UPDATE noon 8/11/12: A devastating rebuttal to this post notes that if you limit the medal count to gold and change the indicator to the Human Development Index, there is no correlation. I have no idea what the point of this is. Researchers devote vast effort to the central question in economic development: "what determines Olympic medals?" The answer is income per capita and population, or in other words total GDP. The following table shows this story fits pretty well.
The big underachievers are (in order of underachievement) India, Mexico, Indonesia, Turkey, Saudi Arabia.
The big overachievers are Belarus, Ukraine, Kazakhstan, Romania, Iran, , and Jamaica.
The lessons seem to be:
(1) World Bank national development strategies in key emerging markets have failed miserably in the Olympics sector.
(2) a history of Communism may not have been so awesome for development and liberty, but it's still amazing for Olympic medals.
(3) Islamist ideology is a mixed medal producer (Saudi Arabia no, Iran yes).
(4) if nothing else works, just run really fast.