# Which is really the best performed Olympic country?

By John Pickering 03/08/2012

Over at Statistics New Zealand the folks have done a great job in producing an alternative medals table for the London Olympics.  They are showing the number of medals won per million population.  They have kindly shared some of the data with me (thanks people) so that I can produce a few graphs and tables of my own. First a message to TVNZ and TV 3 and PRIME TV:

### It is really, really, REALLY, boring to have presented a table of which country has the most medals every night.  It is almost as boring as those worthless tables of currencies and stocks you also insist on presenting for your sponsors.

Now, I have that off my chest, let’s have a look at what is going on…If you’ve had a look at the alternative medal table you will see that today, end of day 6, New Zealand is third on the table with a 0.69 medals per million population (i.e. 3 medals divided by 3.7 Million people). It is apparent to any unbiased observer that the number of medals per million is a much better indicator of sporting prowess than raw numbers of medals.  It is, though, subject to a few anomalies which I hope to point out over the next week or so.

In the meantime I’ve produced two graphs to demonstrate what is happening day by day.  I shall update these a couple of times over the rest of the Olympics.   The first shows the number of medals per million for New Zealand, Australia, China, Great Britain, and USA.  New Zealand started slowly and is accelerating nicely.  The second graph is perhaps more interesting as it shows the ranking in terms of numbers of medals per head of population.  At present Slovenia with 1 medal and a population of a little over a million has the number one ranking and a medals per million score of 0.99.  A couple more medals and New Zealand may pass this.  Of course, if a country with a very low population, say  Nauru, were to win just one medal then their score would be about 100!  This is take home lesson #1.  Look at all the numbers and look out for outliers. Would this make Nauru the country with the greatest sporting prowess?  No.  We would need to look at historical data over many olympics to be certain of that.  Another aspect of the second graph is that it shows how some country’s ranking is trending up and down.  This is influenced by their daily performance, but also by other countries entering the table.  What should be expected as each day goes on that each country will trend towards their final ranking – perhaps bouncing around above and below it (especially if they are “mid table”).  This idea is sometimes called “regression to the mean” and it is very important in statistics because it tells us to be very cautious about putting too much emphasis on the first data we collect.  For example, if every doctor in the country starts collecting data on the number of meningitis cases they see each week. In the first week some may see none, others 1 or 2, but it is quite possible that one of them sees 4.  Could this be an epidemic in their area?  Well a wise doctor would continue to follow and see if there is a trend with the next week or two’s data before jumping to conclusions (although the “precautionary principal” may apply and health boards would be notified).

Have fun following the Olympics.  If you want your favorite country added to my graph – just ask.  In the meantime, check out Statistics NZ’s excellent presentation of the top 10 ranked countries each day.

Number of medals won at the London 2012 Olympics per million population day by day.

The rank (1=top) of the number of medals won per million of population at the London 2012 Olympics