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