William M. Briggs

Statistician to the Stars!

Which country did best in the Olympics?

(This analysis was suggested by reader Joy C., who provided a link to the medal tables.)

China, even disregarding its cheating, grabbed the most gold medals (51 to the USA’s next best 36), but the USA took the most overall (110 to China’s next best 100). Either country, then, could be argued the better one depending on whether you value just gold or all medals.

But are there better ways to compare success than raw totals? For example, tiny Jamaica won 11 total medals, while Poland which is over 10 times as populated took only 10. Obviously, countries with enormous populations have a better chance at taking more medals because they have a larger pool of athletes to draw from. China, for example, has over 1.32 billion souls, with the USA has less than their decimal point, with only 305 million. (Population data gathered from Wikipedia.)

Let’s control for a country’s population and re-rank. Here is a table of some of the top countries with the medal totals normalized by population—total medals divided by population in millions. The number “Medals per million” is the number of medals won per million people.

Rank Country Medals per million
1 Bahamas 6.04
2 Jamaica 4.05
3 Iceland 3.16
4 Slovenia 2.46
5 Australia 2.15
6 Cuba 2.13
7 New Zealand 2.11
8 Norway 2.09
9 Armenia 2
10 Belarus 1.96
15 Georgia 1.37
27 Britain 0.77
36 Canada 0.54
37 Russia 0.51
38 Germany 0.5
39 Italy 0.47
40 Spain 0.39
44 United States 0.36
60 Taiwan 0.17
68 China 0.08

The Bahamas tops the list: they won 2 medals with a population of only 330 thousand, an amazing feat, or perhaps I should say with amazing feet since their medals were in running events. Jamaica has 2.7 million people and won 11 medals. Ranking countries this way puts the USA down at number 44, with China not coming in until 68, with Taiwan ahead of it! Incidentally, the BBC site, one of the many hosting medal count tables, fearfully lists Taiwan as “Chinese Taipei”, which is meaningless because Taipei is only one city in Taiwan. China, with the world’s biggest population, can lower their denominator and do better next time if they institute a new Cultural Revolution. Georgia can also take some comfort for coming in well ahead of Russia (15th to 37th place).

Smaller countries also, as a matter of necessity, have to be more focused. Cuba, for example, won the majority of their medals in various martial arts (boxing, judo, and so on; perhaps they’re expecting something after Castro kicks over). The larger countries have entrants in most sports: both Communist China and the USA won their medals in dozens of events.

Here’s another way to look at the same data. This is a plot of the population (note the logarithmic scale) by the total number of medals won.
Population by total medals
Many of the names are tiny and unreadable, but the general drift can be seen: greater populations help win more medals, just as expected. But not always. India ranks in with over a billion residents, but only garnered a couple of medals. Indonesia and Russia are also hugely populated but have few medals to take home.

As always, money helps. Here is the Gross Domestic Product (GDP), a rough measure of economic output, by total medal count: (GDP estimated from Wikipedia.)
GDP by total medals
China looks like its GDP is just behind the USA, but it isn’t. For example, Japan is second, Germany third then China. Clearly, though, the more bucks the more bang. But as with population, not always. India’s GDP outstrips South Korea’s and Australia’s but it’s medal total is lower. One of the more interesting things about this graph is the wide range of GDPs: over 6 orders of magnitude!

The next step is to see the joint effect of increasing population and GDP. That’s what this next, more difficult, picture shows:
Population/GDP by total medals
Each dot is a country’s Population and GDP; the number beside it is the number of medals won. Darker circles help guide the eye to higher counts. The highest dozen Populations and the lowest GDPs are highlighted for easier recognition. The double bang received from having lots of people making lots of money is easily seen, but the relationship is not perfect.

I am not trying to predict the medal counts for the next Olympics, hence this is no real statistical model. To build one would require the data from previous Olympics, summer and winter, tracking the number of events, the changes in politics and inflation and on and on. Too much work and in the end there would be too much uncertainty that the model proposed is valid. Showing the data plainly is the fairest procedure.

Just for fun, and having nothing to do with the Olympics, here are the top and bottom 10 countries of dollars made per person (GDP divided by population). You can think of this as a sort of measure of citizen efficiency.

Rank Country Dollars made per citizen
1 Luxembourg 104,000
2 Norway 82,000
3 Qatar 81,000
4 Iceland 63,000
5 Ireland 58,000
6 Denmark 57,000
7 Switzerland 56,000
8 Sweden 49,000
9 Netherlands 47,000
10 Finland 46,000
159 Myanmar 270
160 Eritrea 270
161 Malawi 250
162 Ethiopia 250
163 Guinea-Bissau 200
164 Liberia 190
165 Congo 160
166 Burudi 120
167 North Korea 93
168 Zimbabwe 48

The USA makes the list at number 12 with about 45-thousand per person. England at number 11 is just about the same, mere dollars ahead. Non-Arabic Africa is at the bottom of all of these lists.

Of course, Luxemborg and Norway, at the top of this list, have less people that live in my neighborhood, so it isn’t entirely interesting. The largest population of the top 10 goes to Netherlands, which is equal to the population of Manhattan. Oh, the well run European countries! we often hear. But they are so tiny! Zimbabwe, the very bottom of the list, has about 13 million people with a paltry 48 bucks per head. North Korea’s population is estimated at about 24 million, but that was before last year’s winter, so their total dollars per capita could increase next year in that communist paradise.

26 Comments

  1. Just as I thought, Britain was best!!

    How about land area, that has to be an advantage. If your Island only has space for one palm tree with one lonely goat, the pommel could pose some problems; not to mention the marathon.
    When you guys come to London we’re going to make you run round the track the other way.

    How come the USA has the longest national anthem? What’s that about?

    One tiny island nation who’s name I can’t recall, were too late sending in their forms to join the Olympics so were not allowed to play. Shame, they should have let them join in anyway.

    India should steam forward in the coming years if they care about their reputation as a sporting nation, which I believe they do. Watch out China!

    Briggs:
    I noticed that on the list of “citizen efficiency” Britain changed to England. Was this because inclusion of Scotland and Wales and Northern Ireland was more or less flattering to our rank compared to the USA?;)
    According to the Eurofiles and the Scots, there’s no such place! There’s no such nationality as “English” they say! Liechtenstein however, different matter.
    How did China cheat? genuine question, am interested to hear about it. Our commentators are too”PC” to draw attention to this sort of thing.

  2. Briggs

    August 26, 2008 at 9:31 am

    Joy,

    Britain became England merely through laziness on my part. Should be the former. But how do you figure they did best?

    In gymnastics, China let the underage girls play as 16 year-olds. I figure they still earned their medals, though. If they were good enough to beat the others, then they’re still the best.

    Oh, we have the longest anthem because, need I say?, we’re the best country.

  3. Hi –

    Lovely comparison. Well done. But there is one thing that does distort your raw data on “citizen efficiency”, and that is by putting it in US dollars, given the exchange rate changes over the last couple of years. If you were to use constant 2000 exchange rates, for instance, the ranking of “citizen efficiency” changes rather dramatically. Add to that the fact that this is GDP, rather than income, and you can see how this isn’t “citizen efficiency”, but rather simply a general term of labor productivity (there’s no accounting for hours worked, for instance).

    Of course, as long as you *want* the exchange rate effects in there, that’s fine to use. But it does need to be explicitly stated, and that is unclear…at least for this reader. :-)

    Best regards,

    John

  4. Briggs

    August 26, 2008 at 10:07 am

    Quite right, John. These are all gross approximations. There will never be, there can be no, adequate single-number summary of economic output.

  5. Joy and William,

    The US national anthem is based on an old English drinking song, using words by Francis Scott Key. So England is at least partly to blame for the length of the anthem. Of course, if England hadn’t lost the war, we’d have been hearing God Save the Queen. :-)

    There has been some (minority) sentiment for changing the US anthem, mainly to something easier to sing. America the Beautiful, God Bless America and Woody Guthrie’s This Land is Your Land are among several that have been proposed. I doubt it will ever happen.

  6. Hmm, not sure about longer being better.

    We were better because (I could have left it there)

    Notwithstanding the fact that we entered a broad number of events for a nation so small and despite the handicaps: small population, minimal land area, bad weather for outdoor events, lack of altitude, and woefully small GDP, we finished fourth, behind three nations who each had at least one of these advantages.

    And, which is more, our rowers are better looking!

  7. Djohnson:

    Which war? Did we go? Did we blink and miss it?

    Hmm what other titles can I think of for the US anthem?;)

    Britain did clean up in the water sports I “guess Britannia rules the waves”!
    Of course that is a misquote and the original quote is from Queen Elizabeth I:
    “Britannia rule the waves” is an order but is always misquoted as an arrogant proclamation by those trying to make a case against patriotism.

  8. I don’t like giving all the weight to the gold medal. Silver and bronze should have some weight, but clearly not as much. If in charge of devising an Olympic score I would give a gold medal 3 points, silver 2, and bronze 1 point. By this measure China has 223 points, narrowly beating the USA at 220 points.

    For medals per capita bigger countires are decidedly at a disadvantage. Wikipedia says there were 958 total medals awarded. If China won every single medal it would still only have 0.73 medals per million people.

  9. Briggs

    August 26, 2008 at 1:57 pm

    Tesla,

    Fantastic idea. The plots do not look very different, but the rankings per population do change. Here are the highlights:

    Rank Country Medal Score
    1 Jamaica 9.6
    2 Bahamas 9.1
    3 Iceland 6.3
    4 Slovenia 4.4
    5 Norway 4.4
    6 Australia 4.2
    7 Bahrain 3.9
    8 Mongolia 3.8
    9 New Zealand 3.7
    10 Estonia 3.7
    14 Georgia 2.7
    22 Britain 1.6
    34 Canada 1
    35 Russia 1
    44 United States 0.7
    64 Taiwan 0.2
    65 China 0.2
  10. Looking at north versus South Korea is interesting:
    south Korea 13G, 10S and 8B medals = 67 points
    North Korea (DPR) Korea 2, 1, 3 = 11 points
    population South Korea 49.0 million
    population North Korea 23.3 million
    South Korea scores 1.37 per million population
    North Korea 0.47 points per million population
    Capitalism?

  11. Star Spangled Banner is a wonderful song (although notoriously difficult to sing in the normal key of G). However, according to that world renowned centre of excellence (Wikipedia), the National Anthem of Uraguay is reputed to be the longest in performance (around 5 minutes).

    Did you mean “longer” (i.e. than that of the U.K.)? How many verses do you want to include in “God Save the Queen”? While only the first is normally sung there are 3 in what might be called the official version and a fourth is available (and was used, apparently, in place of the third when it was sung at the end of the Beijing Olympics). Others have been used but we generally do not use the prayer for the success of Marshall Wade around 1745:

    Lord, grant that Marshal Wade,
    May by thy mighty aid,
    Victory bring.
    May he sedition hush and like a torrent rush,
    Rebellious Scots to crush,
    God save the King.

    “Rebellious Scots to crush” is not popular with our Scottish Prime Minister!

  12. All I know is that Statistics rules! Trust me, I am a statistician.

    Birggs, thanks for the honorable mention of my native country.

  13. Hmmmm, nice essay Mr Briggs and very enjoyable, but if you really think that the Netherlands have 1.6 million people (Manhattan population), then I’d suggest you would, oh I don’t know, change the dot a number to the right?

    Now come on, I mean yeah, our european countries are small, but please, not that small, I assure you!!

  14. Another thing to consider is the corollary of Tesla’s remarks about biggest countries disadvantages. It comes to mind a comment made by a friend of mine about university grades. To get a 14 (out of 20, a median good grade) one doesn’t have to put much effort, but to put 15, one has to double it. 16 likewise, and 18,19 are disproportionate in effort. It’s exponential.

    Likewise, for a big country, it gets more and more difficult to compete with smaller population countries, for if a small one like mine (10 million) wins four medals (it didn’t happen, but we had a good shot at it), an 8x bigger one, like Germany, has to win at least 64 just to stay even, and China had to win 520 medals, which clearly is impossible.

  15. “longer” meaning those tunes played in the olympics and similar sporting events.

    You illustrate my point in fact: the national anthem has more than one verse but quite rightly we don’t inflict the entire hymn on everyone round the world although I’m all for having the “crush the Scots” verse thrown in for good measure.

  16. Louis Dias:
    Portugal?

  17. Whichever way it is looked at Australia beat New Zealand – and that is all that matters down under. Something else for the Kiwis to get all hot under the collar about.

  18. Joy, yes, and it’s not Louis. Just Luis. Yeah, I know it may be awkward to you, so you are free to call me louis if you like.

  19. HarryG, if the NZ Government flooded as much money into sport as the Aussie Government then perhaps there would be a level playing field. But then as it stands the difference might not be meaningful in a statistical sense. Perhaps William B can comment as an impartial observer?

  20. Briggs

    August 28, 2008 at 6:19 am

    Rob R, HarryG,

    Controlling for money spent, as a proportion of, say, GDP, would be valuable. Do those numbers exist? Well, of course they exist, but can they be had by civilians like us?

    Don’t forget that India, with a huge GDP and population, still did poorly. But who knows how much they spent on preparing for the Olympics? You also have to factor in “spirit”, meaning how much people in the country actually care about the games. This is almost certainly impossible to measure.

  21. Briggs, Rob

    The newspapers here are suggesting that each Aussie gold medal cost us $16.5 million. That is a lot of money. Did I watch the Olympics? – only when it was on the news.

  22. Luis:
    I am sorry for any offence. What a clanger! I use speech software and as I have to check name spelling character by character I am inclined to guess.

  23. A minor point – the BBC didn’t “fearfully list[s] Taiwan as “Chinese Taipei””, as you put it. They called it that because that’s what the country is called, based on its own suggestion, in Olympic competition, and has been since the early 1980s. The BBC is no more being cowardly than you are by calling it Taiwan (an island) rather than its actual name of the Republic of China.

    I too think that ‘Chinese Taipei’ is a nonsense, and I believe that the ROC government is (rightly) trying to change it. But until they do calling a thing by its name is not an example of fearfullness.

  24. Briggs

    September 4, 2008 at 6:17 am

    Paul,

    Nah. I never met anybody who wanted to change the name of their country to “Chinese Taipei” when I was in Taiwan. I also happen to know lots of people from there and they are all very patriotic, even the Blue ones. The BBC wimped out.

    And, though this isn’t the place for it, Japan has more of a claim to Taiwan than does China.

  25. Ah well, if that’s your experience then I guess I was wrong in thinking that the ROC government chose the name for Olympic use in the late 70s. If you can find out who did please let me know and I’ll update the wikipedia entry accordingly.

  26. Briggs

    September 5, 2008 at 7:51 am

    Paul,

    Good idea. Wikipedia has for too long had a reputation for false and misleading data. Your correction will help.

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