Tails Of Great Soccer Players

Jacob Falkovich applies simple statistical reasoning to ask why the Chinese soccer (football!) team is so bad. The population of China is 1.4 billion. But China's soccer team is ranked below Antigua and Barbuda, which has a population of just 90,000 people! 

How can this be? 

Falkovich speculates that soccer success depends on natural ability and something he calls soccer affinity. He assumes soccer ability and soccer affinity are normally distributed. 

This simple model can account for why the ability of the national team depends much more on the average level of soccer affinity in a country than on the total size of the population. His explanation rests on the properties of the normal distribution.

National teams draw from the top of the distribution of soccer ability in a population, i.e. the extremes of the right tail of the normal distribution, the best of the best. 

The best player in China is one in a billion. According to the normal distribution, he is 6 standard deviations better than the average player. If China's population doubled, you would expect to have two players this good. Not enough for a decent team, in other words! But if the entire population of China's soccer ability improved by just one standard deviation (i.e. a shift in the entire distribution to the right), then there would be over 200 players as good.

This explains why interest or affinity in soccer is much more important in predicting how good a team is rather than sheer population size. 

This reasoning applies more generally, as the author explains. The same logic can account for why there are more extremely tall Norwegians than there are Indians despite India's population dwarfing Norway's.