Games about the Olympic Games

The 2008 Olympic Games are over, and as expected, China has been the country with most gold medals (but curiously, not the country with most medals!). It might be easy to think that statistically a country with over 1.3 billion people has to have at least some good athlets. There seems to be a not surprising correlation between population and results in the Olympics.

The idea: Good, we have the following belief

There is a strong correlation between the population of a country and the results in the Olympic Games

is that something real, or am I fooling myself?

The material: To do this, I didn't need too many things, as I just took data from wikipedia about the medal count and the population.

The set-up: I calculated the following score for each country:

• gold medal = 1
  
• silver medal = 0.5
  
• bronze medal = 0.25
  

and then I got the list you can find at the end of this post. If we order it by total score (I preferred to order it by score/million people, which is more interesting), the list is not quite different from the original medal count, which is ordered by gold medals, then by silver medals, and then by bronze medals. China is still the number one, but United States is a bit nearer.

Ordered by score/million people, we see that... Jamaica, with a score of almost 3 is leading! (It pays having good short distance runers) Then we have the Bahamas, Iceland... The first big country is Australia (which has been amazing about every sport that is related with water).

I have made the following graph showing the relation between my score and the population:



Clicking on the graph you will see the original size, with the name of each country for each cross. But anyway, you will not see too much, as most of the countries are piled up in one corner. Maybe you can see better in logarithmic scale:



I have added the linear fit calculated using Origin. If we have to trust in the Origin, the correlation coeficient is 0.398.

This means that there is a weak, direct correlation between results and population. It is what I expected... but not as much as I expected (personally I thought it would have been a correlation around 0.8).

Why is the correlation so weak? I think one reason could be the fact that in most cases the medals are just one or two, which is not enough to get good statistical results, as fluctuations can change a lot the score, so we have "good" information just about countries that have at least ~10 medals

The other reason could be the fact that population is not the only important factor here. For example, the economy of a country is also important.

It's late enough now, so I will not make a graph showing the score versus the GDP, but if somebody does, I am interested in seeing the result.But just let's make one more graph. I choose only the countries that have got at least ten medals (not because they are more important than the other, but because the statistics are more accurate), and here is the result:



Interesting, isn't it? The bigger the country, the smaller the score. And here the correlation is a rather strong: -0.807. It seems that a single athlete has more chances to win a medal if he is from a smaller country (probably because there is less internal competition to qualify for the Olympics). That makes me think of the half-Togolese half-French kayaker Benjamin Boukpeti, who preferred to defend the Togolese flag instead of the French one, because it was much more difficult to qualify as part of the French team. After all, he got the first medal for Togo!

Conclusion: So it comes out that

1) big countries have more chances to get medals, because they have more people to select and train, but the correlation is much weaker than expected.
2) for the individual, being in a big country can be counterproductive, probably because there is more internal competition to qualify for the Olympics.

Hm...

OK, here is the promised table (as I am European, I wanted to see what are the results of my "bigger country", so I have added the data for the European Union below).

For space reasons, the medals are shown in format gold/silver/bronze=total. Population is in millions. And remember, score = #gold + #silver/2 + #bronze/4. (I have made also a map that you can see on Wikipedia).

Country	Pop.	Medals	Score	Score/pop.
1. Jamaica	2.714	6/3/2=11	8	2.948
2. Bahamas	0.331	0/1/1=2	0.75	2.266
3. Iceland	0.316	0/1/0=1	0.5	1.582
4. Bahrain	0.76	1/0/0=1	1	1.316
5. Norway	4.778	3/5/2=10	6	1.256
6. Slovenia	2.029	1/2/2=5	2.5	1.232
7. Australia	21.394	14/15/17=46	25.75	1.204
8. Mongolia	2.629	2/2/0=4	3	1.141
9. Estonia	1.341	1/1/0=2	1.5	1.119
10. New Zealand	4.274	3/1/5=9	4.75	1.111
11. Belarus	9.69	4/5/10=19	9	0.929
12. Cuba	11.268	2/11/11=24	10.25	0.91
13. Georgia	4.395	3/0/3=6	3.75	0.853
14. Slovakia	5.402	3/2/1=6	4.25	0.787
15. Latvia	2.268	1/1/1=3	1.75	0.772
16. Trinidad and Tobago	1.333	0/2/0=2	1	0.75
17. Denmark	5.489	2/2/3=7	3.75	0.683
18. Netherlands	16.445	7/5/4=16	10.5	0.638
19. Hungary	10.043	3/5/2=10	6	0.597
20. Lithuania	3.361	0/2/3=5	1.75	0.521
21. Armenia	3.002	0/0/6=6	1.5	0.5
22. Great Britain	60.587	19/13/15=47	29.25	0.483
23. Czech Republic	10.403	3/3/0=6	4.5	0.433
24. South Korea	48.224	13/10/8=31	20	0.415
25. Switzerland	7.637	2/0/4=6	3	0.393
26. Croatia	4.555	0/2/3=5	1.75	0.384
27. Finland	5.317	1/1/2=4	2	0.376
28. Kazakhstan	15.422	2/4/7=13	5.75	0.373
29. Azerbaijan	8.467	1/2/4=7	3	0.354
-. (European Union)	498.248	87/101/92=280	160.5	0.322
30. Germany	82.218	16/10/15=41	24.75	0.301
31. Panama	3.343	1/0/0=1	1	0.299
32. France	64.473	7/16/17=40	19.25	0.299
33. Bulgaria	7.64	1/1/3=5	2.25	0.295
34. Ukraine	46.059	7/5/15=27	13.25	0.288
35. Russia	141.889	23/21/28=72	40.5	0.285
36. Canada	33.347	3/9/6=18	9	0.27
37. Italy	59.619	8/10/10=28	15.5	0.26
38. Romania	21.438	4/1/3=8	5.25	0.245
39. Sweden	9.215	0/4/1=5	2.25	0.244
40. Spain	46.063	5/10/3=18	10.75	0.233
41. Ireland	4.339	0/1/2=3	1	0.23
42. Kenya	37.538	5/5/4=14	8.5	0.226
43. United States	304.875	36/38/36=110	64	0.21
44. Mauritius	1.262	0/0/1=1	0.25	0.198
45. Zimbabwe	13.349	1/3/0=4	2.5	0.187
46. Poland	38.116	3/6/1=10	6.25	0.164
47. Dominican Republic	9.76	1/1/0=2	1.5	0.154
48. Belgium	10.585	1/1/0=2	1.5	0.142
49. Portugal	10.623	1/1/0=2	1.5	0.141
50. Kyrgyzstan	5.317	0/1/1=2	0.75	0.141
51. North Korea	23.79	2/1/3=6	3.25	0.137
52. Greece	11.147	0/2/2=4	1.5	0.135
53. Austria	8.341	0/1/2=3	1	0.12
54. Japan	127.69	9/6/10=25	14.5	0.114
55. Tajikistan	6.736	0/1/1=2	0.75	0.111
56. Singapore	4.589	0/1/0=1	0.5	0.109
57. Serbia	9.858	0/1/2=3	1	0.101
58. Uzbekistan	27.372	1/2/3=6	2.75	0.1
59. Tunisia	10.327	1/0/0=1	1	0.097
60. Argentina	40.302	2/0/4=6	3	0.074
61. Moldova	3.794	0/0/1=1	0.25	0.066
62. Ethiopia	79.221	4/1/2=7	5	0.063
63. Cameroon	18.549	1/0/0=1	1	0.054
64. Turkey	70.586	1/4/3=8	3.75	0.053
65. China	1325.544	51/21/28=100	68.5	0.052
66. Thailand	63.038	2/2/0=4	3	0.048
67. Chinese Taipei	22.99	0/0/4=4	1	0.043
68. Togo	6.585	0/0/1=1	0.25	0.038
69. Ecuador	13.341	0/1/0=1	0.5	0.037
70. Brazil	187.474	3/4/8=15	7	0.037
71. Israel	7.303	0/0/1=1	0.25	0.034
72. Chile	16.763	0/1/0=1	0.5	0.03
73. Morocco	31.224	0/1/1=2	0.75	0.024
74. Algeria	33.858	0/1/1=2	0.75	0.022
75. Mexico	106.683	2/0/1=3	2.25	0.021
76. Malaysia	27.17	0/1/0=1	0.5	0.018
77. Iran	70.496	1/0/1=2	1.25	0.018
78. Colombia	44.513	0/1/1=2	0.75	0.017
79. Sudan	38.56	0/1/0=1	0.5	0.013
80. South Africa	47.851	0/1/0=1	0.5	0.01
81. Indonesia	231.627	1/1/3=5	2.25	0.01
82. Afghanistan	27.145	0/0/1=1	0.25	0.009
83. Venezuela	27.954	0/0/1=1	0.25	0.009
84. Nigeria	148.093	0/1/3=4	1.25	0.008
85. Vietnam	87.375	0/1/0=1	0.5	0.006
86. Egypt	75.201	0/0/1=1	0.25	0.003
87. India	1136.75	1/0/2=3	1.5	0.001

PS: I have seen that a wikipedian has made some interesting maps showing:

• capita per gold medal.
  
• capita per silver medal.
  
• capita per bronze medal.
  
• capita per medal (in general).