that only one of these two equivalent criteria is actually written into the rules.)

The third tiebreaker is determined by taking the lowest three deductions among the four relevant execution judges and giving the tiebreaker to whoever has the lower average deduction. Given that the first tiebreaker is in effect, this is equivalent to simply tossing out the fifth-highest execution score.

Clearly, this tiebreaking scheme is wholly unnatural and arbitrary (why eliminate the fifth-highest score instead of the second-highest?) If one isn't overly worried about corrupt or incompetent judges, then averaging all six execution scores makes more sense (which would actually give He the gold). But given that the high and low execution scores are discarded and the average of the remaining four execution scores is the same, awarding two gold medals makes more sense than awarding a tiebreaker based on discarding additional information about the scores in an arbitrary manner.