Even more alternative medal comparisons
As a former Australian, I need to point out that the natural denominator for comparisons between Aus and NZ should include sheep as well as people.
On this metric, Australia has one medal per 4.5 million population, and one gold medal per 50 million population. New Zealand has one medal per 4.4 million population, and one gold medal per 11.8 million population.
Looks like New Zealand is still ahead, even if you include sheep in the population. On the other hand, Jamaica leaves us both in the dust.
Thomas Lumley (@tslumley) is Professor of Biostatistics at the University of Auckland. His research interests include semiparametric models, survey sampling, statistical computing, foundations of statistics, and whatever methodological problems his medical collaborators come up with. He also blogs at Biased and Inefficient See all posts by Thomas Lumley »
Assuming olympic ability is randomly distributed among the 7 billion in the world is the expected number of gold medals linearly proportional to country population size?
It might be. The probability that the best in the world comes from a given country is proportional to that country’s population.
But in practice it may not be. Countries can send more than one athlete to the games and each athlete performs with a bit of noise in their performance. I think this gives small countries an edge because large countries can’t send as many competitors as they would like.
Eg NZ sent 26 rowers to London, on this basis China should have sent 7000 rowers. With that many rowers enough would have got luckier than they deserved to clean up the medals.
So what’s a fair way to judge medals on a population basis?
12 years ago
If China sent 7000 rowers it’s unlikely they would have got any extra medals. The ones they sent were their best and as it is speed and endurance and technique based they would be well off the cracking pace set by the best in the world.
If they sent 7000 shooters or archers then the chances are better as they could have a few who with a combination of skill and luck hit near the bullseye and had ‘their day’ so to speak.
12 years ago
I’ve been thinking about this — it’s more complicated.
A more plausible model would be that some relevant ‘ability’ has a distribution over the population, say a Normal distribution, and that the probability of winning depends on differences in scores. That’s the approach David Scott uses for rugby forecasting, and it’s what underlies chess ratings.
If this unmeasured variable has any standard distribution, the maximum score over a population increases quite slowly with population size, so you’d expect number of top athletes to increase more slowly than linearly with population.
On the other hand, as you say, bigger countries can send more people.
It’s also hard to tell what the effective population size is for this purpose (that’s the semi-serious point about the sheep). The proportion of people who could follow a career in sports and for whom it’s financially attractive also vary.
12 years ago
Umm. I meant “you wouldn’t expect number of top athletes to increase much faster than linearly”
12 years ago
A recent episode of the BBC R4 programme More or Less covered this (http://www.bbc.co.uk/programmes/b01l1g64).
They came to a model which includes population size, GDP and “culture”.
Generally the number of medals goes up with populations and over/under achievers are mostly explained with GDP.
Culture is a fudge factor which helps the model with historical happenstance. The example given is India versus South Korea: India’s national sport is cricket, which has no representation, whereas South Korea’s is Taekwondo with up to 8 medals
12 years ago
And we can complicate the model even more, assuming that different sports require different relevant abilities, with countries participating with different sport bundles. Often the smaller the country, the smaller the bundle.
12 years ago
I’ve been following this thread with interest, because when I first heard about the alternative medals table, it struck me that the metric (i.e., number of medals per 10^6 people) is biased against countries with large populations, as follows.
There are 302 events in the 2012 Olympics, which means that there are 906 medals up for grabs. So consider an extreme example. Slovenia has a population of 2 million people. It has one gold. For China to rise above Slovenia on the table, it will need to win >600 golds, which is impossible. The situation becomes a little less biased when you take medal totals, but I believe that the bias remains.
There is an additional bias, as well. Suppose we try to rectify this by simply working out the expected number of gold (or total) medals that a country can win, by taking the total available (i.e., 302 for gold, 906 for total), dividing by 7 billion, and then multiplying by the population size of each country. This gives us the expected number of medals based simply on population size.
If you do this, then Slovenia ends up with ~0.1 gold medal and ~0.3 total. But herein lies another problem. Slovenia actually gets 1 gold medal. Does this mean that Slovenia has performed 10 times better than other countries? It seems to me that the answer is no, because if Slovenia is to get a gold medal it can only get an integer number. Of course, it could be argued that it could have got no gold medal. This is correct, and the way I think about it is this: of all the countries with expected number of gold medals less than 1, some are going to get golds (under the null hypothesis, we could model this using the Poisson, for instance). Therefore, it would be unfair to say that Slovenia has performed 10 times better than other countries.
How do we deal with this type of bias? I am not sure. I have my own ideas, including setting the expected number of medals max[1, expected number]. But I admit this is not a great solution.
12 years ago
Another thing to factor in is that nations with large populations only get to enter one team or one participant in many events whereas a small country can enter one team and one participant as well.
There are some exceptions like how Jamaica can enter 3 sprinters into an event and win all 3 medals but in a sport like rowing each country can enter only one participant so we can’t have say Mahe Drysdale and Rob Waddell both going for gold. I’m trying to think of occasions when we have won multiple medals in the same event and the Triathlon 8 years ago is one when we got gold and silver. Before that though it’s a long way back to our runners doing it.
12 years ago
The New York Times has a nice diagram pointing out different rankings for countries. There is a handy ‘adjust for population’ tick box, which shows Grenada is winning by far.
12 years ago