Ranking Countries in Order of Athletic Level

I never attach importance to the number of gold medals won by different countries in Olympic Games, nor want to find fault with that attained by China in Beijing Olympic Games held this summer. I would just like to point out that the ranks of countries are quite different when the number per population is considered instead of the actual number.

The ranks of countries by the number of gold medals (more than five) in Beijing Olympic Games are as follows (Ref. 1):

1	China	51
2	United States	36
3	Russian Fed.	23
4	Great Britain	19
5	Germany	16
6	Australia	14
7	Korea	13
8	Japan	9
9	Italy	8
10	France	7
10	Ukraine	7
10	Netherlands	7
13	Jamaica	6

On the other hand, the ranks by the number of gold medals per population among the above thirteen countries are as shown below. The first number for each country is the population taken from Ref. 2 in units of one hundred million; and the second number is the number of medals per population multiplied by one hundred million.

1	Jamaica	0.0271	221
2	Australia	0.214	65
3	Netherlands	0.164	43
4	Great Britain	0.610	31
5	Korea	0.482	27
6	Germany	0.822	19
7	Russian Fed.	1.42	16
8	Ukraine	0.461	15
9	Italy	0.596	13
10	United States	3.05	12
11	France	0.645	11
12	Japan	1.28	7
13	China	13.3	4

If we include the countries and regions that won at least one gold medal, the ranks would be different much more. Anyway, the second method of ranking clearly shows that a good fight exhibited by Jamaican athletes including the sprinter Usain Bolt was wonderful in Beijing Olympic Games.

Let us consider two countries A and B, A having much larger population than B, and assume that these countries have the same athletic level. Then, country A is statistically expected to produce a larger number of excellent athletes. This makes the method of ranking by the number of medals favorable to A. In country A, however, the selection of the delegation for Olympic Games would be severer because of the limited number of medals expected, making the method of ranking by the number of medals per population unfavorable to A. Therefore, the method that combines these two methods with certain weights might be adequate to know the proper rankings of countries in order of athletic level.

1. Overall Medal Standings, The Official Website of Beijing Olympic Games August 8-24, 2008.
2. List of countries by population, Wikipedia, the free encyclopedia (26 August 2008, at 07:09).