Wednesday, August 08, 2012

Olympic medals per capita, GDP, team size

The Data Blog at the Guardian's sport section has printed interesting tables of Olympic medals that take the nations' population or GDP or team size into account.

Just to be sure, the table of unadjusted gold+silver+bronze medal scores at the Summer Olympics is led by China (34+21+18), U.S. (30+19+21), Britain (22+13+13), Korea (12+5+6), Russia (10+18+20), France (8+9+11), Germany (7+15+9), Italy (7+6+4), Hungary (6+2+3), Kazachstan (6+0+1), and let me stop at this point.

My ultimate role model for an average nation, the Czech Republic, is somewhere at the 28th place (1+3+1). It's insightful to see how the tables change if you switch from those purely "extensive" scores to "intensive ones".

Some people in Czechia and similar nations could say "the medal score of ours isn't so bad given our size". However, this is usually a myth – at least in our case, it is. If you adjust a medium-size country's score for the population or GDP, you're guaranteed to change almost nothing. So in all the adjusted scores, we're still somewhere at the 30th-40th spot. The Czech Republic simply isn't as small as some people would like to imagine.

Just like Czechia's tally looks mediocre, we must notice that other countries have fell, too. In particular, both German republics – even before the fall of communism – would be closer to the top than the unified Germany seems to be today. Is this drop because of the reduced desire of the Germans to compete against their ideological foes in the other German country?

The top of the table changes brutally if you divide the number of medals by the population. In the gold medals, the table is led by Grenada, Jamaica, New Zealand, Hungary, Slovenia, Croatia, Kazakhstan, Denmark, and the U.K. completing the top ten and defending the good name of the empires. Czechia is 25th, the U.S. is 27th, and China is 36th. As you can see, the Sino-American currency union plummets towards the mediocrity. This is just an innocent reminder of the fact that in most cases, when nations such as China and the U.S. are proud about their being at the top, they're mostly proud about their size, not about any "intensive" quantities. Apologies to the Americans and others for this perhaps inconvenient truth. The size of a nation isn't really a rational reason to be proud about; it's about the choice where you place your identity. I would most naturally place my identity to Czechoslovakia which has 1+4+4 medals at this point, not too bad; but if the Europeans were thinking about the medals for the EU (no one does), the 450-million-citizen EU would of course beat (in the "extensive medal counts") the U.S. plus China combined! ;-)

Because the GDP per capita isn't quite constant over the world, you get a different table when you divide the number of gold medals by the nations' GDPs. Grenada and Jamaica remain at the top. However, a completely new country jumps from the 19th spot in the "per capita" counting right to the bronze medal. What's the name of this country? Yes, it's North Korea. I hope that they will celebrate their being the third best country in the world in the Olympic medals per dollar of GDP. These comrades are followed by other suspects, namely Georgia, Ethiopia, Belarus, and Cuba – before a wealthier country, Hungary, defends the spot number nine. China, Czechia, and America are found at spots 25, 26, and 35, respectively.

An entirely different table arises if you adjust the gold medals per team size. Grenada wins, followed by China, Iran, North Korea, Ethiopia, the U.S., and Kazakhstan. If you count all medals, the table would start with China, Iran, and the U.S. The major new player in this table is Iran, of course, that minimizes the team size in order to minimize the number of casualties in the case that the mullah-in-chief decides to perform a mass terrorist attack against the London Olympic games. Czechia stands at 37th and 48th place in gold and all medals here; those numbers start to be painful.

You may notice that even if you divide the medal tally by the team size, China and the U.S. remain at the top or near the top. Why is it so? Well, it's because the average quality of the team members in similarly large countries is simply higher than the average quality of the team members in smaller countries. And why is this the case? Because there's just a higher degree of competition you have to get through before you make it to the national team of a large nation; the team size simply doesn't quite scale with the population of the nation.

There are clearly some nations that seem more successful than their neighbors – like Hungary, Slovenia, or Croatia, to mention some nearby countries with an impressive score; and there are some countries which are huge and have almost no Olympic successes, for example India. A billion of people hasn't earned a single gold medal yet and the total number of medals is roughly three. I suppose that sport is "too professional" and India may unfortunately suffer from its "third world status" in the sports much like in some industrial activities. Moreover, its political representation doesn't have too strong a need to "prove something to someone".

However, aside from these somewhat extreme examples, the question whether people in a nation should feel proud or special because of their athletes depends on how exactly you compute the scores and how you compare them...


  1. The size of the country shouldn't matter for the amount of medals at the Olympics. It's like saying for ex : "it is so hot for such a small island" :-)

  2. The British aren't known for producing great athletes, despite owning
    and controlling huge swathes of Africans back in the day ;~). So I'm a
    little surprised to see that they rank third in the world in terms of
    winning the most Olympic metals. My guess is that the home-field
    advantage has played a vital role in making this happen.

  3. Haha, funny, Shannon, but from your wording, I am not sure whether you distinguish extensive and intensive quantities and which of the two tables looks more natural to you.

    The statement about the hotness of one's ex is clearly a statement about individual. Statistically, the properties of individuals may be estimated from intensive properties of nations, i.e. from medals per capita.

    Whether one finds "total number of medals from a country" more natural than "medals per capita" is the same question as whether one prefers to talk about the quality of nations so that the size is viewed as a major quality; or whether one talks about the quality of individuals. Both of these things are clearly legitimate but they yield very different results. Just to be sure, my nation's position in all these things is as impartial as you can get because one gets very similar results by both/all methods.

  4. I am not sure whether this comment of yours is a joke I didn't understand or a genuine expression of your fanatical anti-British or "anti-imperialist" attitudes.

    At any rate, your comment, if taken seriously, has nothing whatever to do with the reality. Britain was the 4st most successful country in Beijing 4 years ago

    after China, U.S., Russia, having earned vastly more medals per capita than the U.S., for example. And Beijing wasn't even a British colony, if you talk about the home field. So you should better correct your misconception that Britain doesn't have great athletes.

    Also, let me articulate this explicitly because it's important although off-topic in sports. The number of good athletes in a country in 2012 obviously has no justifiable correlation with the number of slaves held by the country 2 or 20 centuries earlier. Not even with the inhabitants' slave status.

    A much more general message you should learn is that the reality in sports or in any other question in the Universe has nothing to do with what a fanatical leftist such as you would find convenient if it were the truth.

  5. Actually, Lubos, there is a factor in this you haven't considered: large countries are discriminated against in the Games - BECAUSE THEY CAN HAVE ONLY ONE TEAM. They may have a huge number of great athletes, enough for many stand-alone teams, but they can bring only one. And further, in gymnastics for example, each team can only enter two gymnasts in the all-around competition, no matter if they have five who are the best in the world! We big countries are SO put-upon.

    Anyway, keep up your good work against the forces of lunacy, that is warmies and socialists, and in furthering the notion of a rational perspective on life.

  6. Right, good point, Jeffrey. That's the same point I mentioned when I was explaining why the U.S. and China are still at the top even if the medal tally is divided by the team size - the last method to sort the countries.

    Well, perhaps one should clarify that large countries that aren't sophisticated enough end up with one team only. My birth country, Czechoslovakia, managed to have two teams in London. You may try to emulate us, too! ;-)

  7. I note that today is the 110th birthday of Paul Dirac and that the British have also produced some pretty notable scientists, Isaac Newton, for example.

  8. To me the major quality to take into account should be individuals first. You can have a big team from a big country with very good individuals with excellent records; but the main goal at the Olympics is to be the best. And that stands above nations. So indeed I don't think the size of a country is too important in the amount of medals...

    (I'm suspiscious about China winning so many gold medals in swimming. I would bet that they will have to return their medals within a few weeks... just like the Irish girl had to do 8 years ago).

  9. Hello Lubos,

    I wounder what results one would get comparing weighted (per Capita) success of the Super Athletes....

    US may still end up on the Top, but maybe there are surprises there.



  10. Hejnova got bronze. We can get potentially another 2 golds from Spotakova and Vesely.

  11. There is also the statistical phenomenon of regression at work here. The Olympic Games sample for remarkably good athletes. The number of medals from a large country may fairly measure the chance that a remarkable athlete emerges. But break that country into many smaller countries and the medals will not be evenly distributed. You will get a few "remarkable" standouts, purely from random clumping.

    This might be tested. Can you break a large country like the US up into medals by state? I predict large states like California will have more medals but have middling performance by capita. There will also be a few small states with "remarkable" per capita performance, perhaps rivaling your small nation standouts.

  12. This is simplistic, as science often is when applied to things like athletics because so many variables are involved (this reminds me of scientists on Wall Street and also of the climate science). China has a population that is 4.3 times the US but checking the NYT this morning the US now leads int he overall medal count 82 to 77 and trails by 2 in the gold. Given the sports which remain it won't be surprising for the US to extend its lead over China and to take the lead in the gold category as well. France and the UK have about the same population size but the UK has 20 more medals than France. Jamaica kicks butt over all the European countries regardless of size when it comes to track. The fact is, sports has different values in different cultures and people grow up in different environments so size alone does not explain US dominance. Chinese dominance comes from a top down effort by the government to gain national prestige. Sports is simply built into US culture from childhood. Europeans do too of course but the difference between France and the UK shows that something else is going on besides population size. Also, don't be politically correct - to say having a population of African descent makes not difference is not being honest. It is simply reality that people of African descent excel at certain sports. This is a compliment to people of African descent not a slight. When was the last time a white male medaled in the 100 m? 200 m? Just look at the runners that make it to the finals in those events.

  13. Hi Lugos, how to explain the fact that Hungary and Finland consistently lead the per capita gold medals and total medals rankings over many years?

    Is there something in the Finno-Ugric genes, perhaps? ;))

    At present Hungary ranks second in the per capita gold list and seventh in the total gold list, while Czechia is 27th and 32d.. Although both of them were part of the same empire for many years!

  14. Hi Lubos,

    How to explain the fact that Hungary and Finland have consistently led the all time per capita gold medals and total medals rankings?
    Is there something in the Finno-Ugric genes perhaps? ;))
    As I post this, Hungary ranks in London second in the per capita gold list and seventh in the total gold list, in both categories well ahead of Czechia - although both were parts of the same empire for many hundred years..
    Never mind, Pilsen beer has always been number 1 in the world - cheers!

  15. Hi Atilla, Finno-Ugric folks came somewhere from India, so by their having extra medals, they're just trying to compensate India's complete inability to win a gold medal.

    So when you clump the nations to the proper historical confederations, the Finno-Ugro-Indian athletes are near average and the fact that the Hungarians are much better than the average Finno-Ugo-Indians is of course due to the fact that they had the privilege to share the monarchy with Czechs, Slovaks, and Austrians. ;-)

  16. India is an Aryan country, just like Czechia :D

    However, as anyone with access to google can find out, Finno Ugric folks came from the territories of present time Kazakhstan, which is consistent with the good performance of the Kazakhs..:)
    By the way, the Croats and the Slovenians have also much better results than the Czechs.. Come on Lubos.

  17. Even by total medals per GDP Hungary is still 12th vs. Chechia's 28th.. (the Slovaks seem to fare better since they liberated themselves from Czechia :))

    These figures seem to contradict your theories in your post.

  18. Good, Atilla, your fixes are legitimate and important. I must admit: the athletic savages from the extended Balkans simply impress me! It's amazing how many medals may be earned by a nation that even find the Nagymarosz hydroplant too hi-tech. ;-)

    Of course, Hungarians are role models in many respects. For example, a guy rides in a train and there's a sexy blonde in his coupe. He tries to start a conversation. Where is she going from? She answers she's returning from a sexuological congress. What were they solving? Which nation had the best male lovers.

    And what did they find out, the chap asks? They found out, she explains, that the best lovers are native Americans and Hungarians.

    Oh, I forgot to introduce myself, the chap says. My name is Isztvan Vinetou. ;-)

  19. Sorry, this is a completely silly table. Czechia has a much better score than Slovakia, 1-3-3 vs Slovak 0-1-3. The first is clearly better than twice the second, in any sensible measure.

    Morever, in 1 hour, we're rather likely to gain the second gold medal.

    Viktoria Pilsen is now playing against Ruch Chorzow, Poland. Soccer. In the 55th minute, the score is 4:0 for Pilsen which, if combined with the result in Poland, gives 6:0. You may try to guess which team will make it to the European League playoffs. ;-)

  20. Counting the medals of "Austria-Hungary": 12 gold, 34 total (and the medals from Transylvania and Galicia are not even included).. About the same as Russia..

  21. Interesting - at the World Championships, Jamaica has more than twice as many medals as France, despite France having a population 20 times as large. Size? Don't think it matters so much.

  22. Hungarians specialize at swimming and canoe/kayak. In these disciplines they just throw a truck full of medals into water, all contestants receive a bucket, jump i to the water and try to get as many medals as possible.

  23. Obviously, what also matters is that there are many medal collections distributed for the same thing, like running. That explains a large portion of similar Jamaicas, I guess. The medals are not really "independent" in the algebraic sense.

  24. From the standpoint of the Universe, which does not care about silly human contrivances like "IQ", you may be only 0.6% ahead of me, too. At least this is so if one counts *all* the control and processing activity perfomed by the brain and if one views willed mental exertions as accounting for merely a tiny fraction of the overall workload of the brain :)

  25. Dear Eugene, please, let me remove the personal dimension here. I don't know for sure who's smarter or whatever.

    But my point was indeed exactly the opposite of yours. When it comes to things related to intelligence and human creation etc., the differences between what the individual people - and whole nations or the whole mankind - achieve or may achieve is vastly higher than 0.6%. It may really be counted in lots of orders of magnitude.

    Take the maximum energy in particle physics at which one may explain what's going on. It was increased by a dozen of orders of magnitude. The accuracy with which people could have computed the anomalous magnetic moment of the electron increased by ten digits - the error margin dropped by 10 orders of magnitude within decades - too. And that's still nothing else compared to truly "qualitative" things that the human brain may change and is changing. These changes are vastly greater still. There's no room for being excited that one thing is 0.6% faster than a competing thing.

    You may use some different scales nonlinearly related to mine so that the big differences between people's mental achievement - either comparing different people or different epochs or whatever - will look small. But I still think it's obvious that my scale is more natural than yours. The changes that are happening in intellectual developments are vastly more profound than the improvements of the 100-meter-sprint world records. This is not something I may "rigorously prove" because the profoundness can't be quantified by indisputable criteria and comparing sprint e.g. with high energy physics is like comparing apples with oranges. Still, it seems that what I say is obviously true and important.

  26. Hi Carbone, don't forget fencing, wrestling, gymnastics, boxing, athletics, pentathlon, waterpolo, shoting and wightlifting.. disciples where they had upwards from 20 medals in the olympics..
    Oh those tricky Hungarians. They enter the revolving door after you and they emerge before you.. How dastardly! :D

  27. Don't be silly, Atilla. The diversity of the disciplines in which Hungary has medals in 2012 - or in which it had medals over the history - is no different from the diversity of disciplines in which we have - or we have had - medals.,mod=16&sourceid=chrome&ie=UTF-8#hl=cs&sclient=psy-ab&q=czech+medals&oq=czech+medals&gs_l=serp.3...97168.97557.0.97692.,or.r_gc.r_pw.r_cp.r_qf.&fp=591c93d8c17fd423&biw=1413&bih=706,mod=16&sourceid=chrome&ie=UTF-8

  28. Hey Lubos, don't be small-minded. I do not talk down the merits of world champion Pilsner beer and of Svejk! :)

    Attila left alone Rome, because he was asked so nicely by Pope Leo.. He contented himself with the gold and the silver.. ;)

  29. Dear Atilla, good that the Hungarians learned it 2,000 years ago and they may use the same skills with the EU today. ;-)

    Have you listened to the translation of Czech folk songs to Hungarian?

  30. Good old times.. :))
    Did you know these:

  31. hi, we ex-yogoslavs beet you there - we have 6 teams :)))

  32. Bok, Rado. Good for you. The price you pay is that you not only beat us but you beat each other, too. ;-)

  33. Clearly David Czerny, author of 'Red Bus Trying to Relieve Itself' has won the Gold medal for 'Most Derivative and Uninspired Monumental Waste of Artistic Subsidy' at the current Olympics.

  34. I think it's still more inspired than the official sculpture of the Olympics no one has noticed yet

    the DNA or whatever it is. Or the logo that Iran cleverly believes to say "Zion", while the 5 Olympic circles oibviously stand for a swastika:

  35. Regarding the picture, it reminds me of the old adage, "if you can't make it good, make it big, and if it still isn't good, paint it red."

  36. Jaroslav ZárubaAug 15, 2012, 2:22:00 AM

    Sorry if someone mentioned that already, but isn't there a limit on how many men/women can be from each country? So even if 10 fatest sprinters were from Jamaica only 2 Jamaican sprinters can travel to the Games. Which, naturally, favors continents fragmented into many countries... like Europe.
    Therefore we can't really combine medals from European countries to beat China or US.

    Correct me someone if I am wrong.

  37. Right, I completely agree. To fragment your country into pieces is a way to get a higher total number of medals.

    For a while, I was convinced that yours is the name of the sport reporter.... Robert Záruba. ;-)

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