So I was browsing the web about a week ago when I saw this article: Yahoo: Fourth Place Medal Article

Like many avid fans of the Olympics, the author expresses discontent at the IOC’s current system of “ranking” countries on their performance during the games. While I do not agree with the article’s proposed alternate medal system, the author does bring up a good issue that I have though about many times in the past, i.e., what is the best way to rank how countries perform during the Olympic games? While most of the world seems to go with the IOC’s standard of “gold medals first”, the U.S. media sticks stubbornly with the “overall count”. Obviously, there are flaws with both schemes, and it is the goal of this article to point out those flaws and propose a more fair ranking system for the Olympics games.

First, the flaws. One obvious problem with the IOC’s current system is that it discounts silver and bronze medals completely. Essentially, a country with 3 golds, 1 silver, and 2 bronze would be ranked higher than a country with 2 golds, 10 silvers, and 5 bronze. While this example is a bit extreme, it does effectively illustrate the problem with the IOC’s medal system. On the flip side, the U.S.’s “overall medal count” system overcompensates for this problem, because it makes gold, silver, and bronze medals all equally weighted, which is equally absurd. How can one country with 1 gold, 1 silver, and 10 bronze be ranked higher than another country with 8 golds and 1 silver? Clearly, the answer lies in coming up with some sort of weight adjusted scheme for accounting for medals, which is what the author of “Fourth Place Medal” proposes in the above article. The article uses a 25-10-5 point scheme for gold, silver, and bronze medals respectively, as well as a “marquee system” for giving more points to “high profile events”? While the point system is certainly a step in the right direction, giving more point for certain events just seems like a pathetic attempt to justify the U.S.’s overall victory at Vancouver. As one reader aptly pointed out, if you take away the doubling of points for the marquee events, Canada would still be on top.

However, I would argue that Fourth Place Medal does not go nearly far enough with its weighted ranking system. After all, there are at least two additional factors (population and income) that have a significant impact on a country’s performance during the Olympics. Kaufman’s article (http://blogs.worldbank.org/governance/who-won-the-beijing-olympic-medal-race), which is based on the 2008 Olympic Games, does a good job of accounting for these factors. In his scheme, gold, silver, and bronze are on a 3-2-1 weighted scale, and medals are weighted per capita (based on population). This system makes more sense, as it mitigates the ranking bias towards larger countries. Indeed, countries with bigger populations (by sheer probability) will have a bigger pool of gifted athletes, thus allowing them to send a stronger delegation to the Olympics. However, I was surprised at how easily Kaufman dismissed the use of GDP in his ranking scheme. His reasoning is as follows:

“Even economists will criticize me; some may say that instead of the per capita measure I should be calculating medal ranks relative to the country’s GDP, so to try and get an ‘efficiency’ ranking of sorts.  But this does not make sense, because of governance: it would be easy for Zimbabwe and North Korea to be ranked at the top of the medal totem pole (per unit of GDP), simply by misgoverning the country to such an extent that they run it to the ground.  Then the denominator (GDP) in the calculation virtually disappears, propelling them to the top of such ill-advised relative medal count ranking…”

However, the question is why would any country misgovern itself in such a way that would decrease its GDP? Simply to get bragging rights at the Olympics Games? I think not. Rather, I think the majority of the nations in the world try and govern themselves in a manner that will increase the total well-being of the nation as a whole. And while it is debatable the the extent to which GDP and well-being correlate with each other, GDP and GDP per capita figures are nonetheless used all the time to measure a country’s prosperity. Indeed, if we take GDP to be a reflection of a country’s wealth/resources, than “richer” countries will have an advantage when it comes to training and developing athletes for international competition.

Now that we have established that population, GDP, and a weighted system for medals are all needed in our ranking scheme, the question is how much of an impact should each of these factors play in determining the final breakdown. First, there is a question of how the medals themselves should be weighted. The most popular schemes are 5-3-1 and 3-2-1. Both systems, in my opinion, overvalues the silver medal. If you ask any athlete whether they would rather have 2 silvers or 1 gold, I think the majority of them would want the gold. In fact, the gap in value between gold and silver is probably much higher than the gap between silver and bronze. To keep things simple, we’ll use a 5-2-1 scheme. Notice that it’s essentially the same is Fourth Place Medal’s 25-10-5 system. We see that the gap between the top three, Canada, U.S., and Germany, shrinks considerably. After taking into account population, we get Norway as the runaway winner. Canada is now 5th, the U.S. 20th, and China, hampered by its enormous population, now dead last despite winning 33 weighted medals. Doing the same procedure for GDP, we see that Norway once again tops the list,with Belarus a surprise second. Nor so surprisingly, China, the U.S., Japan, and Great Britain are all at the bottom of the list.

Putting it all together: The logical next step would be to combine these two schemes and use GDP per capita. The result is…surprise! China is on top, and by a large margin. Why? Because in this case, China’s huge population actually helps it. Because it’s population is so big, China’s GDP per capita is small, despite the fact that it boasts the third largest economy in the world. Furthermore, the top 5 countries ranked on this scheme are ranked 26, 21, 15, 5, and 20th in the the per capita rankings and 22, 18, 13, 12, and 23rd on the GDP rankings, hardly what we want. Norway, which we expect to be the outright winner, is in 10th place. So where did we go wrong? We want our final ranking to be a function of both population (p) and GDP (g). If we express this in mathematical terms, we can write R = F(p,g). However, if we use the GDP per capital scheme, then we are saying that R = F(g/p). We instead want the two input factors to be independent of each other. So the best way to incorporate this into our final ranking system is to have our function be a weighted average of the GDP and per capita ranking schemes, which is what I ended up doing. In doing so, I also took weighted medal rankings for both GDP and population. That way, the different between certain rankings is more evident. For example, in the per capital ranking, instead of having Norway being 1 and China 26, China has a weighted ranking of 564. That is to say, China’s population is 564 times that of Norway.

Finally, we need to decide whether GDP or population is more of a factor in determining Olympic medals. In the spreadsheet, I have the default set to 50-50%, but you can change the values to whatever you want and see what interesting results appear. You can also mess around with medals count to see how many medals a country would need to win so that they could achieve a certain rank in the new system.

Things to note: A the 50-50 level, the system seems to favor small countries more, with the exception of Canada. The list is almost identical to that of the per capita ranking.

*The top ten is filled with countries whose climates tend to be more accommodating of winter sports. This brings us to an important point. Nations such as Norway and Switzerland experience tons of annual snowfall while China may not get much at all. While climate/weather may not be a factor for certain sports such as curling or ice skating (since they take place in indoor facilities), it makes a huge difference for sports such as cross country skiing and luge. The question is how you factor this into the final ranking. Theoretically, one could make an index based on the number of inches of snowfall a country gets on average every year, or the number of days of “winter” a country experience, but such data is extremely difficult to collect accurately.

At the end of the day, the lesson is that no matter how complicated you make a model, it can never be perfect, and while the ranking system that I derived today is an improvement over most, it still doesn’t take into account a lot of necessary factors. Still, weather factor excluded, I’m willing to call Norway the official winner of these 2010 Vancouver Games.

FOR THE FULL SPREADSHEET CLICK HERE: 2010 Olympics Medal Analysis (click save link as…)