Medals table: The alternative rankings for London 2012

Athletes on a podium Image copyright Thinkstock

China has made a flying start in the 2012 Olympics, predictably. But how many medals should we expect a country to win, based on its size and wealth? In other words, which countries are punching above - and below - their weight?

Every four years, about 200 nations compete at the summer Olympics. But statistically, the playing field is uneven. The bigger a country's population, for example, the bigger its pool of potential athletes.

Wealth is important too, not only because a rich country can provide better sports facilities and infrastructure but also because, in many countries, families need a certain level of wealth to pay for training or even to spare their children - who might otherwise be working - for that training.

So here is an interesting thought experiment. If you take into account the fact that some countries are richer than others, and some have more people, can we work out what the final medal tally should look like, based only on those factors?

Meghan Busse from the Kellogg School of Management at Northwestern University in the US helped us with the sums. She says the US should come top of the 2012 Olympic table with 51 medals, followed by China, Japan and Germany.

Britain, she says, should come 8th with 32 medals. Some 62 countries would get at least one medal and another 143 wouldn't get any.

But of course, this is probably not the best way to predict what will actually happen. If one looks at the Beijing Olympics in 2008, quite a number of countries got far fewer - or far more - medals than Busse's model would have predicted.

Some countries such as Brazil and India underperform because, says Busse, although they have very large populations, their GDP per capita is quite low.

"Either people who are lucky enough to be endowed with that athletic ability do not have the leisure to be able to develop their talents, or they don't happen to live in a place where there are sports programmes and sports facilities," she explains.

There are cultural factors at play too. For instance, according to Busse's model, India should be ranked 5th in the world with 34 medals. But in 2008, it got just three.

Dan Johnson, an economics professor at Colorado College in the US, says that is in part because Indians happen to prefer non-Olympic sports, particularly cricket.

Countries which have a history of playing sports included in the Olympics will, of course, fare better. And some sports offer more medals than others.

South Koreans are particularly fortunate in this regard. They love taekwondo - a sport for which there are a lot of Olympic medals, with categories for men and women, and multiple weight classes.

"South Korea can field a flotilla of athletes and walk away with a truckload of medals," says Johnson, "whereas India's passion for cricket translates into zero medals."

On the other hand, although we expect countries such as the US and China to do well, they actually perform even better than their population and GDP would suggest. Busse says this is because Americans are particularly keen on sport, while in China talented children are sent to special academies at an early age.

Australia is another country which is keen on sport, particularly swimming, getting 46 medals in 2008, when Busse predicts them just 25.

Some countries from the former Soviet Union with small populations and low GDP per capita do better than expected too. They are still reaping the benefits of institutional investments made years ago, for political reasons, when the USSR pushed for medal success.

Cuba is also well known for punching above its weight, gaining 24 medals in Beijing. But due to insufficient economic data, they have not been included in these predictions.

So, if what we want to do is predict the final medal tally as best we can, relying on GDP per capita and population is not enough. Johnson has created a more sophisticated model using more factors.

Source: Meghan Busse of Northwestern University, based on population and GDP per head. Dan Johnson of Colorado College, based on population, GDP, past record and host-nation advantage

First, he measured the difference between what countries should get based on population and GDP, and what they really got over the last 60 years. He then created an average of "winningness", as he calls it, for each country.

On top of that, says Johnson, host countries can expect to win 18 more medals than usual at their own Games, and enjoy a lesser spike in the years before and after.

"There is a legacy effect," says Johnson, "so in the subsequent two games, we see a mini spike of about five [extra] medals overall in the two subsequent Olympics."

Using population and GDP figures, "winningness" and factoring in the hosting advantage, Dan Johnson predicts the US will come top of 2012 medal tally with 99. Russia, he says, will come second, China third and Britain fifth with 45.

That 45 figure for Britain looks wrong because it is less than Team GB achieved in 2008, suggesting that their host advantage in 2012 is weak. But Johnson says that the numbers reflect the fact that his model analyses performance over 60 years, and in 2008 Britain did far better than usual.