I know many of my readers are looking forward to the upcoming Winter Olympics. The question is how many gold medals our nation will win this time. Well, if you don't want to know, you should not read this post.

Professor Daniel K.N. JohnsonDaniel K.N. Johnson (Colorado College) and Ayfer Ali created in 2000 a method to determine how many medals a given nation would win in the Olympics. This method is not based on statistics or observations of athletic performance, but of other social parameters in the nation. The formula has proven to be remarkably accurate for the past five Olympics, and one has to ask: will it be for this one also?

Before every Olympics, Johnson and Ali is crunching the numbers, and publishes who they think will be the winners. Newspapers print an article about itBBC - The economics of the Olympic Games (2002), and this year is no differentAftenposten - Spår canadisk medaljerush (norwegian). Both Johnson and Ali work at Harvard, and their field is economics. Why would the performance of a nation in the Olympics be governed by economics? It's time to dig into the scientific paper.

The method

The duo first released a paper in 2000, and then re-released it in 2002. Both versions can be found on the InternetGoogle Scholar search for Tale Two Seasons Johnson Ali. The following is a summary of the article where I focus on relationships that seems to affect a nations chance to win a medal.

The article is called A Tale of Two Seasons: Participation and Medal Count at the Summer and Winter Olympic Games and attempts to investigate how the economic and political situation in a nation impacts its chance to participate and win medals. By assuming linear relations between the number of participants and the number of medals won, and several economic and political factors, they can even predict future results. To determine the coefficients in the relation they use data from Olympic Games from 1952 and to today.

They quickly establish a relation between participation and success. If you have many participants you have a better chance of winning. Rich countries can afford to send more athletes, as well as give better training in advance. In the entire history of the Olympic Games, all African nations combined share a little over 2% of all summer medals. Countries with a large number of people have a larger population to choose from, giving them a chance to assemble a better team. The climate in a country will have a great impact on their performance; no African nation has ever won a winter medal. Being the host nation turns out to be a huge advantage, since the host nation on average has 210 more participants than it would have otherwise. Also the neighboring nations have an advantage, at least for summer games.

Less than half of the 241 nations that competed in the 1996 Summer Olympics have ever won a medal in any event, summer or winter. Nations that won at least one summer medal average 5 times the population of non-winning nations, and over 50% higher GDP per capita (per head). In 1952, one in twelve (1/12) of the winter Games participants was from the top 10% of nations ranked by income per capita. In 2002, this number was one in two (1/2), or half of the participants.

Countries in temperate zones (with some degree of winter) tend to have higher income levels, and they also encourage both summer and winter participation. This means that a cold climate have a positive affect on participation for both seasons. Interestingly, political system also plays a significant part. In fact, single party and communist systems wins on average 18 summer medals (10 winter medals) more than their peers, even though they do not send more participants.

Taking all the above into consideration, the formula that Johnson and Ali arrived at looks like this:

where:
medals is the number of medals won by nation i
GDP is Gross Domestic Product per capita of nation i
POP is the population of nation i
HOME indicate hosting nation
NEIGH indicate immediate geographical proximity to host
POL indicate political system
LFROST is the share of land feeling a light frost
HFROST is the share of land feeling a heavy frost
t is a time trend
MED is the number of available medals
u is a nation-specific error term
? is the unexplained error

In the article you can find a table with all the coefficients depending on winter and summer Games. The equation is quite straight forward, but it's difficult to understand how excatly these parameters can determine who wins the most medals. In a moment we will see exactly how much sense it makes. I want to mention that the article continues with an interesting analysis on how much money a gold medal is worth for a nation, and how much the GDP would have to increase per capita to earn the nation one more medal. I will not discuss it here, but if you are interested I refer to the article.

Earlier results

In the end the article predicts the medal count for the 2002 Winter Games, and compares them to the actual medal count. We can do something even more interesting: compare many Olympic Games. Johnson has calculated the correlation between their prediction and the actual results for the last five Olympic Games. I have created this small table with the results:

The correlation factor for the last 5 Olympic Games
The correlation factorCorrelation on Wikipedia tells us something about how to sets of data matches. It is defined from -1 to 1, where -1 means completely opposite and 1 means identical. The results speak for itself. There is a clear trend that Johnson and Ali can predict how a nation should perform based on income per capita, population, climate, and political structure.

This year

And then it is time for this year's predictions. Johnson published them in a press release some days ago. You can read the release in the embedded document below.

So Canada and Russia will come out on top. I asked my sport-expert (my brother) what he thought of this, and he did not think these results were realistic. He reasoned that Canada is not strong enough in cross-country skiing, and there are many medals in these events. It's interesting that Johnson arrive at his results without considering any sport-related relationships, while most sport-experts will not consider the parameters that Johnson uses. I have decided, as an experiment, to wager 100 NOK (about 12 €) on both Canada as most winning, and Russia as most gold-winning. I'm not really expecting to win, but it will make things more interesting.

Conclusion

Johnson and Ali conclude their article by discussing what the results means. One should not read them as a solid betting-tip, but rather as how well a nation is expected to perform. Any anomalies can reflect personal characteristics of athletes, trainers and coaches. In other words: just the way it's supposed to be. They further conclude:
"There is a measurable, continuing advantage to certain nations in the Olympic Games. We should be aware of that fact when we compare outcomes across nations, and when we set our own national goals for medal counts."

So this year, when I'm looking at the number of medals per nation, I will not judge by the total number, but rather how they perform relative to their expected performance.
So enjoy the Vancouver 2010 Winter Games, and good luck Cana.. I mean: Norway!