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Sunday, August 12, 2012

Canadian Medal Count: Not Bad

Every summer Olympics, some Canadians despair at our low medal count: not only do all more populous developed countries (except for Spain, who can console itself with its soccer team) beat us hands down, but Australia, with just 2/3 of our population, does so too. Certainly, the COC's objective of a Top 12 finish at summer games has once again been missed - Canada was 13th by total medals, two shy of the Netherlands and Ukraine. However, the obvious explanation for this is that much of our athletic talent is involved with winter sports, so one should take the winter Olympics into account before despairing.

(We should also note that with 18 medals, Canada ties its best performance at summer games conducted outside the US, albeit with less gold than in Barcelona or Beijing.)

Are summer and winter medals comparable? I think so. While fewer countries contest winter sports, there are also many fewer medals available at the winter Olympics: just 86 events in Vancouver versus 302 in London. The ratio is probably roughly right.

Here's a list of countries with at least 10 medals total from Vancouver and London (ties are broken by the number of gold, then silver) [updated to account for the doping incident in women's shot put]:
1. USA 141
2. CHN 99
3. RUS 97
4. GER 74
5. GBR 66
6. FRA 45
7. CAN 44
8. JPN 43
9. KOR 42
10. AUS 38
11. ITA 33
12. NED 28
13. NOR 27
14. UKR 20 (all summer)
15. SWE 19
16. HUN 17 (all summer)
17. ESP 17 (all summer)
18. BRA 17 (all summer)
19. CZE 16
20. AUT 16 (all winter!)
21. POL 16
22. BLR 15
23. KAZ 14
24. CUB 14 (all summer)
25. SUI 13
26. NZL 13 (all summer)
27. IRI 12 (all summer)
28. JAM 12 (all summer)
29. KEN 11 (all summer)
30. AZE 10 (all summer)

As you can see, Canada, in fact, does quite well, drawing level with much more populous countries like Japan and France, and handily beating Italy and Spain. And this is not a host country effect: Canada won only two more medals in Vancouver than in Turin. (Britain, however, increased its medal count by 18 between Beijing and London.) The only countries that are well ahead of Canada are the US, China, Russia, Germany and Britain. The first four all have more than twice Canada's population, while Britain is over 80% more populous and would likely have a much smaller lead had it not been the host country this year.

We also notice that there's a clear Top 13: the G8 countries, China, Korea, Australia, the Netherlands and Norway, who is 118th by population... (If only it produced as high quality soccer referees as athletes!)

One might be tempted to look at population per medal in order to establish a "fair" comparison. However, this ignores the fact that the number of entries into the competition is far from proportional to population: in most team sports, only one entry per country is allowed, and even in most individual sports, the limit is one, two or three. As a result, you just can't expect the US to win 9 times as many medals as Canada.

Then of course, there's the issue of each country's resources. Obviously, given similar populations, rich countries will have a much easier time than poor ones. Witness hapless India, with just 6 medals despite having more than 1/6 of the world's population. Pakistan, Nigeria and Bangladesh, the world's 6th, 7th and 8th most populous countries with over 150 million people each, have no medals at all!

A better way of looking at this data might be to plot the number of medals against total GDP. You wouldn't be looking for a straight line, but rather a concave curve, due to the lack of proportionality of competitive entries to population. And what to put on the GDP axis is not clear. First, it should likely be some mix of GDP at market prices and GDP at purchasing power parity (PPP, which adjusts for differing price levels between countries): a top-level athlete's consumption basket has a significant international component, so going by PPP alone would be misleading. Second, it should exclude "subsistence" GDP - something between the $1.25/day = $457/year/person poverty line used by the UN and $1,000/year/person, which is roughly the number for Afghanistan, the poorest country to win a medal in London (both figures PPP). Somebody should do this - looking at the various news outlets, many people have been paid for doing much less...

If we look only at rich countries, though, plotting medals against population works pretty well, since almost everyone's GDP PPP per capita is between $25,000 and $50,000. (It's still true that you'd want to fit a concave curve rather than a line.) Now, I'm feeling lazy, but just looking at the numbers, Norway and Australia would, unsurprisingly, be the big overachievers, while Japan, Italy and Spain would be the worst underachievers. Canada would likely lie above the fitted curve.

In terms of gold, however, the story might be different for Canada. Of course, in this cycle, thanks to the gold explosion in Vancouver, Canada has 15 gold medals out of 44. But usually, gold accounts for much less than one third of Canadian medals (3 in the summer and 7 in the winter is normal).

So, given the concentration of Canadian athletic resources in winter sports, our athletes' performance at the London games is right about what you'd expect - a bit better in terms of total medals, though a bit worse in terms of gold.

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