No nation left behind

Below is the complete table of all medal-winning nations in the 2008 Summer Olympics. As you can see, the countries are not ranked according to the number of gold medals won, nor according to the total number of medals. Because it is quite clear that a (G)old medal is more valuable than a (S)ilver medal, which in turn beats the (B)ronze medal. This leads to the concept of 'medal points', which can be computed according to at least two different principles:

MP = 4*G + 2*S + 1*B

or

mp = 3*G + 2*S + 1*B

People seem to matter

Both MP and mp have been computed in the table below. But as I have already argued in 2006 Winter Olympics, this would still be an unfair way of comparing the athletic achievements of all participating nations. For example, Great Britain, with its 60 million inhabitants, is bound to have a greater potential number of capable athletes than a nation with just a third of that population, like Australia (21 million). Hence some kind of adjustment for population size would be in order.

As was already discussed in 2006 Winter Olympics, simply dividing the 'medal points' by population size would probably give too much weight to the population factor. A reasonable modification is to divide the 'medal points' by the (L)ogarithm of the (P)opulation size in order to arrive at a fair comparison of the results of the nations, i.e. to compute the statistics MP/LP and mp/LP given below.

In the table below all nations have been ranked according to the statistic MP/LP. The statistic mp/LP is also presented, but the outcome is almost the same -- mp/LP gives a different ranking in very few cases, e.g. Cuba vs. Jamaica). And in both cases the US wins convincingly.

Money matters too

Isn't this rather close to a completely pointless exercise? Well, yes, to be truthful. But fisticuffs and even wars have been fought over disagreements about sporting results. So being armed with brainless statistics may give you an edge in your next pub brawl. Furthermore, if you happen to belong to a small nation, it gives you a nice pseudo-sense of grandeur. What about the Netherlands (pop. 16 million), beating populous Japan (127 million)? Not to mention minuscule Iceland (pop. 0.3 million), leaving several fair-sized countries like Mexico, Indonesia, Portugal and Greece behind -- merely by some creative (and in fact reasonably defensible) computing.

This fairness game could reasonably be carried on to even prouder extremes. Population size matters, yes. But as you can see from the table, poor countries seem to perform less well than rich nations. So wealth matters too. After the next Olympics (2010 Winter Olympics) it would probably be interesting to divide the 'medal points' by the logarithms of each nation's GDP, thus reducing the revoltingly unfair advantage enjoyed by rich countries in the sports arena.

```Country               G   S   B    MP   mp     Population   MP/LP  mp/LP

United States        36  38  36   256  220    303 824 646   73,51  63,17
China                51  21  28   274  223  1 330 044 605   66,44  54,08
Russia               23  21  28   162  139    140 702 094   51,46  44,15
Australia            14  15  17   103   89     21 007 310   44,35  38,32
Great Britain        19  13  15   117   98     60 943 912   42,01  35,19
Germany              16  10  15    99   83     82 369 548   33,95  28,47
South Korea          13  10   8    80   67     48 379 392   29,80  24,96
France                7  16  17    77   70     64 057 790   27,44  24,94
Italy                 8  10  10    62   54     58 145 321   22,43  19,53
Jamaica               6   3   2    32   26      2 804 332   22,10  17,96
Cuba                  2  11  11    41   39     11 423 952   19,92  18,95
Ukraine               7   5  15    53   46     45 994 287   19,90  17,28
Netherlands           7   5   4    42   35     16 645 313   18,91  15,76
Japan                 9   6  10    58   49    127 288 419   18,68  15,78
Belarus               4   5  10    36   32      9 685 768   18,13  16,11
Spain                 5  10   3    43   38     40 491 051   16,49  14,57
Norway                3   5   2    24   21      4 644 457   14,40  12,60
Canada                3   9   6    36   33     33 212 696   14,28  13,09
Kenya                 5   5   4    34   29     37 953 838   13,18  11,24
Hungary               3   5   2    24   21      9 930 915   12,02  10,52
New Zealand           3   1   5    19   16      4 173 460   11,72   9,87
Kazakhstan            2   4   7    23   21     15 340 533   10,52   9,61
Slovakia              3   2   1    17   14      5 455 407    9,79   8,06
Poland                3   6   1    25   22     38 500 696    9,67   8,51
Georgia               3   0   3    15   12      4 630 841    9,01   7,20
Czech Republic        3   3   0    18   15     10 220 911    8,96   7,46
Romania               4   1   3    21   17     22 246 862    8,95   7,24
Denmark               2   2   3    15   13      5 484 723    8,62   7,47
Brazil                3   4   8    28   25    196 342 587    8,50   7,59
Mongolia              2   2   0    12   10      2 996 081    8,13   6,77
Slovenia              1   2   2    10    9      2 007 711    7,68   6,91
Ethiopia              4   1   2    20   16     82 544 838    6,86   5,49
Switzerland           2   0   4    12   10      7 581 520    6,38   5,32
Azerbaijan            1   2   4    12   11      8 177 717    6,27   5,75
Bahamas               0   1   1     3    3        307 451    6,15   6,15
Netherlands Antilles  0   1   0     2    2        225 369    5,67   5,67
North Korea           2   1   3    13   11     23 479 089    5,48   4,64
Estonia               1   1   0     6    5      1 307 605    5,37   4,48
Turkey                1   4   3    15   14     71 892 807    5,25   4,90
Latvia                1   1   1     7    6      2 245 423    5,18   4,44
Zimbabwe              1   3   0    10    9     11 350 111    4,87   4,38
Bulgaria              1   1   3     9    8      7 262 675    4,84   4,30
Bahrain               1   0   0     4    3        718 306    4,67   3,50
Finland               1   1   2     8    7      5 244 749    4,65   4,07
Argentina             2   0   4    12   10     40 481 998    4,60   3,84
Sweden                0   4   1     9    9      9 045 389    4,60   4,60
Uzbekistan            1   2   3    11   10     27 345 026    4,51   4,10
Lithuania             0   2   3     7    7      3 565 205    4,51   4,51
Thailand              2   2   0    12   10     65 493 298    4,26   3,55
Croatia               0   2   3     7    7      4 491 543    4,24   4,24
Iceland               0   1   0     2    2        304 367    4,14   4,14
Armenia               0   0   6     6    6      2 968 586    4,07   4,07
Trinidad and Tobago   0   2   0     4    4      1 047 366    3,92   3,92
Dominican Republic    1   1   0     6    5      9 507 133    3,03   2,53
Belgium               1   1   0     6    5     10 403 951    2,97   2,48
Mexico                2   0   1     9    7    109 955 400    2,96   2,30
Portugal              1   1   0     6    5     10 676 910    2,96   2,46
Greece                0   2   2     6    6     10 722 816    2,96   2,96
Indonesia             1   1   3     9    8    237 512 355    2,67   2,37
Panama                1   0   0     4    3      3 309 679    2,63   1,97
Ireland               0   1   2     4    4      4 156 119    2,47   2,47
Austria               0   1   2     4    4      8 205 533    2,09   2,09
Serbia                0   1   2     4    4     10 159 046    1,99   1,99
Tunisia               1   0   0     4    3     10 383 577    1,98   1,49
Iran                  1   0   1     5    4     65 875 223    1,77   1,42
Cameroon              1   0   0     4    3     18 467 692    1,76   1,32
Kyrgyzstan            0   1   1     3    3      5 356 869    1,74   1,74
Chinese Taipei        0   0   4     4    4     22 920 946    1,69   1,69
Tajikistan            0   1   1     3    3      7 211 884    1,61   1,61
Nigeria               0   1   3     5    5    146 255 306    1,58   1,58
India                 1   0   2     6    5  1 147 995 898    1,48   1,23
Singapore             0   1   0     2    2      4 608 167    1,20   1,20
Algeria               0   1   1     3    3     33 769 669    1,19   1,19
Morocco               0   1   1     3    3     34 343 219    1,18   1,18
Colombia              0   1   1     3    3     45 013 674    1,13   1,13
Ecuador               0   1   0     2    2     13 927 650    0,93   0,93
Chile                 0   1   0     2    2     16 454 143    0,90   0,90
Mauritius             0   0   1     1    1      1 274 189    0,90   0,90
Malaysia              0   1   0     2    2     25 274 133    0,83   0,83
Sudan                 0   1   0     2    2     40 218 455    0,77   0,77
South Africa          0   1   0     2    2     48 782 755    0,74   0,74
Vietnam               0   1   0     2    2     86 116 559    0,68   0,68
Moldova               0   0   1     1    1      4 324 450    0,61   0,61
Togo                  0   0   1     1    1      5 858 673    0,57   0,57
Israel                0   0   1     1    1      7 112 359    0,54   0,54
Venezuela             0   0   1     1    1     26 414 815    0,41   0,41
Afghanistan           0   0   1     1    1     32 738 376    0,40   0,40
Egypt                 0   0   1     1    1     81 713 517    0,34   0,34
```

NOTE: Decimal commas are used in the table, instead of decimal points. In taking logarithms, the populations were not counted in units of millions (MM), but in units of 100 000 (= 0,1 MM) thus avoiding negative logarithms for small nations with less than 1 MM (but > 0,1 MM) inhabitants.