It's interesting but I can not find any correlation at all. So I'd guess the conclusion is that olympic medals have nothing to do with population size or money.
Instead it has everything to do with if the country cares or not. India clearly doesn't.
There's a slight anti-correlation with population size. Large nations with conventionally "successful" olympic programs (USA, China, Russia) are well below median in medals per capita.
My guess is that this is because there's an upper limit on entrants. The USA and China might be much more likely to get medals, but they're still limited to three per event at maximum. There might be events where a big nation (China and diving comes to mind) might be able to get even more medals, but can't because they only have so many slots.
That's the noise you'd expect from a random process. Any country with an Olympic program has some chance of earning a medal. Thus, given a sufficiently large number of small countries, you'd expect that a random subset of those nations would earn a higher number of medals per capita than the big players. That Jamaica is at the top of the list is a decent example -- without the unexpected, astronomical weirdness of Usain Bolt, they'd have half as many golds.
The larger programs have a greater number of chances to win, but normalizing by GDP or national population doesn't tell you anything about the overall probability of an athlete from country X winning a medal (which is arguably what you want to know). To get that information, you'd have to normalize by something else -- like size of team, or program expenditure, or some factor that's more directly related to athletics than GDP or population.
Yes I agree. To make the list statistically valid you should probably only look at those countries with more than say 15 or 20 medals. I wonder who comes out on top then? :)
Tough to say. What this (perhaps) suggests is that there are more good athletes per capita in Cuba than in Japan.
But there are a lot of confounding factors, so I wouldn't read too much into it. For example, one needs to consider the amount of money invested into training and selection of athletes. The US is somewhat lackadaisical about selecting athletes at a young age, whereas the eastern bloc countries tend to be a bit more motivated....
The best I could do was an "authoritarian index", using the
(GDP / Population) / Gold Medals and Total Medals. If you rank them by that, you see some pretty nasty countries near the top, and nice countries near the bottom.
Zimbabwe, North Korea and China round out the top three... Ethiopia is ok but does lack freedom of the press, etc.
Then look at the bottom of the list: all free market, liberal democracies. Finland, Belgium,etc, Bahrain, arguably the most democratic country in the Gulf, Slovenia, etc, on the way up.
There are statistical blips of course. Jamaica is near the top because they are just that aweseome. Also, I just made this up so it's probably completely wrong.
To put forth the very rough and completely unscientific theory:
A more authoritarian country is willing to put in more effort, per dollar of GDP and amount of population, to get gold medals. They've got more to prove.
So I'd guess the conclusion is that olympic medals have nothing to do with population size or money.
Instead it has everything to do with if the country cares or not. India clearly doesn't.
I partly agree your views that performance at global events depends a lot on how much priority and importance a particular society (and hence it's government) gives to sports.
But money does matter a lot. Countries who are doing well in global sports arena, either have a very strong government sponsored program (e.g. China) or solid private backing (USA?). It does take a lot of investment to churn out superstar sport-persons.
Till now sports was not on the highest priority list here, and add to that pains of a huge developing nation, the state sponsored program is just for namesake. Interestingly the first individual gold medal winner (in shooting) for India, comes from a very affluent family, and even has his own private shooting range.
Once more money, and more 'focus' comes in, things would definitely change.
Instead it has everything to do with if the country cares or not. India clearly doesn't.