Last summer in London I experienced the 2012 Summer Olympics. Many were preoccupied with the ‘total medal count’, which counts the number of golden, silver, bronze, and total medals per country (pick that category in which your country is performing best). Of course, the total medal count is not a ‘fair competition’. Some countries have a larger population, which gives them a bigger pool of athletes to fish from. Other countries are richer, which gives them more resources to facilitate the searching and training of potential medal-winners. I wanted to put the achievements of countries into perspective, and more specifically, to be able to say things like “given its population size and wealth, [insert country of interest] performed well during London 2012” with a bit more confidence. As for my motivation: indeed, I come from a small country,  whereas my girlfriend comes from the U.S. – last summer I heard “The Star-Spangled Banner” way more often than “Het Wilhelmus“.

I ran simple multivariate regressions with data that relate to the Summer Olympics of 1980, 1984, 1988, 1992, 1996, 2000, 2004, and 2008, for 170 countries. Countries that never won a medal or even qualified for going to the Olympics provide information as well, which is why every country for which I could find sufficient data is included. Below, I will describe the specific regressions and the used variables, followed by the reasoning behind their selection. I will then present a ‘prediction’ of the London 2012 total medal count for some chosen countries. Finally, I’ll answer the question: Who is the true winner of the London 2012 Summer Olympics?

Dependent Variables

The dependent variables are percentage of gold medals, percentage of silver medals, percentage of bronze medals, and percentage of total medals. I did not use just the number of medals, because this would give problems if the results are used for out-of-sample predictions, since the total number of medals that can be won at Olympic Games can (and most likely will) differ over time. Also, in some sports where for instance elapsed time decides about the medals, two athletes with an equal clocked time will sometimes get both, say, a silver medal.

Independent Variables

Population: Countries that have more citizens have an arguably larger chance to develop medal-winners, which is why the size of the population is included. I also include the square of population figures, since the relation might not be entirely linear, for instance when taking into account that the number of to-be-enrolled athletes is limited (a country may train 1 million rowers, for every category it can only enroll one team).

GDP per capita: Countries that are wealthier can afford to spend more on the selection and training of athletes, which is why GDP per capita levels are included. For similar reasons as in the case of population levels, I also include the squares.

Latitude: I include the absolute value of the average latitude of the country. Countries that are closer to the equator might be more likely to perform well at Summer Olympics, because the sports practiced are ‘summer sports’, and they experience ‘more summer’, which might give their athletes an advantage. Similarly, countries further from the equator, that are generally colder, are more likely to perform better at Winter Olympics.

Size of the land: I am not sure how it would exactly affect the expected number of won medals, but I still included the size of the land, measured in squared kilometers.

Host: Countries that host the Olympics are likely to win more medals, because of the home crowd and perhaps a more familiar climate. A dummy variable is included to take this effect into account.

Lagged value of total medals: Countries with former Olympic medal-winners have an advantage for several reasons. Firstly, there is the limited sharing of best practices – if a country finds a winning strategy, there is every reason not to disclose it. Secondly, medal-winners might afterwards be employed by their country to train potential medal-winners, where ‘winners (might) produce winners’. Thirdly, if a country has been successful in winning Olympics medals, this might attract funds to select and train future athletes, and it might function inspirationally for young to-be athletes. Therefore, a lagged variable is included, being the number of total medals won by the country at the previous Summer Olympics.

Results

All explanatory variables are significant at a 1% confidence level. If a country hosts the Olympics, it is expected to win about 6% more medals, and even 9% more gold medals. Richer, larger, and more populated countries are expected to win more medals. Initially, rises in GDP per capita and population levels lead to a higher expected number of won medals, but this relation becomes weaker the higher the initial levels become. This confirms that GDP per capita and population levels are non-linearly related to the expected number of won medals. Surprisingly, I find a positive estimated coefficient for the absolute value of latitude; apparently, the farther from the equator, the more likely a country is to win medals. Finally, also the lagged value of total medals is positively significant.

We can use the 2012 values for the independent variables to calculate the expected percentages of won medals. Then, can multiply the calculated expected percentages of medals with the total number of medals that were to be distributed in London to obtain the expected number of won medals. Below you can find the (rounded) expected number of medals (total, gold, silver, and bronze – all estimated separately) for most European countries, China, and the U.S.

Please bear in mind that this is not the most accurate prediction possible. To achieve that, different methods are available. It was my intention to provide some sort of table that can be used to evaluate how good countries are performing on the London 2012 Olympics, taking into account the mentioned factors.

Creating a ‘fair ranking’

Most attempts to create a ‘fair ranking’ take into account the population size (or GDP) by computing some kind of ‘medals per capita’. But this is still an arbitrary decision. Do we take into account only the number of people, or how rich a country is? And with what weights? The above already solved this: regression analyses decided about the weights of the factors that were deemed important.

But, what medals are we talking about? The total number of medals – hence assuming that golden, silver, and bronze medals carry equal weight?  I guess we can agree that a golden medal is worth more than a silver, and a silver more than a bronze, but then? I do not think that we can escape a (random) decision as to how gold medals are valued compared to silver and bronze medals.

Here, some point-based ranking systems are discussed. For instance, the ‘simple point system’, denoted by (3:2:1), gives 3 points for a golden medal, 2 for a silver medal, and 1 for a bronze medal. Similarly, the (4:2:1), (5:3:1), (5:3:2), and (6:2:1) systems are mentioned. We can use such a system to assess how well countries have performed during the 2012 Summer Olympics.

To see how, let’s take the United States as an example. My calculations point out that the U.S. were expected to gather 84 medals: 30 golden, 28 silver, and 30 bronze medals (numbers are rounded). Using the (3:2:1) system, this results in a total expected score of about 165 points. The U.S. actually won 104 medals: 49 golden, 29 silver, and 29 bronze medals, resulting in a total realised score of 225 points. Now, we could say that the U.S. scored (225/165*100%=) 136%. A good score!

Using the final medal count we can do this for all countries, use the calculated percentages to rank them, and thus also decide which country is the true winner of the London 2012 Olympics! See here, the results, where countries are ordered by the (3:2:1) ranking system and where the column headers indicate which ranking system is used:

It is a partial ranking, because not every country is included in it. I might do so later on, to obtain a complete ranking.

For now, Moldova: felicitări!