The London Olympics are over, what a success they have been. Many Australians however are pondering the performance of our athletes, as we only placed 10th.
Only placed 10th?? By whose count?
The current rankings, which are published by most of the international media, rank countries by order of Gold medals won. How can this be at all sensible or fair, since it ignores silver and bronze medals entirely? If you are going to give out prizes, those prizes ought to be worth something.
There is another popular ranking system which we also see; which tallies the total number of medals won. This is also patently simplistic. Why should a bronze count as much as a gold?
The uncritical acceptance of these two simple-minded scoring systems around the world reflects an astonishing mathematical naivety. Surely we can do better in the 21st century! For a country like Britain to put on such a complex, dazzling show is inconsistent with its media performing just a cursory back-of-the-envelope calculation to determine rankings.
More than a hundred years ago, a fairer ranking system whose proposed by the English press: each gold is worth 5, each silver is worth 3 and each bronze is worth 1. So using a little bit of multiplication and addition, we get a much clearer and more equitable picture of how different countries performed—in total. Of course one can argue about the weightings, but I personally think these are quite sensible.
With such a weighted ranking system, all medal winners contribute to their countries standing, but on a scale that is reflective of the different levels of achievement. If we had adopted this, silver and bronze medallists would be happier knowing that their win has contributed to the national account, and we would see fewer dejected athletes having just placed second or third in the world!
My calculations of the Weighted Ranks for the London Olympics are available at http://www.maths.unsw.edu.au/news/2012-08/weighted-olympic-rankings-london-2012-n-j-wildberger. Australia places 8th, not 10th; while Great Britain gets beaten into third place by Russia—perhaps this is the reason the British press don’t promote this fairer system this year!;— Spain goes from 21st to 14th, and Canada goes from 35th place to 22nd.
Congratulations to all our athletes for their excellent 8th place in a highly competitive meet. Let’s hope that the Olympics Committee can consider instituting this weighted ranking system as the gold standard for Rio, or that at least the international press can think about adopting it. A little mathematics can go a long way!