re: Is there are more dumb way to judge Olympic success than medals per capita?

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The Olympic committee only allows a certain number of athletes in each country to compete in a specific event.

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Yes, but a smaller country has a smaller pool of athletes from which to choose than a bigger country. Therefore, the competition is increased in the bigger countries, so they have a higher chance of sending someone who is better than a smaller country does. So the "per capita" metric is more valid than you seem to think.