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The Rio Olympics have yet to start, but of one thing we can be confident - the US and China will top the medals table when it's all over on Sunday 21 August. But why are they always so successful? And can we predict which other countries will do well this year?

In terms of the overall medals won, the US, China and Russia can be relied on to top the list. It was like this in 2012, 2008 and 2004, though in 2000 China tied for third place with the host nation, Australia.

This year, Russia will most likely drop down the table, because of the disqualification of many of its competitors. So another country is likely to take third place - but which?

According to one theory, the countries that do best in the Olympics are either big or wealthy or both.

Media playback is unsupported on your device Media caption How to predict Olympic success

Having a big population means that they have a large pool of athletes to draw from. Being wealthy means that they can afford the facilities and the time to train.

But Dr Julia Bredtmann, an economist at the RWI - Leibniz Institute for Economic Research in Essen, has come up with a predicted medal table based on countries' size and wealth, that doesn't look very convincing.

Prediction based on population and wealth Country Medals 1= China, US 25 3 India 22 4= Germany, Japan 20 6= Brazil, France, Indonesia, Russia, UK 19

When you consider that the US won more than 100 medals in 2012 and India only six, it's clear that it would be a mistake to bet too much money on this outcome.

The same model predicts Saudi Arabia will win 13 medals at Rio, because of its high GDP and relatively large population, even though it had not won a single medal until the 2012 games.

"It's a good starting point but by using other factors we can at least explain a little bit more and improve the predictions," says Bredtmann.

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Another important factor, she says, is "sports culture" - how many people take part in sport, how much money is invested in sport, and how important sporting success is to the country - but as this cannot be easily captured in data, Bredtmann looks instead at the number of medals won in previous Olympic Games.

"What can be shown is that there is a large persistence in Olympic success," she says. "There are some countries that always win medals and some countries that will never win a medal."

With her colleagues Sebastian Otten, also from the Leibniz Institute, and Carsten Crede of the University of East Anglia, Bredtmann has put together a sophisticated prediction model based on previous results, population size, wealth and a number of other factors (see below for the full list).

This model predicts the following medal table.

Predicted 2016 medal table (ignoring Russian ban) Country Medals 1 US 98 2 China 84 3 Russia 77 4 UK 62 5 Japan 46 6 Germany 42 7= Australia, Brazil, France 33 10= Italy, South Korea 27

But this doesn't take into account the disqualification of many Russian athletes.

A very crude way of doing this would be to take the two categories of event where all Russian athletes have already been banned - track and field, and weightlifting - and to re-allocate the 24 medals Russia won in these events in 2012.

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Under this scenario, Bredtmann and her colleagues see Russia dropping two places in the table, and the UK moving up into third place.

Predicted table (re-allocating 24 Russian medals) Country Medals 1 US 100 2 China 86 3 UK 64 4 Russia 53 5 Japan 47 6 Germany 43 7= Australia, Brazil, France 34 10= Italy, South Korea 28

This doesn't take account of the full number of Russian athletes being banned, so in reality the damage done to Russia's medal haul is likely to be greater.

Note that in all of Bredtmann's predictions Brazil features in the top 10. It won 15 medals in 2008 and 17 in 2012, placing it well down the medal table, but the host-country effect in the Olympics is well-documented. Because of the extra investment in sport, and the advantage of performing in front of a home crowd, host countries usually do well, and Bredtmann predicts Brazil will roughly double its previous medal haul.

Those who remember the last World Cup, however, will realise that this is not a done deal.

Factors used by Bredtmann and colleagues

Past Olympic success: Medals won in the past can be seen as an indicator of "sports culture". Australia and the Netherlands for example always perform quite well, although they do not have a large population. Sporting prowess is important to them though, and many people take part in sport.

Host-country effect: The UK hosted the 2012 Olympics and won 65 medals compared to 47 at the previous Games. This is a recognised pattern. Performing in front of a home crowd, combined with extra investment in sport, gives the country a medals boost. At this year's Games, we would expect Brazil to benefit from this effect.

Future-host effect: Australia won 27 medals in 1992, but a full 41 medals four years later - probably due to increased investment in sport in the run-up to the 2000 Sydney Games. The UK, meanwhile, increased its medal haul from 30 to 47 between 2004 and 2008, prior to hosting the 2012 Games. Brazil, however, broke the pattern and did not perform particularly well at the 2012 Games. At this year's Games, we would expect Japan to benefit from the future-host effect.

Wealth: Countries with a high GDP, like Germany or the USA, can afford to invest in sports facilities, and their populations have enough leisure time and money to take part in sports. This may not be the case in poorer countries.

Population: A big population means a big talent pool to choose athletes from - in China's case, 1.36 billion people.

Planned economies: These countries tend to invest more in sport because they value the prestige that sporting success brings. China and Cuba are good examples. Countries that were formerly planned economies, such as Russia and Ukraine, may also continue to profit from these past efforts.

Majority-Muslim population: In majority-Muslim countries women are less likely to participate in sports and become athletes. Consequently, these countries usually send fewer or no female athletes, and fewer athletes means fewer chances to win medals.

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