# Maddenation

## The Luge

Watching the Luge event, I was struck by the closeness of the race. The difference between Gold and Silver was 0.11 seconds over 4 runs! This is less than the standard deviation in the times of the separate runs. The difference between the slowest and fastest run times for the winner, Zoeggeler, was 0.3 seconds. A simple statistical “t-test” indicates that there is no significant difference between the times of the top four finishers.

To be rigorous, one should consider each set of runs separately, as they took place on different days and at different times of the day. For example, everyone had his slowest time on the first run, and it seems fair to compare how each competitor did head-to-head under the same conditions. Even using this more rigorous analysis (t-test for paired samples) the medal winners are not significantly different, and the fourth place American, Benshoof, was just barely significantly different (95% confidence level) from the winner.

Yet, Zoeggeler was also the Gold medalist four years ago. And clearly, the top racers in the world are always at or near the top. If we relax the typical confidence level used for statistical comparisons, we see that, based on the paired t-test, there is a 25% chance that Zoeggeler’s win over Demtschenko was purely random luck. Similarly, there is about a 19% chance that the silver-bronze order was just luck. This seems about right, actually. We have the feeling that, were the event to be held again, the finish would probably be different. Yet the gold medal winner goes on to fame and fortune, while the rest of the pack (with few exceptions) is forgotten.

Dad • Observations • 02/13/06 • 6 comments
## Comments

David • 02/13/06 • 10:42 PM:You’ve done it again Dad! Bravo! Really, I like this entry. Your keen mind has dissected the Luge like nobody else could (and like nobody’s business). I think I forward it to the math nerds at school to see if they might use it. I don’t really do that kind of stuff - yet wait - perhaps with Chi-Square analysis, which is used in bio statistics all the time. Perhaps you could comment/elaborate on the “simple statistical” somethings (some jarble) that you’re talking about.

Patrick • 02/14/06 • 12:08 AM:I’m not so sure your claim that “the gold medal winner goes on to fame and fortune, while the rest of the pack (with few exceptions) is forgotten” is entirely accurate. How many gold medalist lugers can you name? What commercials are they on? I doubt even that other countries afford their lugers the fame you seem to think they achieve.

As for statistical analysis, at least this is a timed event, and the timing mechanism is pretty accurate. How about the same sort of problem in a judged event? How do you explain a silver medal to a kid who just got one tenth less in the overall judging?

David • 02/16/06 • 2:38 PM:This article was written for you Dad. It’s from SciAm and it’s about figure skating judging. It works perfectly into this piece. Here’s the original article.

The guy, John (Ralph Waldo) Emerson, makes a great point on how the new system is not necessarily more fair than the old; and how adding in a computer (to randomly select only some of the judges scores) can skew results dramatically. In the author’s words, “Let’s leave the computers out of it”.

Do YOU agree?

Dad • 02/17/06 • 11:02 PM:I agree completely. I haven’d paid much attention to the new system, and the “explanations” I have heard have focussed on how the points are determined by each judge. I hadn’t heard about the random selection of 9 judges by computer.

Emerson is right, and his data comparing all 220 possible combinations of judges clearly shows the potential bias. Even without statistics, it’s easy to imagine a “low grading” judge that gets included for some skaters and not for others, thereby affecting scores.

My question is, how can the international Olympic committee, with all it’s resources and all the incentive to avoid the judging debacle that occurred in Salt Lake City, come up with such an obviously flawed system?

Dad • 02/18/06 • 12:14 AM:While the “t-test” can be simply applied using Excel or other software, the underlying analysis justifying its use is hardly simple. The t distribution was first deduced by W. S. Gosset, a chemist at the Guinness brewery in Dublin, in 1908. He wrote under the pseudonym “Student,” and his test is usually referred to as “Student’s t-test.” Consult your statistics book for details.

When we’re comparing sample means (say, the average of 4 Luge runs) then the t distribution comes into play. If we’re interested in the variance of the samples, these will be distributed according to the Chi-square distribution. Both distributions are really families of curves that depend on the degrees of freedom.

Dan • 02/25/06 • 12:39 PM:I won the Skeleton last November and it was because I was the best skeletoner, not because of luck.

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