Standard medal league tables are unfair, whether they rank countries in terms of the number of gold medals they won, or their overall number of medals.
Some countries have larger populations - giving them a deeper pool from which to draw athletic talent - and some are richer, allowing them to invest more in sport.
Before the Games started, BBC Radio's More or Less programme decided to level the statistical playing field by working out how many medals nations could expect to win based on population and GDP alone.
"If you use those predictions as a kind of benchmark, then you can ask the question, who's done well and not so well relative to that prediction - who won more medals than they should have, and who won fewer," says Meghan Busse from the Kellogg School of Management at Northwestern University in the US, who helped with the sums.
US
53
India
-28
Russia
52
Indonesia
-21
China
43
Mexico
-19
GB
33
Turkey
-17
Ukraine
14
Brazil
-16
Hungary
13
Saudi Arabia
-16
Belarus
12
Taiwan
-14
Jamaica
12
Venezuela
-14
Kenya
11
Austria
-13
Australia
10
Belgium
-13
Source: Meghan Busse of Northwestern University. Figures show gap between medals won and Busse's forecast based on population and GDP
Some of London 2012's over-achievers fall into one of three categories:
But some of the biggest over-achievers were those at the top of the table. The US, China and Great Britain, three of the top four medal winners in 2008 and 2012, actually got more medals than might have been expected on the basis of GDP and population.
Listen to More or Less on BBC Radio 4 and the World Service, or download the free podcast
Busse estimates that Great Britain should expect to get 32 medals when in fact they got 65 in total. She attributes this in part to the fact that host countries tend to invest more in sport in the years preceding the Olympics.
And even Australia, which has lamented its performance in 2012, winning 11 fewer medals than at the Beijing Olympics, is still punching above its weight (10 extra medals), according to Busse.
The countries that under-performed also fall into various categories, including:
Some of these over-achievers and under-achievers over-achieve and under-achieve on a regular basis. But even if you take into account past performance, as well as GDP and population - as Dan Johnson, an economics professor at Colorado College does - there were still some surprises.
1
US 104
1
US 51
1
US 99
2
China 88
2
China 45
2
Russia 82
3
Russia 82
3
Japan 41
3
China 67
4
GB 65
4
Germany 36
4
Germany 60
5
Germany 44
5
India 34
5
GB 45
6
Japan 38
6=
France 33
6
Australia 38
7
Australia 35
6=
Brazil 33
7
France 37
8
France 34
8
GB 32
8=
Italy 31
9=
Italy 28
9
Italy 31
8=
Japan 31
9=
S Korea 28
10
Russia 30
10
S Korea 29
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
Iran, Jamaica, New Zealand and Japan won many more medals than Johnson expected.
At the same time, he thinks Germany, Brazil, Romania, Bulgaria, Indonesia and Greece all fared surprisingly badly. It is the predictions that go wrong which make the Games so fascinating, Johnson says.
"The Olympics are all about athletic excellence", he says, "and it's most important to cheer when that excellence occurs in unexpected places."
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