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Monday, March 1, 2010

Not All Medals Are Created Equal

I can't resist a quick post about the Olympics!

Much has been said about the US setting a new Winter Olympics medal record (37), and Canada setting a new Winter Olympics gold medal record (14). But what would the medal count look like if we weighted each medal according to some measure of significance?

Obviously, what's significant for a country may not be for another. Even then, I'm pretty sure even Koreans would agree that hockey medals mean more than speedskating ones. I used the following simple formula for determining the weight of each medal, and I think it produces intuitive results:

Square root of number of athletes on a team, rounded to the nearest integer
+1 if the event is the only Olympic event for (almost) every athlete competing in it
+1 if the event features a weeklong tournament

For example, hockey medals are worth 5+1+1=7, curling medals are worth 2+1+1=4, while 33 other medals are worth 2 and the remaining 49 are worth 1. This produces the following weighting of sports:

Cross-country 14
Hockey 14
Speedskating 14
Biathlon 12
Freestyle Skiing 12
Snowboard 12
Alpine Skiing 10
Short Track 10
Curling 8
Figure Skating 8
Luge 6
Bobsleigh 5
Nordic Combined 4
Skeleton 4
Ski Jumping 4

Freestyle and snowboard appear overweighted at first glance. But I would argue that each of these "sports" is actually 3 sports: for example, ski cross and aerials are just as far apart as alpine skiing and cross-country, and more so than the two kinds of speedskating.

The total weight for the 86 events is 137 (69 for ice sports and 68 for snow sports), so I then multiply by 86/137 and round to the nearest integer to produce the adjusted medal count.

Top 10 Countries by Weighted Medals (actual in parentheses)
USA 42 (37)
CAN 37 (26)
GER 27 (30)
NOR 20 (23)
AUT 14 (16)
RUS 13 (15)
CHN 13 (11)
FIN 12 (5)
FRA 10 (11)
SWE 10 (11)
Canada and Finland are the big winners. The US gains as well, while all other countries lose out, but only slightly.

Top 12 Countries by Weighted Gold Medals (actual in parentheses)
CAN 24 (14)
USA 9 (9)
GER 8 (10)
NOR 7 (9)
SWE 6 (5)
KOR 4 (6)
SUI 4 (6)
CHN 4 (5)
AUT 4 (4)
NED 3 (4)
RUS 3 (3)
AUS 3 (2)
O Canada! Even if I had weighted the hockey and curling medals at 2 instead of 7 and 4, Canada's normalized gold total would still be 18. That's right - not only did Canada win the most medals ever, but it tended to win them in team events and in events where athletes did not have multiple chances. The latter means that to get to 14, Canada couldn't rely on a handful of sports that happen to have lots of events: amazingly, despite the huge overall total, Canada did not win more than 2 gold medals in any sport, and no Canadian athlete got more than 2 medals of any colour. Canada is also the only country to have won gold in a majority of the 15 sports (9).

So, in summary: once you apply some kind of sensible weighting scheme to events, the Canadian performance at the Games is even more impressive!


CanadianSense said...

Gold Medal winners are the only ones really remembered.

Can we remember the silver medal winners behind Mark Spitz?

From Zero to 14 on home soil is unmatched on homsoil by any winter olmpic super power.

Norway, US, Germany have always done well. Only Norway has a smaller population but they have always done better than us.

We owned the podium in 2010.

Election Watcher said...

Well, Joannie Rochette's bronze will probably be remembered more than most golds. But of course, you're right, with the caveats that other medals are remembered:

1. when there's a compelling story;
2. when they're won by an athlete that also won many other medals;
3. when they have historical significance (e.g. if we had won our first ever medal in men's cross-country skiing);
4. when they're in hockey (remembered as disappointment).

I might add that 14 gold in the Winter Games is unmatched, period, home soil or not.

Norway's performance is amazing Games after Games, but I'll point out that 8 of their 9 golds came in cross-country and biathlon. It also helps that they get so much oil money that the government has saved a year's worth of GDP...

But isn't it oh so Canadian that our media rank us 3rd, while everyone outside of North America ranks us 1st? I'll point out that Radio-Canada used to rank by gold, but switched to total medals this time because of the COC objective and because Canada has historically done better by the latter metric...