The Games are over, let the analysis begin.
We’ve had some fun with ranking countries’ performance at the London Olympics according to medals per million (medals per capita) or medals per 100 billion of Gross Domestic Product (see my tables below). As I predicted a few posts back, the medals per capita will be one by a country with very low population and few medals – Grenada is the winner here. It seems obvious when we think about it that a country with a population of just 100,000 (0.1 Million) may end up with a very high medals per million score if they win just 1 or 2 medals (even though that is still a difficult feat). What is not so easy to see is that countries with very high populations have a “limit” for their performance that is very much lower. With just ~900 medals on offer and a population of over 1340 million China’s possible maximum medals per million score is just 0.67 (compared with Grenada’s 9000). It is this breadth of this range of possible values that causes the bias in the ranking system.
I like to visualise data. The two graphs below show the bias for the “Official Rankings” (you know, the ones that rank according to number of golds first, silvers second and bronzes third) and for the medals per capita. The bias is obvious because the points on the graph are not scattered without any discernible pattern all over the graphs. The “Official Rankings” obviously are biased towards countries with greater populations, the Medals per capita is biased towards countries with lesser populations. Obviously, dividing by population does not remove the bias, merely shifts the bias. Note, that the scales on the “y” axis are what we call “log scales”. This enables us to see all the data more easily (ie countries with 100,000 and 1.3 billion can be displayed on one graph). What is not shown on the graph is the 122 countries ranked 80th equal who won no medals at all.
Later this week, once I am happy with my grant writing and get my head around some data I am trying to analyse I shall attempt to put together an equation which will better help us answer the important question of the day – “Which is the greatest olympic nation?”
Top graph: The Official Rankings verse Population (note the log scale).
Bottom graph: The Ranking of number of medals won per million population v population
As expected, a country with a small population has grabbed the top medal position when Grenada (population, 104,000) grabbed a gold. WIth a medals per million score of 9.6 they are only likely to be beaten by a country with even smaller population. Meanwhile, Jamaica has moved into 5th position with 5 medals, all in athletics. If this was health stats, then these two situations would be examples of “outliers.” Worthy of study in and of themselves, but having a distorting influence on the overall population statistics. Also of interest is that perhaps Great Britain is reaching a plateau, meanwhile China continues to fall as sports they are not traditionally strong in dominate the second week of competition.
The weekend success of a New Zealand rowing pair put them in gold medal position on the medals per capita table. They have now sneaked ahead of Slovenia. Denmark are in bronze medal position with Australia solid in fourth. The big mover over the weekend was Great britain moving from 17th at the end of day 6 to 11th at the end of day 9.
Do richer countries perform better than poorer? Is sporting prowess more important to a country’s leaders than feeding their population? Or does this table reflect real sporting prowess. You be the judge. North Korea (DPR Korea) leads the medals per US$100 Billion of Gross Domestic Product (2010 figures from the UN statistics), Moldova and Mongolia are not far behind. New Zealand ranks 17, still well ahead of Australia, 31. Oh well.
Number of medals won per US$100 Billion of GDP by the end of day 9 in the London 2012 Olympics
On the seventh day they did rest – I think not. Aotearoa a land of couch potatoes – absolutely; sitting down wins medals! Super cyclists and outrageous rowers took New Zealand’s medal tally to six on the seventh day of the London Olympics. All medals have been won sitting down (and two-thirds of them going backwards). New Zealand has surged to silver position on the medals per capita table; now with more than one medal per million population. Only Slovenia is ahead with its 3 medals and a 1.48 Medals per million score.
But wait, here come the Aussies, jumping from 7th place to 4th place overnight as they also picked up 3 more medals.
In yesterday’s blog I raised the issue of outliers – little countries with one great athlete could do leap ahead. To be eligible for the medals per capita medals should countries win medals in more than one discipline (say 3)? Should there be a minimum number of athletes who win medals (say 3)? How do we deal with outliers – give me your ideas. Also, don’t forget to tell me if you want your country represented on the graphs.
Medals per capita – day 7, London 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