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There is such an obsession with rankings.  And being at the top in medal standings seems so important to so many.   So much so that larger issues got overlooked during the Olympics. 

And in spite of such obsession, nobody seems to get the medal ranking race straight.  Who really won?  Hard to tell, for unsuspecting reasons.  Lets see.

For starters, the media in the US tends to show us tables which rank countries according to the total medal count.  That puts the US at the top, having accumulated 110 gold, silver and bronze medals, against 100 medals for China.

 Officially, the IOC tries not to officially rank countries, but their tables list countries ranked by their number of gold medals (see Sydney and Athens’ results).  Following this criterion, as it is common in the much of the rest of the world, China comes out clearly on top, with a total of 51 gold medals, against only 36 for the US.

So far so good, and not much new.  Enter my economist bias.  First instinctive reaction is to reject either criteria, asking why do we have to choose between two absurd extremes in terms of implicit medal weights?: one extreme giving as much weight to a bronze medal as to a gold one, while the other extreme simply saying that only gold glitters and thus silver and bronze are worthless – zero weight.

As economists, we would argue that silver should have some weight, but less than gold, and so should bronze, but less than silver.  A simple scheme would value a gold medal as the equivalent of 3 bronze medals, and silver as the equivalent of 2 bronze medals, arriving at the 3, 2, 1 weights respectively for gold, silver and bronze.  Who would win the Olympic medal race under such weighted scheme? 

China and the US virtually tie for first, with China officially accumulating 223 ‘bronze equivalent’ medals, and the US taking 220 medal equivalents.  So China would stay slightly atop presuming that no one gymnast gold medalist is officially declared to be underage and disqualified, in which case such slight advantage would evaporate.

So who actually won the medal count race, China or the US?  Perhaps neither.  Enter my economist bias again, where I would question an excessive obsession with mere cumulative totals, disregarding huge differences in country size.  This matters, since population size provides the potential pool of gifted athletes.  Remember that there is reason why as economists we are enthralled with ‘per capita’ measures.  And in fact population size is one of the best explanators of total medal haul at Olympics, even if many other factors matter as well (including being the host country, governance, etc.).

So, who won most medals per million inhabitants?.  You guessed it: Jamaica did, and Australia gets a very special mention indeed. 

If we only look at how many gold medals per capita the country athletes got, Jamaica would have been the runaway winner by 'Bolt light years', with well over 2 gold medals per million people, compared with only about 0.04 gold medals per million people for China, and 0.12 per million for the US.

But as an economist we pretend to be consistent, so let us look instead at the cumulative weighted medals (bronze equivalent) per capita. The table below shows the results for the ‘top 30’ countries according to this medal per capita criterion.  Again, Jamaica atop: it got about 10 (bronze) medal equivalents per million people.

And among notable others following this per capita medal ranking, witness Norway (4.5 medals equivalent per million), Australia, Slovenia, Mongolia, New Zealand, Cuba (3.5), Georgia (2.7) and Latvia, all among the top ranked 15.  And the UK (1.6 medal equivalent per million) places a rather respectable 22nd place.  This bodes well for their 2012 London Olympics, because there is always an additional host country boost on medals.   You cannot find the US in this table, because it would rank only 44th out of the 197 country participants.  China would be 66th.

Foul!, some will cry, no doubt. I may soon hear that all what counts is absolute total power, who cares about per capita anything...or about softer power.  Those more subtle may remind me that even if the size of country delegations vary a lot, the number of athletes per sport is capped at the Olympics, and, further, for most team sports only one team per country can compete. 

But the point is that even if the number of participants per country is not proportional to its population, larger countries not only have larger Olympic contingents, but can rely at home on a much larger qualifying pool of athletes, vetting the very top talent required to then go to the Olympics to win a medal.  Further, studies suggest that there is also a ‘large market superstar’ effect: more talented people finding more financial returns by being in a larger market, which provides an additional advantage to very large countries.

Still, let me be considerate to larger countries, and analyze the rankings only among those with over 20 million people, as shown below in Table 2.  39 out of 52 such large countries obtained medals, and a number of those large countries performed well even on a per capita basis. Australia is the runaway standout, with 4.4 (bronze) medal equivalents per million inhabitants, followed by the solid performances of the UK (1.6) and South Korea (1.4), then by France, Canada, Germany, Ukraine and Russia (1.0-1.2), then by Italy, Spain, Kenya and Romania (0.8-0.9). 

Still, some will continue to cry foul.  Even economists will criticize me; some may say that instead of the per capita measure I should be calculating medal ranks relative to the country’s GDP, so to try and get an ‘efficiency’ ranking of sorts.  But this does not make sense, because of governance: it would be easy for Zimbabwe and North Korea to be ranked at the top of the medal totem pole (per unit of GDP), simply by misgoverning the country to such an extent that they run it to the ground.  Then the denominator (GDP) in the calculation virtually disappears, propelling them to the top of such ill-advised relative medal count ranking…

So we could stick with Jamaica atop, with Australia getting an honorable mention, in the per capita rankings.  And in giving top honors to Jamaica, we are erring on the safe side: if we would have allowed flexible weights given to gold, silver and bronze according to the actual difference in performance between the first, second and third best athletes, then Jamaica would win by a landslide -- thanks to the stunning gap between Bolt (and some of his Jamaican teammates) and all others!

Ok, in ending, some may still tell me: who cares about counting medals!  Indeed, this is an exercise in minor relativism, first, in order to move away from the medal rank obsession among huge powers.  And second, I am trying to insinuate that it may be futile to have a foolproof method of figuring out which country wins the medal count, even if we thought it was important to do so.  While the original context was not exactly the same, it is relevant to revisit the (Nobel Prize-winning) Arrow’s ‘Impossibility Theorem’ of well over 50 years ago, proving that there is no one superior way of rank ordering.  Arrow won then, Bolt won now.  The rest is relative.