London 2012 Adjusted Medal Rank

UPDATE: All stats and figures below have been updated with the final medal counts as of August 12, 2012. Prior medal equation had population weighted at 1x and GDP/cap weighted at 1.85x.

I was watching the Olympics with my brother last week, and we were discussing what the best way to rank countries is. Some media outlets rank by number of Gold medals and others by number of total medals (Gold + Silver + Bronze). I think total medals is better because it takes a little bit of luck out of the equation (i.e. in some competitions, amongst 3 very good athletes, luck is more likely to be involved in determining who is the best among the 3).

But total medal count doesn't take into account factors that are "outside" short-term control. Total population is what first comes to mind, but also GDP. If there are a lot more people in the country it's more likely there will be more Olympic athletes and thus more medals. If GDP per capita is high, athletes would presumably have more resources and better opportunities for training.

This link I found on Hacker News shows adjusted medal counts for both population and total GDP.

I think a better way of adjusting the rank is by using both population and GDP/capita and doing a regression analysis to find each country's "Expected Medals". The countries would then be ranked on the difference between their expected and actual medals.

Regression analysis

It's been a while since my college stat class, but here we go. The equation for Expected Medals based on the final medal count is:

Total medals = 4.4 + population / 21,610,238 + GDP per cap / $5,364

According to Excel these variables account for 28% of the difference in medal count. So you could say that 72% of the factors that go into a country's medal count are unrelated to population or GDP/cap.

But this equation is a little off from reality because it would mean countries with very low populations would be expected to get at least 4 medals. So after fiddling with the equation a bit, I got rid of the "4.4" base and overweighted GDP/cap by 2x and population by 1.1x to zero-out the excess medal count for all countries. Why overweight GDP more than population? Because I personally think that variable matters more. Here's the new equation:

Total medals = 1.1 * population / 21,610,238 + 2.0 * GDP per cap / $5,364

This gives a little more credit to the smaller countries and countries with low GDP/cap. So without further adieu, here are the final rankings:

Rank Country Total medals Expected medals Excess medals 1  

U.S.A. 104 33.9 70 1  

Russian Federation 82 12.1 70 3  

Great Britain 65 17.6 47 4  

Germany 44 20.5 24 5  

Republic of Korea 28 10.3 18 6  

China 88 70.6 17

 Click here for the full table in Google Docs.

The U.S. still wins! Lest you think I'm biased, the only adjustments I made actually favored most other countries in the ranking (those with lower GDP/cap, like Russia and China). If you see any flaws here or think there's a better way please comment.