Who are the best team in the Olympics?

Given that I'm a Leo (since I was born in August) and that 2012 is an Olympic year, I thought that this would be quite nice and appropriate as my next favicon. I wonder if I'd get sued? 

[By the way, as I'm writing, Andy Murray, one of the people in my team, has just got into the final of the tennis tournament. Well done Team Me!] 

Anyway. I was reading an article in the Guardian, which discusses an alternative way of ranking the Olympic teams with respect to the medals table, produced by a group of statisticians at Imperial College. 

The obvious way is to simply count the number of medals won. But of course there is some confounding going on $-$ for example, bigger countries have a larger "pool" of potential athletes from which to get their participants. Similarly, wealthier countries could (theoretically) invest more money in sport, thus making them more likely to win medals.

So they have produced a few alternative ranking systems, based on weighting the observed numbers and accounting for a few key variables (although it's not very clear what they've actually done to produce the weights). 


I think that's kind of reasonable, but it doesn't account for (at least) one important factor: the underlying assumption is that every medal is worth the same. But that's not true for all sports. Some countries, albeit small, may be powerhouses in a given sport. Thus, winning a medal is not quite so unlikely: North Korea winning gold in judo is not quite shocking, is it?

Nevertheless, I think it's interesting to see that if you plot the official ranking against that based on each nation's GDP (which by the way I think would have been a much better way to report the data, instead of the big table given by the Guardian) only North Korea (PRK) remains in the top 10. 

Moreover, I'm not sure that GDP is actually the best variable to consider here: yes, richer countries have theoretically more money to spend on training athletes. But take for example Italy. We are in the top 10 official ranking but move to only the top 30 when accounting for GDP. However, in fact the actual amount of money that the government allocates to sport is quite low with respect to the actual GDP (possibly excluding football, as my hooligan wife suggests).