Ranking the countries according to the number of gold medals in 2012 London Olympics, or according to the number of all medals, or according to the medal points (gold + 1/2 silver + 1/3 bronze), respectively, provides the following sequences:
US Chin GBR Russ Kore Fran Ger Hun Ita Aus Kaza Jap
US Chin Russ GBR Ger Jap Aust Fran Kore Ita Neth Ukra
US Chin Russ GBR Ger Fran Jap Kore Aust Ita Ukra Hun
which are non-identical but similar. If arranging the countries according to medal points per capita, a totally different sequence is obtained:
Jama New Zea Trini Hun Slove Lith Croa Denm Aust Monte Carri Geor
At first twelve positions, the two systems overlap only in Hungary and Australia. The arrangement according to the number of medals draws countries with large populations and with sport traditions to the top of the sequences, whereas the arrangement according to the per-capita-medals moves rather smaller countries, not without sport traditions either, to the top. The former way obviously favors large population countries; the latter way favors smaller countries, among others because the olympic teams are limited to three athletes per country in many disciplines. If the number of medals were a simple function of the population size, only one of the parameters would suffice for ranking the countries, but it seems that the medal number and the per capita medal number reflect two different aspects. Therefore, combining the two aspects may be the best way how to characterize the achievements of the countries. That is what is done in the following table for London 2012 Olympics.
The first column shows the medal points (S1) for all the countries which gained at least one medal in the London 2012. Fifteen small Carribean countries, each having less than half million population, including Bahamas and Grenada, are combined in one geographical block under the name Carrib. The second column (S2) is the medal point per 10 million people (=10S1/P, wherein P is the population in million). The third and the forth columns (R1 and R2) are the ranks of the country among 84 countries arranged according to either S1 or S2. The fifth column is the mean value of the two ranks R1 and R2, and the countries are arranged in the table according to the increasing mean value of both ranks. If two countries have the same mean value, better medal achievement S1 decides. It is seen that the sequence now is:
Hun Aust NewZea GBR Jama  Neth Cuba Denm Russ Kore Croa Fran
Combining the countries ranks in the total medal count and in the count per capita well balances various aspects and seems to be the best way how to assess the Olympic achievements of the countries. The position of a country in the new list thus obtained, "supra rank" R, optimally reflects its achievements. Two countries in which the two systems (based on total medals versus total medals per capita)overlapped, namely Hun and Aust, catch the first two positions among countries arranged according to the supra rank R. Hungary indeed remains one of the most successful countries through all the modern Olympic Games.
As for the five Olympic rings, among the most successful 50 countries from about 200 London 2012 participants, 30 belong to Europe, North America and Australia (of total 53 countries in those continents), 11 to Asia (of total 44), 6 to South and Central America (of total 37), and 3 to Africa (of total 53 African countries).
US Chin GBR Russ Kore Fran Ger Hun Ita Aus Kaza Jap
US Chin Russ GBR Ger Jap Aust Fran Kore Ita Neth Ukra
US Chin Russ GBR Ger Fran Jap Kore Aust Ita Ukra Hun
which are non-identical but similar. If arranging the countries according to medal points per capita, a totally different sequence is obtained:
Jama New Zea Trini Hun Slove Lith Croa Denm Aust Monte Carri Geor
At first twelve positions, the two systems overlap only in Hungary and Australia. The arrangement according to the number of medals draws countries with large populations and with sport traditions to the top of the sequences, whereas the arrangement according to the per-capita-medals moves rather smaller countries, not without sport traditions either, to the top. The former way obviously favors large population countries; the latter way favors smaller countries, among others because the olympic teams are limited to three athletes per country in many disciplines. If the number of medals were a simple function of the population size, only one of the parameters would suffice for ranking the countries, but it seems that the medal number and the per capita medal number reflect two different aspects. Therefore, combining the two aspects may be the best way how to characterize the achievements of the countries. That is what is done in the following table for London 2012 Olympics.
The first column shows the medal points (S1) for all the countries which gained at least one medal in the London 2012. Fifteen small Carribean countries, each having less than half million population, including Bahamas and Grenada, are combined in one geographical block under the name Carrib. The second column (S2) is the medal point per 10 million people (=10S1/P, wherein P is the population in million). The third and the forth columns (R1 and R2) are the ranks of the country among 84 countries arranged according to either S1 or S2. The fifth column is the mean value of the two ranks R1 and R2, and the countries are arranged in the table according to the increasing mean value of both ranks. If two countries have the same mean value, better medal achievement S1 decides. It is seen that the sequence now is:
Hun Aust NewZea GBR Jama  Neth Cuba Denm Russ Kore Croa Fran
Combining the countries ranks in the total medal count and in the count per capita well balances various aspects and seems to be the best way how to assess the Olympic achievements of the countries. The position of a country in the new list thus obtained, "supra rank" R, optimally reflects its achievements. Two countries in which the two systems (based on total medals versus total medals per capita)overlapped, namely Hun and Aust, catch the first two positions among countries arranged according to the supra rank R. Hungary indeed remains one of the most successful countries through all the modern Olympic Games.
As for the five Olympic rings, among the most successful 50 countries from about 200 London 2012 participants, 30 belong to Europe, North America and Australia (of total 53 countries in those continents), 11 to Asia (of total 44), 6 to South and Central America (of total 37), and 3 to Africa (of total 53 African countries).
| S1 | S2 | R1 | R2 | (R1+R2)/2 | |
---|---|---|---|---|---|---|
1 | HUNGA | 12 | 12 | 12 | 4 | 8 |
2 | AUSTRA | 19 | 8.26 | 9 | 9 | 9 |
3 | NEW ZEA | 8.7 | 19.8 | 16 | 2 | 9 |
4 | GBR | 44 | 7.1 | 4 | 15 | 9.5 |
5 | JAMAICA | 7.3 | 27 | 21 | 1 | 11 |
6 | NETHER | 12 | 7.06 | 13 | 16 | 14.5 |
7 | CUBA | 8.5 | 7.73 | 17 | 13 | 15 |
8 | DENMAR | 5 | 8.93 | 26 | 8 | 17 |
9 | RUSSIA | 48 | 3.36 | 3 | 32 | 17.5 |
10 | KOREA | 19.3 | 3.9 | 8 | 29 | 18.5 |
11 | CROAT | 4.2 | 9.76 | 32 | 7 | 19.5 |
12 | FRANCE | 21 | 3.23 | 6 | 34 | 20 |
13 | KAZACH | 9.2 | 5.4 | 15 | 25 | 20 |
14 | BELARUS | 6.5 | 6.5 | 22 | 18 | 20 |
15 | GER | 25 | 3.05 | 5 | 37 | 21 |
16 | CZECH | 6.5 | 6.2 | 23 | 19 | 21 |
17 | UKRAIN | 15 | 3.26 | 11 | 33 | 22 |
18 | LITHUA | 3.2 | 10 | 38 | 6 | 22 |
19 | US | 70 | 2.23 | 1 | 44 | 22.5 |
20 | GEORG | 3.5 | 7.78 | 35 | 12 | 23.5 |
21 | SLOVEN | 2.2 | 11 | 43 | 5 | 24 |
22 | TRINIDA | 2 | 14.8 | 46 | 3 | 24.5 |
23 | ITALIA | 16 | 2.62 | 10 | 40 | 25 |
24 | AZERBA | 5 | 5.43 | 27 | 24 | 25.5 |
25 | CARRIB | 2 | 8 | 47 | 11 | 29 |
26 | JAPAN | 20 | 1.56 | 7 | 52 | 29.5 |
27 | SWEDEN | 4 | 4.21 | 33 | 27 | 30 |
28 | SPAIN | 9.3 | 2.02 | 14 | 47 | 30.5 |
29 | CANADA | 8 | 2.29 | 19 | 43 | 31 |
30 | MONGOL | 2 | 7.14 | 48 | 14 | 31 |
31 | NORWE | 2.8 | 5.6 | 40 | 23 | 31.5 |
32 | ROMAN | 5.2 | 2.74 | 25 | 39 | 32 |
33 | UZBEKI | 2 | 6.9 | 49 | 17 | 33 |
34 | IRELAND | 2.5 | 4.78 | 41 | 26 | 33.5 |
35 | CHINA | 59 | 0.44 | 2 | 66 | 34 |
36 | SWITZ | 3 | 3.75 | 39 | 30 | 34.5 |
37 | LATVI | 1.3 | 6.19 | 53 | 20 | 36.5 |
38 | IRAN | 7.5 | 1 | 20 | 58 | 39 |
39 | KENYA | 5.7 | 1.33 | 24 | 54 | 39 |
40 | N. KORE | 4.7 | 1.88 | 29 | 49 | 39 |
41 | SERBIA | 2.2 | 3.1 | 44 | 36 | 40 |
42 | MONTEN | 0.5 | 8.06 | 72 | 10 | 41 |
43 | POLAND | 5 | 1.28 | 28 | 55 | 41.5 |
44 | ESTONI | 0.8 | 6.15 | 62 | 21 | 41.5 |
45 | BRAZIL | 8.5 | 0.44 | 18 | 67 | 42.5 |
46 | ARMEN | 1.2 | 3.6 | 55 | 31 | 43 |
47 | SLOVAK | 1.5 | 2.78 | 51 | 38 | 44.5 |
48 | S. AFRIC | 4.3 | 0.84 | 31 | 59 | 45 |
49 | ETHIOP | 4.5 | 0.54 | 30 | 64 | 47 |
50 | COLOMB | 3.8 | 0.81 | 34 | 61 | 47.5 |
51 | CYPRUS | 0.5 | 5.95 | 73 | 22 | 47.5 |
52 | QATAR | 0.7 | 4.1 | 68 | 28 | 48 |
53 | TUNIS | 1.8 | 1.68 | 50 | 50 | 50 |
54 | FINLAN | 1.2 | 2.22 | 56 | 45 | 50.5 |
55 | DOMIN.R | 1.5 | 1.6 | 52 | 51 | 51.5 |
56 | TURKEY | 3.3 | 0.44 | 37 | 68 | 52.5 |
57 | ARGEN | 2.2 | 0.55 | 45 | 63 | 54 |
58 | PUERTO | 0.8 | 2.16 | 63 | 46 | 54.5 |
59 | GABON | 0.5 | 3.13 | 74 | 35 | 54.5 |
60 | MEXICO | 3.5 | 0.31 | 36 | 74 | 55 |
61 | BELGI | 1.2 | 1.06 | 57 | 57 | 57 |
62 | BOTSW | 0.5 | 2.5 | 75 | 41 | 58 |
63 | MOLDO | 0.7 | 1.94 | 69 | 48 | 58.5 |
64 | BULG | 0.8 | 1.08 | 64 | 56 | 60 |
65 | BAHRA | 0.3 | 2.5 | 78 | 42 | 60 |
66 | SINGAP | 0.7 | 1.35 | 70 | 53 | 61.5 |
67 | INDIA | 2.3 | 0.02 | 42 | 84 | 63 |
68 | VENEZ | 1 | 0.37 | 58 | 71 | 64.5 |
69 | THAILA | 1.3 | 0.2 | 54 | 78 | 66 |
70 | GREECE | 0.7 | 0.65 | 71 | 62 | 66.5 |
71 | UGAND | 1 | 0.3 | 59 | 75 | 67 |
72 | ALGER | 1 | 0.27 | 60 | 77 | 68.5 |
73 | TAIWAN | 0.8 | 0.35 | 65 | 72 | 68.5 |
74 | KUWAI | 0.3 | 0.83 | 79 | 60 | 69.5 |
75 | EGYPT | 1 | 0.12 | 61 | 79 | 70 |
76 | PORTUG | 0.5 | 0.47 | 76 | 65 | 70.5 |
77 | MALAYS | 0.8 | 0.29 | 66 | 76 | 71 |
78 | HON KON | 0.3 | 0.42 | 80 | 69 | 74.5 |
79 | INDONES | 0.8 | 0.03 | 67 | 83 | 75 |
80 | GUATE | 0.5 | 0.34 | 77 | 73 | 75 |
81 | TAJIKIS | 0.3 | 0.38 | 81 | 70 | 75.5 |
82 | AFGANI | 0.3 | 0.12 | 82 | 80 | 81 |
83 | SAUDI | 0.3 | 0.11 | 83 | 81 | 82 |
84 | MAROC | 0.3 | 0.09 | 84 | 82 | 83 |