# Weighting For Medals at Sochi

February 21st, 2014 at 11:17 am

I don’t know about you, but when I hear “total medal counts” for the Sochi Olympic Games, I always wonder, “sure, but why count all three medal levels as equal?”

That is, surely gold is worth more than silver which is worth more than bronze.  Shouldn’t there be some weighting scheme to factor in those rankings?  Granted, any such scheme is arbitrary–and maybe, if we’re taking the high road, as we always should, outside the spirit of the games.

Still, what happens to the rankings if you use the simplest of weighting schemes, 3 for gold, 2 for silver, 1 for bronze?

SOCHI MEDAL COUNT, 2/21, UNWEIGHTED AND WEIGHTED TOTALS

Source: As of 11am today.

Just grabbing a sample of medal-board leaders, in fact, the rankings change quite a bit when you apply these weights.  Canada, in third place re totals, jumps to first and the US fall from first to third.

Go ahead and try this at home–perhaps you have your own weighting ideas.  I’ve thought about other factors if one wanted to dive more deeply into this, like considering population size (should be positively correlated with success just based on naïve skill distributions; if your top 1% of speed skaters includes 500 people versus 5 people, you should win more, all else equal), per-capita income, climate (I don’t blame the Zimbabwe skier who come in 61st).

But–putting aside the important caveat about violating the spirit of the games–at least we’d want to think about weighting medals when we tote them up.

#### 10 comments in reply to "Weighting For Medals at Sochi"

1. Andi says:

See also Bill Mitchell’s alternative 2012 Olympic Medal Table, with rankings by GDP, Population and GDP per Capita. He also uses your 3 / 2 / 1 weighting for gold / silver / bronze.
http://www.billmitchell.org/sport/medal_tally_2012.html

A very unusual order of nations!

2. Dave says:

You are correct! People try to weight these things just like you say!

I’ve been wondering about a perfect weighting scheme myself, and I cannot create one. I’ll accept yours because I have no other.

3. Tom in MN says:

Should give the poor people that get 4th a weight of -1.

I root for athletes to get personal bests at the Olympics, too much is made of the medals, when 4th in the world is still very impressive.

4. Pauley says:

Under 3 + 2 + 1 = 6, a tie for gold skews the weighting a bit. 2 golds @3 + 1 bronze = 7.

5. Jon says:

How about a weighting based on metals prices? That bronze won’t feel nearly as special then! 🙂

6. Graham Chalmers says:

I can’t think of any way to come up with an optimal weighting, but during the summer 2012 Olympics I experimented with a weighting system based on the number of other athletes “defeated”. For example if 8 swimmers compete, the gold medalist has beaten 7, the silver medalist has beaten 6, and the bronze medalist 5. The number of significant competitors could vary with the event, of course, but a 3/2/1 weighting seems to say the bronze medalist is only 1/3 as good as the gold medalist. A 7/6/5 weighting seems more fair to me. A tie for gold would give each 6.5 say. This doesn’t take into account the margin of victory of course.
To fairly compare countries, it seems the top n athletes should get weights of (n-1)/(n-2)/(n-3)/(n-4)/……, where n might be 7 to 10. Or it could be n/(n-1)/(n-2)/(n-3)/(n-4)/… so the last gets a weight of 1 instead of 0.
In 2012 I was interested in comparing Michael Phelps with Larisa Latynina, who had more individual medals than Phelps (14 to 11, I believe). I used 7/6/5 and counted 1/4 of a medal for a team medal. Phelps came out ahead.

I would note that one thing that seriously distorts the medal counts is the IOC’s bizarre way of doing the counting. It seems to me that it ought to reflect the actual number of medals awarded. For example, Canada ought to be getting credit for 40-odd gold medals for having won the men’s and women’s ice hockey tournaments. Winning a 2-week hockey tournament ought to count for more than having the best time skiing downhill one time.

8. wufnik says:

In track they use a 5/3/1 weighting, to ensure that 1st place counts for more than second and third places combined. This seems reasonable. Using this approach, you get the following:

. sum wtd 5/3/1
Russia 13 11 9 33 107
Norway 11 5 10 26 80
Canada 10 10 5 25 85
US 9 7 12 28 78
Netherlands 8 7 9 24 70
Germany 8 6 5 19 63
Switzerland 6 3 7 11 46
Belarus 5 0 1 6 26
Austria 4 8 5 17 49
France 4 4 7 15 39
Poland 4 1 1 6 24

Canada moves into second place under this approach, and Austria moves up a couple of places.