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Which nation won the 2006 Winter Olympics?

Is this an at all sensible question? For one thing, it’s patently chauvinistic. Here you have all the best athletes in the world, peacefully assembled in Turin, Italy, participating in fair competitions in the interest of Peace and International Brotherhood. And then you have the gall to ask which NATION is the winner! Isn’t this completely defeating the purpose of the Games and the high Olympic Ideals?

Well, yes -- in the politically correct theory it certainly is. But we all know that in reality international sporting events have only marginal connection with Olympic Ideals and International Brotherhood. More often than not they function as clever psychological outlets for nationalistic or chauvinistic grievances. The truth of the matter is that international athletic competitions are at times fought out as intensely as actual red-hot wars. But there is a huge practical advantage in keeping conflicts confined to the sporting arena: they are fought out without costly bombs, guns or casualties (other than accidental bruises or broken limbs).

Remember “4-3” in 1968

Remember the 1968 Ice hockey World Championships? Russian tanks had just invaded Czechoslovakia, brutally crushing the "Prague Spring", a non-Moscow-authorised Czechoslovak attempt to create "socialism with a human face".

The 1968 WC hockey finals were played between Russia and Czechoslovakia. Russia had been the undisputed ice hockey champion for many years. But against all odds the Czechoslovaks outdid themselves, fighting with the fury and the backing of a whole nation. They won by a narrow margin: 4-3. “4-3” became a defiant national symbol, scrawled all over the walls of Prague and infuriating the Russian occupying forces.

Seen in this light, it is perhaps not entirely irrelevant to try to sort out what nations were the winners of the 2006 Winter Games.

Olympic Winter Games are of course most unfair, excluding all countries that lack snow and ice, or making the going tough for countries which only have suitable climatic conditions in a part of their territory, e.g. Italy, France and the US. But among countries with similar climates (e.g. Northern Europe, Canada and Russia), comparisons are not entirely unreasonable.

Medals in summary

Here is a summary of the 2006 Olympic results in terms of the number of medals won by each nation, ranked in the order of gold medals won. But the other medals are also important. Moreover, gold, silver, and bronze medals should be given fair relative weights -- gold is of course better than silver, which in turn beats bronze.

Below I have consequently also computed two different "medal points" for each country: (1) "MP" = 4G+2S+1B and (2) "mp" = 3G+2S+1B. "MP" assumes that G(old) is twice as valuable as S(ilver) and four times more valuable than B(ronze). "mp" follows a simpler 3-2-1 scheme; here S(ilver) medals get a larger relative weight than in the "MP" formula.

It's evident that the ranking of the nations would change if "medal points" were considered; Norway and Finland would move up considerably and Canada would pass Russia.



                 MEDALS     MEDAL POINTS
COUNTRY          G  S  B      MP  mp

Germany         11 12  6      74  63
USA              9  9  7      61  52
Austria          9  7  7      57  48
Russia           8  6  8      52  44
Canada           7 10  7      55  48
Sweden           7  2  5      37  30
South Korea      6  3  2      32  26
Switzerland      5  4  5      33  28
Italy            5  0  6      26  21
Netherlands      3  2  4      20  17
France           3  2  4      20  17
Estonia          3  0  0      12   9
Norway           2  8  9      33  31
China            2  4  5      21  19
Czech Republic   1  2  1       9   8
Croatia          1  2  0       8   7
Australia        1  0  1       5   4
Japan            1  0  0       4   3
Finland          0  6  3      15  15
Poland           0  1  1       3   3
Slovakia         0  1  0       2   2
Bulgaria         0  1  0       2   2
Belarus          0  1  0       2   2
United Kingdom   0  1  0       2   2
Ukraine          0  0  2       2   2
Latvia           0  0  1       1   1


The winners?

From the gold medal ranking above it appears that Germany, USA, Austria, Russia and Canada are the 2006 Olympic Winter Games winners. The two different methods of computing "medal points" make an important difference only in the case of Norway and Finland, who won a high proportion of S(ilver) medals.

But is this really fair? Now I’m not only thinking of the climatic unfairness that befalls countries like Australia, the UK and USA (where large parts of their territories are unfit for winter sports), nor of the fairness (or lack of fairness) regarding medal point computation. My question concerns rather the unfairness of comparing nations with hugely different population sizes. Can you really compare the achievements of Norway (pop. 4.6 million) to those of Russia (pop. 143.4 million)? Of course not.

Taking population seriously

So here is a table where the two types of "medal points" are divided by the population of each country. The ranking becomes strikingly different:



                 MEDALS   MEDAL POINTS   POPULATION   MP/POP   mp/POP
COUNTRY          G  S  B     MP  mp       millions     x 100    x 100

Estonia          3  0  0     12   9         1,333     900,23   675,17
Norway           2  8  9     33  31         4,593     718,48   674,94
Austria          9  7  7     57  48         8,184     696,48   586,51
Switzerland      5  4  5     33  28         7,489     440,65   373,88
Sweden           7  2  5     37  30         9,002     411,02   333,26
Finland          0  6  3     15  15         5,223     287,19   287,19
Croatia          1  2  0      8   7         4,496     177,94   155,69
Canada           7 10  7     55  48        32,805     167,66   146,32
Netherlands      3  2  4     20  17        16,407     121,90   103,61
Czech Republic   1  2  1      9   8        10,241      87,88    78,12
Germany         11 12  6     74  63        82,431      89,77    76,43
South Korea      6  3  2     32  26        48,423      66,08    53,69
Latvia           0  0  1      1   1         2,290      43,67    43,67
Slovakia         0  1  0      2   2         5,431      36,83    36,83
Italy            5  0  6     26  21        58,103      44,75    36,14
Russia           8  6  8     52  44       143,420      36,26    30,68
France           3  2  4     20  17        60,656      32,97    28,03
Bulgaria         0  1  0      2   2         7,450      26,85    26,85
Australia        1  0  1      5   4        20,090      24,89    19,91
Belarus          0  1  0      2   2        10,300      19,42    19,42
USA              9  9  7     61  52       288,368      21,15    18,03
Poland           0  1  1      3   3        38,635       7,76     7,76
Ukraine          0  0  2      2   2        47,425       4,22     4,22
United Kingdom   0  1  0      2   2        60,441       3,31     3,31
Japan            1  0  0      4   3       127,417       3,14     2,35
China            2  4  5     21  19      1311,316       1,60     1,45


And the winner is …

Now Germany is cut down to size and icy Russia has been beaten even by sunny Italy. The winner is –- yes, you have guessed quite correctly –- Estonia, with Norway in the second place. The two computational methods "MP" and "mp" make no difference in the ranking of the nations, except that in the "mp" case the race between Estonia and Norway becomes quite close.

(Population figures taken from CIA statistics)
NOTE: In the tables above decimal commas are used instead of decimal points.

* * *

ADDENDUM:
Medal points divided by the logarithms of the populations

(update March 7, 2006)

In a /msg filoraene points out that the number of Olympic participants from each nation is limited by the rules of the Olympic Games. This will also affect the outcome, in addition to the effect of the population differences between the participating nations:

What if a country has 7 top-notch athletes and can only send 3 as a result of this rule? It does not invalidate your argument that the population size matters, but it does diminish the influence of population size. The truth is somewhere between ignoring population size and a straight division. Perhaps a division by the square root? This thought struck me as the Dutch ice skating team had many very good athletes of roughly the same level and could only send a limited number.

In response to filoraene’s perfectly reasonable argument I have computed a new table (see the table below), this time by dividing the medal points "MP" (for simplicity "mp" was skipped) by the logarithms of the populations, instead of the populations themselves (I believe that logarithms are more justifiable than square roots).

As can be expected, switching to population logarithms has a profound effect on the ranking of the more populous nations. China jumps up from a jumbo position to rank 17, USA from rank 21 to 8, Russia from 16 to 9.

However, Estonia is still the undisputed winner, even if the second place in this "logarithmic Olympic contest" goes to Austria instead of to Norway (which falls back to 3rd place). (Interestingly, the Netherlands, which had rank 9 in the "straight division" table, falls back to rank 12 in the logarithmic table.)



             MEDALS                    MP/lg(POP)
COUNTRY      G  S  B  MP   lg(POP)       x 100

Estonia      3  0  0  12   0,1248       9613
Austria      9  7  7  57   0,9130       6243
Norway       2  8  9  33   0,6621       4984
Sweden       7  2  5  37   0,9543       3877
Germany     11 12  6  74   1,9161       3862
Switzerland  5  4  5  33   0,8744       3774
Canada       7 10  7  55   1,5159       3628
USA          9  9  7  61   2,4599       2480
Russia       8  6  8  52   2,1566       2411
Finland      0  6  3  15   0,7179       2089
South Korea  6  3  2  32   1,6851       1899
Netherlands  3  2  4  20   1,2150       1646
Italy        5  0  6  26   1,7642       1474
Croatia      1  2  0   8   0,6528       1225
France       3  2  4  20   1,7829       1122
Czech Rep.   1  2  1   9   1,0103        891
China        2  4  5  21   3,1177        674
Australia    1  0  1   5   1,3030        384
Latvia       0  0  1   1   0,3598        278
Slovakia     0  1  0   2   0,7349        272
Bulgaria     0  1  0   2   0,8722        229
Belarus      0  1  0   2   1,0128        197
Japan        1  0  0   4   2,1052        190
Poland       0  1  1   3   1,5870        189
Ukraine      0  0  2   2   1,6760        119
UK           0  1  0   2   1,7813        112


/ QED

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