And the Winner Is...

...Grenada? Who'd have thought?

Let's assume human talent for any given skill follows a statistical distribution (like a bell curve). So any random sample of a significant number of people would follow that distribution. Let's further assume that human talent is equally distributed across the planet. If it really was completely equal, then the people from one nation would form a random sample, and the distribution of talent within that country should conform to that same distribution as the world population. With me so far?

So, the point of the Olympics, it seems, is to incite nationalism and unhealthy pride, and cause condescension towards people with different skin color, language, or social customs inspire warm fuzzy feelings among all members of the human race by demonstrating how people from our country are obviously so much better than you because we won more medals and that mean's we're a superior race and you should be bred out of existence the athletic talent, courage, determination, and perseverance of people from every nation.

This brings up the topic of who "won" the Olympics. Typically, this is figured by gold medal count (since no one cares about silver or bronze). This year, the US "won" the Olympics by bringing home the most gold medals (46), compared with second-place China (38). But is this really the best indicator of "winning"? If skill was distributed equally across the globe, then you would expect those nations with more people to have more athletes at the top of the bell curve, and therefore more gold medals. So really, there's nothing unexpected about the top two gold medal winners also being the third and first most populous countries. This would even happen if, on average, Americans and Chinese fell below the curve on athletic talent.

With this in mind, let's take a look at the gold medal winnings. The Olympics web site has a chart of all medaling nations and how many medals each one won, comparing that with Wikipedia's list of countries by population allows us to calculate how many medals were won per 100 million residents of each country. This way, we can figure out which countries really did earn more medals than would be expected for equal talent distribution.

Sorted this way, we find the real winners of the Olympics:

Country	Gold medals	Population	Gold medals per 100 million residents
Grenada	1	105,000	952.3810
Bahamas	1	353,658	282.7590
Jamaica	4	2,705,827	147.8291
New Zealand	5	4,434,590	112.7500
Hungary	8	9,962,000	80.3052

Yes, Grenada with a population of 105,000 took home one gold medal, giving it the highest gold-medal-to-resident ratio. However, you may note, they only won one gold medal, which may indicate sample size issues. Only 0.0015% of the world's population lives in Grenada, but the minimum non-zero percentage of gold medals that can be won is about 0.33% (302 gold medals were won, in total; one gold medal is 0.33% of the total). Since fractional gold medals can't be won, there is no way for Grenada to have won a percentage corresponding to its percentage of world population.

So let's up the sample size of gold medals and only consider countries that won, say, at least 10 (only the top seven medal winners):

Country	Gold medals	Population	Gold medals per 100 million residents
Great Britain	29	62,262,000	46.5774
Republic of Korea	13	50,004,441	25.9977
France	11	65,350,000	16.8324
Russia	24	143,117,000	16.7695
USA	46	314,147,000	14.6428

And so, there you have it. The host nation takes the gold, winning 4.6577e-7 medals per resident. With only 0.89% of the world's population, she proved she had 9.60% of the talent. Clearly, she is most above the bell curve when it comes to athletic ability.

Or Is She?

This brings up another issue, though, and that is opportunity. Great Britain being a) a rich b) first-world nation that c) hosted the games, had the most opportunity to send athletes to the games. The world's best underwater basket weaver or left-handed duck slapper or yellow-bellied sap sucker may live in Toopoortoeatanythingbutdirtistan, and simply be unable to compete. Britain may, in a sense, have won by default. How do we test this?

One way might be to compare the number of athletes each country entered, then use that to figure how many gold were won per athlete. This way, countries that flooded the games with athletes (and would therefore be expected to win more medals) can be accounted for.

So, after finding a list of all 10,903 athletes at the 2012 London games (courtesy The Guardian), we can find out how many athletes each nation entered, then figure out the medals won per athlete:

Country	Gold medals	Athletes	Gold medals per athlete
China	38	379	0.1003
Grenada	1	10	0.1000
USA	46	534	0.0861
Ethiopia	3	35	0.0857
Jamaica	4	50	0.0800

There's Grenada again, at number 2. Limiting it to countries with at least 50 athletes, to get a good sample size:

Country	Gold medals	Athletes	Gold medals per athlete
China	38	379	0.1003
USA	46	534	0.0861
Jamaica	4	50	0.0800
Iran	4	53	0.0755
North Korea	4	56	0.0714

Britain isn't even on the list. With 556 athletes (the most of any nation), she won only 0.0522 medals per athlete. So she only won so many medals, because she had so many competitors, and thus more opportunities than any other nation to win gold medals.

So from this measure, China takes home the gold.

You can view my complete spreadsheet here:

A few interesting things I noted while assembling the data.

• The US really was a solid contender. She was not over-represented, with 534 athletes (4.90% of the total) representing 4.47% of the world's population, giving her a representation factor of 109.57% (percent of athletes divided by percent of world population). That 4.90% of athletes won 15.23% of the gold medals, giving her an athlete competitiveness factor of 311% (percent of golds over percent of athletes), and a world competitiveness factor of 340.76% (percent of golds divided by percent of world population). Any way you slice it, she is well above the curve.
• While South Korea completely demolished North Korea in golds (13 vs. 4), North Korea actually outperformed on a per-athlete basis. With 56 athletes (0.51% of the total), DPRK took 1.32% of gold medals, for an athlete competitiveness of 257.88%. Compare that with RK's 4.30% of golds from 2.34% of athletes for a competitiveness factor of 184.05%. RK was much more over-represented, with 329.41% representation factor, compared with DPRK's 146.75%. But that, in itself, probably says something.
• China was, interestingly, extremely underrepresented. They had 379 athletes (3.48% of the total) representing 19.16% of the world, for a representation factor of 18.14%. Despite this, they took home 12.58% of the gold medals, which gives them their world-leading 361.98% athlete competitiveness. More than 1 in 10 Chinese athletes took home a gold, with more than 1 in 5 taking home a medal of some sort (not accounting for multiples).
• I found it odd that the first and second most medaling nations were the first and third most populous. Where's number 2? For a while, I thought India wasn't even in the games, since I couldn't find them in the list. Eventually, I noticed them: 83 athletes (0.76%) representing 17.21% of the world, for a representation factor of 4.42%, making it the most under-represented medaling nation. They won 0 golds, 2 silver, and 4 bronze. Quite clearly, they just don't care about our petty sporting squabbles. I was reading something about why they're so underrepresented. It's suggested that, unlike China, they have nothing to prove on the world stage and also they don't focus on athleticism as much as intelligence. Which makes sense. If the US or China is the jock, India is the nerd that gets bullied and does our homework and technical support for us.
• Grenada was the most over-represented country, with 10 athletes (0.09%) representing just 0.0015% of the world, for a representation factor of 6114.53%.
• The most underperforming athletes from medaling nations in terms of percent of all medals divided by percent of athletes, are Portugal (14.17%), Morocco (15.74%), Venezuela (16.43%), Egypt (19.37%), and Greece (21.59%). Of those nations that won gold medals, the most underperforming (percent of golds divided by percent of athletes) are Canada (12.89%), Argentina (25.42%), Sweden (25.79%), Serbia (31.12%), and Colombia (33.12%).
• I think this data is biased in favor of countries that prefer solo sports as opposed to team sports. I'm not sure how medals are listed, but I believe its per sport won, not per athlete. So if ten athletes play on a team and win one gold for that team sport, that country's athletes will appear less efficient (one gold per ten athletes).