Several rankings have been proposed as to how to determine which country is winning the Olympic medal race. Here I’m only going to look at the medals in isolation. Folks have suggested dividing the medals by the countries’ populations, by the GDP or by the number of athletes. You could factor in the sport popularity, fourth place rankings or time zone differences. You could even rank the countries by how well they exceeded expectations on online betting sites. I would like to see that. But it’s too complicated to do here.

Back to the medals alone. That means three numbers per country.

Clearly,

1) Using the total number of medals leaves out some important information. 3 golds is obviously better than 3 bronzes.

2) Using the number of golds leaves out some important information. 3 golds and 3 bronzes is obviously better than 3 golds.

I’m not the first one to suggest weighting the numbers. It’s progress, but it punts on how to do it. I’ve seen 4, 2 and 1. I’ve also seen 5, 3 and 1. It’s pretty easy to make up numbers, but it’s more satisfying to have a rationale. Here I propose the <i>distinguishing power</i> rationale. There’s only one gold medal. There’s also only one silver medal, but somebody else did better, so silver has half the distinguishing power of gold. Similiarly, bronze has 1/3 of gold. The actual weights don’t matter as long as the ratio is right. 6, 3 and 2 are the smallest integers that express the distinguishing power ratios.

And finally the rankings (today), as a percentage of the leader:

China 100%

United States 93%

Russia 49%

Britain 43%

Australia 36%

Germany 31%

South Korea 27%

Japan 24%

France 24%

Italy 20%

## Final Olympic Medal Race Results « Wellons’s Weblog said

[…] bronze, country ranking, gold, medal race, olympics, ranking, silver, statistics When I wrote a post proposing a way to rank countries in the 2008 Olympics, it wasn’t yet over. Now that we have final results, let’s see how we […]