Weighting Olympic Medals

While watching coverage of the 2008 Olympic games this summer, I have noticed a trend in the reporting of medal counts. When the reporters speak about individuals who are competing in the Olympics, a lot of weight is given to the fact that they are earning gold medals and not just silver or bronze.

Take the Michael Phelps story, for example.

On Sunday morning, Phelps swam the butterfly leg on the 4×100-meter U.S. medley relay that held off Australia in a world record-setting victory, giving Phelps his eighth gold medal of these Games and his 14th over all.

He had previously come close to the record, but as far as the count of Olympic medals go, this would not have been quite as impressive had he not won all 8 gold medals. Don’t get me wrong. I am not playing down his accomplishment. Rather I am setting a basis for my argument that follows.

Below is a table of the medal count for the Olympics¹ as of this afternoon.

Medal Count

Rank	Country				Total
1	United States	22	24	26	72
2	China	39	14	14	67
3	Russia	8	13	15	36
4	Australia	11	10	12	33
5	France	4	11	13	28
6	Britain	12	7	8	27
7	Germany	9	7	7	23
8	South Korea	8	9	6	23
9	Japan	8	5	7	20
10	Italy	6	6	6	18

This table is the one that is shown daily with updates. One of the things that jumped out at me when I first saw it reported was that the country in second place (China) had more gold medals than the country in first (United States). This bothered me because it goes against my logic of ranking.

If one athlete wins three bronze medals and another wins one gold medal, the athlete with the bronze medals is not placed on the top platform for any of the award ceremonies. Three bronzes indicate third best in the world in each of those events. The athlete with only one gold medal is the best athlete in the world in that one event.

Gymnastics and Diving Scores

Both gymnastics and diving take a similar approach in their scoring systems. Each routine or dive is given a difficulty rating which serves as an adjuster to the scores awarded by the judges. Gymnastics adopted this more recently, but it was deemed a necessary change as competitors who performed less difficult routines could often come away winning gold medals.

Putting a difficulty rating on the routines gives a starting score advantage to those athletes who try more challenging feats. Rightfully so. This is the Olympics, after all, and we’re supposed to be seeing the best the world has to offer, not the easiest routine that will score a perfect 10².

So the divers and the gymnasts step up their game. Shawn Johnson from the United States was expected to win a gold medal in the individual floor exercise at this Olympic games. She performed an exquisite routine and a technically difficult one as well. However, in the end, she had to accept the silver medal.

On the individual level, these medal metals are meaningful. Gold is better than silver is better than bronze is better than the rest. Even so, good sportsmanship pervades the games, and athletes are proud to even compete in the Olympics, let alone win a medal. This is as it should be. When we look at the countries overall and the medals they have earned, we are given another picture, though.

Weight. What?

I am an American. I would love to see the United States rank first in the Olympic games in many events. On the other hand, I would like to see a fair ranking of the achievements. I do not think that total medal count alone is indicative of a country’s overall performance. Looking at just the United States and China, you can see that China has won a commanding number of gold medals, and is not terribly far behind in earning the other medals.

What I propose is that a weight be assigned to the medals for a more accurate portrayal of which countries have the best athletes in the world. For illustrative purposes, let’s just assign a simple arbitrary weight of 3, 2, and 1, respectively to gold, silver, and bronze. Doing this paints a very different picture of the rankings. Take a look at the table below.

Weighted Medal Count

Prev	Rank	Country				Total
2	1	China	117	28	14	159
1	2	United States	66	48	26	140
4	3	Australia	33	20	12	65
3	4	Russia	24	26	15	65
6	5	Britain	36	14	8	58
7	6	Germany	27	14	7	48
8	7	South Korea	24	18	6	48
5	8	France	12	22	13	47
9	9	Japan	24	10	7	41
10	10	Italy	18	12	6	36

I have left the previous ranks — the “Prev” column — for comparison. Notice, there is quite a bit of difference when the weights are applied. France drops from 5th place down to a 8th. China moves up to first displacing the United States. While Australia and Russia are tied in this scenario, Australia moves to third place by virtue of having won more overall gold medals.

I believe this is a more accurate representation of how the countries are performing in the Olympics. Remember that this chart is only the top ten. Some countries just below the top ten could possibly move up as well. Using this method of weighting, gold and silver medals would have more meaning on a national level again.

I believe this, or a similar method, is what we should use when ranking countries in the Olympic games. I am not a statistician, and what little I know of statistics is probably grossly misused here, so I welcome any comments/criticisms/feedback.

Is quality over quantity a better metric in this case?

Update (08/19/2008)

I am not the only one who believes that weighting is the more accurate measure. Wesley N. Colley keeps a regularly updating medal count that includes raw count and a weighting methodology, ranking nations by weighted score.

The weighting factors are as follows.

• Gold — 6
• Silver — 3
• Bronze — 2

Wesley provides an explanation for this weighting selection.

Gold medals are weighted by a factor of 6, silver medals by a factor of 3, bronze medals by a factor of 2.

The reasoning is simple. One person has won a gold medal. Two people have won at least silver, and three people have won at least bronze. The weightings simply reflect these factors.

Note that this weighting system is consistent with many golf tournament payouts, in which the 2nd place finisher receives half the prize money of the champion and the 3rd place finisher receives a third as much as the champion.

See, I knew someone out there had a better methodology, but damned if I wasn’t close.

Footnotes

1. via New York Times ↩
2. Not that I am even 1/10 capable of doing any of the routines, so all of them are impressive to me. ↩

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