In "gold medal tally by per million population", Jamaica was winning with 2.1582 as of Saturday afternoon. The runner-up was Bahrain and Estonia the third. China was 45th, the US 31st , Russia 26th, India last.
Of course this analysis deals will those who actually won gold medals - about 160 countries did not get any Gold medals at all.
For a very detailed analysis of the 2008 Beijing Olympics Medal Tally see: Olympic Medal Tally Analyzed. No Gold Medals for War, Occupation & Genocide - some of the major success factors were wealth and sports investment; population and gene pool size; population genetic factors; sports culture and "sports culture"; serendipity (e.g. baton dropping); and socio-economic and geopolitical factors - thus of the circa 105 countries who did not get any medals at all, all but 5 tiny European principalities (Andorra, Liechtenstein, Monaco, Luxembourg and San Marino) were subject to violent European colonial occupation in the post-war era, variously with appalling attendant abuse and devastation.
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