Aug 27, 2012

Olympic Medals - Countries Absolute Rank

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).

     
                
                          S1              S2              R1            R2            (R1+R2)/2
1HUNGA12121248
2AUSTRA198.26999
3NEW ZEA8.719.81629
4GBR447.14159.5
5JAMAICA7.32721111
6NETHER127.06131614.5
7CUBA8.57.73171315
8DENMAR58.9326817
9RUSSIA483.3633217.5
10KOREA19.33.982918.5
11CROAT4.29.7632719.5
12FRANCE213.2363420
13KAZACH9.25.4152520
14BELARUS6.56.5221820
15GER253.0553721
16CZECH6.56.2231921
17UKRAIN153.26113322
18LITHUA3.21038622
19US702.2314422.5
20GEORG3.57.78351223.5
21SLOVEN2.21143524
22TRINIDA214.846324.5
23ITALIA162.62104025
24AZERBA55.43272425.5
25CARRIB28471129
26JAPAN201.5675229.5
27SWEDEN44.21332730
28SPAIN9.32.02144730.5
29CANADA82.29194331
30MONGOL27.14481431
31NORWE2.85.6402331.5
32ROMAN5.22.74253932
33UZBEKI26.9491733
34IRELAND2.54.78412633.5
35CHINA590.4426634
36SWITZ33.75393034.5
37LATVI1.36.19532036.5
38IRAN7.51205839
39KENYA5.71.33245439
40N. KORE4.71.88294939
41SERBIA2.23.1443640
42MONTEN0.58.06721041
43POLAND51.28285541.5
44ESTONI0.86.15622141.5
45BRAZIL8.50.44186742.5
46ARMEN1.23.6553143
47SLOVAK1.52.78513844.5
48S. AFRIC4.30.84315945
49ETHIOP4.50.54306447
50COLOMB3.80.81346147.5
51CYPRUS0.55.95732247.5
52QATAR0.74.1682848
53TUNIS1.81.68505050
54FINLAN1.22.22564550.5
55DOMIN.R1.51.6525151.5
56TURKEY3.30.44376852.5
57ARGEN2.20.55456354
58PUERTO0.82.16634654.5
59GABON0.53.13743554.5
60MEXICO3.50.31367455
61BELGI1.21.06575757
62BOTSW0.52.5754158
63MOLDO0.71.94694858.5
64BULG0.81.08645660
65BAHRA0.32.5784260
66SINGAP0.71.35705361.5
67INDIA2.30.02428463
68VENEZ10.37587164.5
69THAILA1.30.2547866
70GREECE0.70.65716266.5
71UGAND10.3597567
72ALGER10.27607768.5
73TAIWAN0.80.35657268.5
74KUWAI0.30.83796069.5
75EGYPT10.12617970
76PORTUG0.50.47766570.5
77MALAYS0.80.29667671
78HON KON0.30.42806974.5
79INDONES0.80.03678375
80GUATE0.50.34777375
81TAJIKIS0.30.38817075.5
82AFGANI0.30.12828081
83SAUDI0.30.11838182
84MAROC0.30.09848283