Sep 5, 2012

Supra Rank of the Countries in the Olympic Games

It has been shown that the best way how to rank the Olympic achievements of the countries is to take the average of two ranks: one based on the medal number and the other on the medal number per capita, providing "supra rank". The medal number is well summed by medal points: S1 [= G + S/2 + B/3, where G, S, and B are the number of gold, silver, and bronze medals,
respectively]. The medal points per capita are suitably characterized by medal points per ten million: S2 [= 10*S1/P, where P is the population in million]. For a median country which has ten million people, like Hungary, S1 = S2. When listing the countries according to decreasing S1, the country's position in the list yields the total medal rank R1, and when listing the countries according to decreasing S2, the country's per capita rank R2 is obained. Both ranks reflect rather different aspects, and when taking the average value of the two ranks, (R1+R2)/2, and listing the countries according to the increasing value of this average value, a new rank for each country among all the countries - supra rank R - is obtained. Arranging the countries according to R smoothens "rank noises" resulting from too large and too small population values. The values G, M, S1, P, and S2 for the countries participating in 2012 London Olympics were tabled, as well as the values R, S1, S2, R1, R2, and (R1+R2)/2, where M is the sum of all medals.

In the long table below, all modern Olympic Games from 1896 till 2012 have been included, and all countries participating in them, while calculating S1 and S2 for each country and for all the games in which the country participated. The medal points S1 and S2 for each country have been divided by the number N of the Olympic Games in which the country participated. Together, twenty seven modern Olympics have been organized, three were canceled during two world wars. Many countries have disappeared and many new have been formed during the last 120 years, some countries boycotted some games, and only a few countries participated in all twenty seven games. The countries which obtained at least one medal in their history have been listed according to their decreasing value of medal points per one Olympic participation, S1/N, and rank R3 in the list for each country has thus been obtained. Similarly, medal points per one Olympic game per capita have been calculated as S2/N, the countries arranged according to decreasing value of the parameter, and so rank R4 has been obtained for each country. Thus each country has been ranked among 135 countries according to the medals per one Olympic Game (R3 between 1 and 135), and per one Olympic Game per capita (R4 between 1 and 135). The average of the two ranks, (R3+R4)/2, has been calculated and the countries have been re-arranged according to the increasing value of this average; when more countries had the same average value, the number of total gold medals per one Olympic Game per capita decided about the final position in the list. The position in the new list provides supra rank R of the country in all the games, which seems to truly reflect the total Olympic achievements in the modern Olympic Games for each country. See the table below. Some geographical areas are included more times; for example, the item "Germany" shows the results for united Germany till 1952 and after 1992, without including the results for East Germany and West Germany which are included separately. The medal counts have been taken from http://en.wikipedia.org/wiki/All-time_Olympic_Games_medal_table and the population sizes from http://en.wikipedia.org/wiki/List_of_countries_by_population.
Strangely, the best absolute achievements in all modern Olympics, when measured by supra rank R, goes to a country which does not exist any more - to East Germany. Among countries doing well in Olympics are Western countries with old Olympic traditions, as well as Communist countries, which wish to show their superiority but cannot compete in economy or any other field. East Germany combined these two factors. Mercilessly they screened the whole population from early childhood, supporting natural skills of people by all available physical and chemical means, and so they surpassed much geater West Germany. Relative high supra rank of West Germany, and also of united Germany in the table shows that natural talents of German people also contributed a lot. The second table, seen below the long one below, compares the countries positions when five different criteria are used.

                                    N                 R3               R4              (R3+R4)/2   10*G/N/P          
1East Ger531219.13
2Hungar251258.56.71
3Sweden 2615610.55.78
4Finland 24193117.77
5Belarus 5181114.52.54
6Bulgaria1922915.53.64
7Soviet Un913216.52.19
8West Ger562917.51.78
9Cuba 19211618.53.37
10Australia25142318.52.43
11Russia 543318.51.86
12Norway 242812204.64
13Romania 201725212.31
14Denmark263113222.96
15Czechia5272023.52.66
16Germany15741241.42
17Great Br27840241.40
18New Zea223614254.30
19Ukraine 51139251.49
20USA26248251.19
21Jamaica16448263.92
22Czechosl162626262.36
23Switzer273022262.19
24France 27943261.14
25Netherla25233026.51.84
26Italy261044271.29
27Estonia1151427.56.32
28Slovakia 5371827.52.57
29Kazakhst5243127.51.91
30Georgia 54117292.67
31Slovenia65210313.24
32Croatia 64719332.33
33South Kor161650331.01
34Poland20204934.50.83
35Belgium 253337351.37
36Bahamas15702369.43
37Japan 21136237.50.49
38Azerbaija5393838.51.30
39Canada 25255238.50.68
40Lithuania 85424392.36
41Latvia 105721391.45
42Yugosla16345544.50.81
43Kenya 13296044.50.50
44Greece 274545451.03
45North Kor9355846.50.63
46Armenia5583546.50.61
47Austria26494647.50.82
48Mongolia12613447.50.61
49China9591480.17
50Spain 22326548.50.36
51Trini Toba16712849.50.95
52Grenada 89775211.28
53Serbia 3555454.50.47
54Uzbekis54664550.34
55Montene2842755.50.00
56South Afr184369560.25
57Ireland 20625156.50.98
58Turkey 213876570.25
59Argentina23507361.50.20
60Moldova 5695662.50.00
61Ethiopia12428563.50.21
62Tonga 811515650.00
63Namibia 67953660.00
64Iran 16488767.50.12
65Bohemia37363680.00
66Zimbabw96872700.26
67Portugal 237270710.16
68Brazil214010371.50.06
69Morocco13598672.50.14
70Uruguay 20836674.50.30
71Iceland191074274.50.00
72Tunisia 137575750.22
73Suriname121044775.51.56
74Qatar 8926176.50.00
75Dominic13787978.50.24
76Mexico 2253105790.05
77Taiwan16679279.50.05
78Kyrgyzst5857479.50.00
79Algeria126496800.11
80Puerto Ri17907180.50.00
81Thailand1560104820.07
82Luxembo221125784.50.89
83CostaRic149377850.17
84Tajikistan 58684850.00
85Bermuda171353685.50.00
86Egypt 2165109870.04
87Israel 158789880.08
88Indonesi1456120880.02
89Chile22809788.50.05
90Colombia187410790.50.02
91Burundi 58894910.23
92Cameroo1382100910.12
93Venezuel177710691.50.04
94Nigeria 1563121920.01
95Cyprus91186792.50.00
96Panama1610583940.18
97Uganda 148110894.50.04
98Barbados1113159950.00
99Djibouti81256896.50.00
100Macedon51138297.50.00
101Hong Kon15999898.50.09
102Gabon 91197898.50.00
103Singapo1510395990.00
104UAE89810199.50.15
105Lebanon 161069399.50.00
106India 2366135100.50.00
107Pakistan 16761261010.01
108Malaysia1489114101.50.00
109Syria 12941121030.04
110Bahrain 8126801030.00
111Mozambi9951131040.05
112Botswana9120881040.00
113Mauritius8127811040.00
114Ecuador13101110105.50.05
115Eritrea 4109102105.50.00
116Peru 17961181070.02
117Kuwait 12117991080.00
118Ghana13102119110.50.00
119Philippine20911311110.00
120Saudi 101001221110.00
121Guyana16134901120.00
122Zamb111101161130.00
123Haiti 15116117116.50.00
124Paraguay 11122111116.50.00
125Srilanka 16114123118.50.00
126Tanzania 12108129118.50.00
127Vietnam 141111331220.00
128Togo 9130115122.50.00
129Afgani131211271240.00
130Côte d'Ivo121241281260.00
131Senegal 131281241260.00
132Guatema131291251270.00
133Sudan 11123132127.50.00
134Niger111321301310.00
135Iraq 13133134133.50.00

The 135 countries from the above table have been arranged in five different ways, thus obtaining five different lists, and the first twenty most successful countries from each list are shown below. The first column, denoted R1, relates to medal points in all Olympics; the second column, denoted R2, relates to medal points from all Olympics per capita; the third column, denoted R3, relates to medal points from all Olympics divided by the number N of games in which the country participated (medals points per one Olympic game); the fourth column relates to the number of points per one Olympic per capita; and the fifth column relates to the supra rank R of the country as shown in the long table above. It can be seen that each way of arranging the countries emphasizes certain features, but the supra rank seems to be the most balanced measure.

R1R2R3R4R
USAFinland Soviet UnEast GerEast Ger
Soviet UnSweden USABahamasHungar
Great BrHungarEast GerFinland Sweden
France BahamasRussia EstoniaFinland
ItalyNorway ChinaHungarBelarus
GermanyDenmarkWest GerSweden Bulgaria
ChinaEast GerGermanyGrenada Soviet Un
HungarBulgariaGreat BrJamaicaWest Ger
Sweden New ZeaFrance BulgariaCuba
AustraliaEstoniaItalySloveniaAustralia
East GerJamaicaUkraine Belarus Russia
Russia SwitzerHungarNorway Norway
Japan AustraliaJapan DenmarkRomania
Finland Cuba AustraliaNew ZeaDenmark
Romania NetherlaSweden Tonga Czechia
NetherlaRomania South KorCuba Germany
South KorGrenada Romania Georgia Great Br
Canada Belgium Belarus Slovakia New Zea
PolandGreat BrFinland Croatia Ukraine
Cuba CzechosPolandCzechiaUSA