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Wednesday, September 03, 2008

The Olympic Games Medals analysis

302 golds: The Olympic Medal table analysis

302 gold medals were handed out in Beijing. Add to that 303 silvers, and 353 bronze medals, and you get a total of 958 medals won during the 16-days of Olympic competition.

When you consider that 10,500 athletes were in Beijing, then it's actually quite interesting to calculate that on average, one in 11 athletes leaves the Games with a medal!

Of course, that's not necessarily true, for two reasons. The first is that there are many multiple medal winners, like Michael Phelps, who won 8 all by himself. I guess one might say that his achievements account for 77 people who suddenly fall out of the calculation pool! On the other hand, team medals are counted as one, even though 20 athletes might win one. So, a German hockey team consisting of 20 guys each has a medal, but it's reflected as a single medal, which might eventually cancel out the multiple-medal winners like Phelps, Bolt and co. So it's interesting to note just how many medals there are on offer, once you make it to the Games, of course!

Today's post is a look at where those medals went (not to individuals, but to nations), and to figure out just who the real Olympic champions are. China topped the medal table, by virtue of its 51 golds. That's 17% of the gold medals on offer. But then China has 20% of the world's population, so what does it mean? The USA top the charts in terms of TOTAL medals won (110 compared to China's 100). But they are also the wealthiest nation, so should that be expected? And how do we evaluate Jamaica, Kenya, Ethiopia - smaller countries, with limited resources, who stole the show in Beijing in specific areas? That's what this post is all about.

The Gold-rush: China's remarkable rise

As mentioned, China was always going to be a superpower once it invested in sport. With a population of 1.3 billion to choose from, finding 100 medallists would not seem a mission impossible. But making it happen is no mean feat. For one thing, not all those 1.3 billion are in the "selection pool", and massive talent ID is required to tease out those athletes, train them and prepare them for competition. And this is what China has done so well. An investigating into China's sporting system in 1994 revealed that they have 4000 Coaches at the elite level! In a sport like rowing, for example, they have 1,200 full-time rowers, divided into squads of 60 to 70. That's an amazing system, at a huge cost of course, but it's partly responsible for producing the success they achieved.

But there's something more to China's success - it is not simply a numbers game. Take a look at the following table showing China's medal hauls at the last 3 Games:

Two things jump out:

First of all, China's ascent to the top of the charts has been achieved entirely by winning more GOLD medals. Their silver and bronze medal haul has remained unchanged since 2000. But they've almost doubled the number of golds.

Second, when you sum up the last 3 Games, China wins more golds than it does silvers and bronzes COMBINED! That's quite extra-ordinary, given the number of medals won. In terms of pure statistics, you'd expect some kind of "normal" distribution of golds-silvers and bronzes. The table and graph below shows the USA and Australia's returns, compared to the Chinese:

So it's quite clear that the Chinese have figured out how to get straight to the top, win the Gold, and not win any silvers or bronzes! Of course, home-ground advantage might be a factor, because an athlete in contention may find that extra 2% that pushes them from second or third into first.

But I suspect there's more to it than this. It's still a vague idea in my own mind, but I think this is an indication of massive investment into specific events. There is no half-measure, no stone unturned. The Chinese identify their potential medal winner and invest so heavily in that person or team that they become a clear favourite. That kind of targeted approach produces people with clear gold medal chances, and is testament to massive investment in individuals. Second or third are not options, given the preparation that must go into creating a vastly superior athlete. That's the only reason I can think of - the target is set, to win gold, and then they hit it. Pretty simple in principle, obviously very difficult in practice.

The underdogs: The small nations have their say

One of the more interesting means to analyse Olympic success is to convert the medals into a population per medal value. That is, compare the medals won PER PERSON, rather than an absolute number. This gives the "minnows" a chance to shine, because it's quite clear that unless something is very wrong, a nation of 200 million SHOULD win more medals than a nation of 200,000! So let's have a look at medals won as a function of the nation's population (note: the population figures are up for debate, I suppose, but this is not a census, it's just to make a point, so they're accurate enough!)

The Bahamas, then, are the undisputed champions of population per medal. They regularly win 2 medals per Games, and with a tiny population, have a remarkable ratio. The USA and China suddenly fall off the top perch, and win only 1 medal per 2.7 million people or 13 million people, respectively. That places them outside the top 40 on the population adjusted table. South Africa, meanwhile, fare poorly in Beijing, thanks to the lonely silver we won. Previous Games were much better, and it's understandable why fans are so disappointed.

Australia are the best of the "big" nations. It can be a little misleading doing this analysis, because the relationship between medals and size is not necessarily a straight line. So the Aussies, thanks to their intelligent investment in sport, make the most of what they have and do incredibly well given their relatively small size.

Just a note on this table - strictly speaking, one should try to "weight" the medals by awarding three points to gold, two to silver and one to bronze, and then work out a score. If you do this, then Jamaica come out on top, ahead of the Bahamas, courtesy their sprint domination and 6 gold medals in Beijing.

The source of big returns for small numbers?

So, to generalize slightly, the Caribbean islands tend to dominate this list. They are small, and yet regularly win a handful of medals, mostly in the sprint events (in Beijing, both the Bahamas and Jamaica won all their events in athletics). That is testament to the genetic potential of the atheltes in those countries. That's a debate that was had in the comments section of one our recent posts, and it's worth discussing again in the future - the genes for speed.

But for today, we'll stick to management-related issues. I believe the key to making the most of this genetic potential (which I'll assume exists, though I appreciate that it's not clear-cut) is to facilitate competition with a focus on specific sports. Your emails have informed us that the school athletics system in the Caribbean islands is enormously strong, and this is the big driver of these medals.

Add to this a culture of the sport (which is why the school system is so strong), plus the existence of "aspirational heroes and role models", and you have a mix that will ensure that talent comes through, despite relatively small investment and a small population. If anything, the smaller population helps the athlete come through. Lastly, the focus is not too broad - there is no swimming team, no fencing, no table-tennis to detract from limited resources. The eggs are placed in the basket that will produce results, and that means a much simpler system to run.

There is of course much more to it than this, but the post is running away with me now! So to spare some of your reading time, I'll cut the discussion on the "minnows" short, and also say that we'll pick up the Olympic Medal Analysis in a second post tomorrow. There, we'll discuss medals won per dollar GDP, and figure out which countries get the best returns given their financial resources. We'll also dissect the big failures (South Africa, mostly, since I'm here and biased that way!)

Join us then!


Jasper said...

FYI: http://crookedtimber.org/2008/09/02/best-sporting-nation/

Anonymous said...

Can you do a similar analysis if medals are counted by the total number of athletes receiving medals, not by the number of sports for which medals are handed out. Football (US soccer) teams have around 18 athletes, basketball around 10 and so on. Team sports are given short shrift in the per sport, or more accurately, per event, counts.

Clearly, no one count of medals will be the perfect count, but I think weighting medals by the size of the teams would be interesting.

Anonymous said...

Chess is another activity targeted by China's leadership, and an increasing number of Chinese (male and female) Grandmasters feature near the top of the FIDE rating list. But a visitor to China will find no (western) chess clubs anywhere.

What is the value of these medals and records (chess, rowing, whatever) that are so unrepresentative of the popularity of the sport in question? To put it another way, it's not just the distribution of China's medals that's not normal, it's the distribution of their participants - either world-beaters, or non-existent. Doesn't that seem a little ... off?

Anonymous said...

Considering top sporting nations, population, expenditure etc, another way might be to include an algorithm that looked at the *spread* of medals over different sports. That would reduce the significance of the West Indian medal count.
It pretty much all points one way though . . .

Anonymous said...

Your use of the ratio population:medals is unfortunately flawed. The easy way to see this is to look at the upper boundary condition. I'll stick to round numbers to keep it simple.

If China won every medal the minimum achievable ratio is 1,300,000. For the US it's 300,000. Yet for Australia it's 19,000!

The problem is that the medal count is fixed while population is variable. Small countries have an unfair advantage with your metric, though with a large variance.

Unknown said...

Regarding the relative weighting of medals, have you seen this Hasse diagram of the 2008 Olympic medal table?

Anonymous said...

Do you think it would be interesting to check the relationship between the number of athletes per country sent and how many medals won? I mean, china had (correct me if im wrong) like 300 athletes and won 100 medals. South africa sent 110 athletes and won 1 medal....

Anonymous said...

I'd like to follow up on my comment last night (I was tired and stopped at criticism rather than offer a solution).

A better measure is to allocate the (fixed) medal pool to each country in proportion to its fraction of total population. Let's call the total population for the summer games 6.6 billion, since pretty much everyone participates in some way.

Now we can establish expected values of medal counts were all countries equal in their results, again keeping numbers very much rounded. For China it's about 200, for USA it's 45, and for Australia it's 3. Comparing deviations from this expected value may help you show what you want.

Keep in mind there are still problems with such a simple scheme. Some examples are:
- Large countries have less 'room' to excel to the upside.
- One or more large countries that have a heavy medal haul cause other countries to deviate to the down side.
- Small countries suffer a quantization effect. Norway, for example, with an expected medal count of 0.7 needs to exceed by 50% to reach 1 medal and by 200% to reach 2 medals.

Well, there are lots of other difficulties. For example:
- Is a 4th place worth nothing? Medals are an incomplete measure of performance.
- One super-athlete (like Phelps) depresses the performance measure of other countries.

I suppose that's why they offer PhD's in statistics. Still, you can most likely still get a lot out of even a simple analysis like the one I suggest above.

Anonymous said...

how is it possible that there were more silver and bronze than gold?

Anonymous said...

In the combat sports (judo, twaekondo, boxing, wrestling) there are 2 bronze medals for every gold - Perhaps the reason for the "extra" silver medal was that a 2nd place in an event was split?

Dr. Stephen Seiler said...

The Olympic medal count analysis is a standard quadrennial exercise that is both fun and flawed. We just have to accept that. We have to remember that there is a major saturation effect in play here; you cannot send more than perhaps 1-4 athletes in each discipline (varies a bit), so the advantage of large population carries only up to a point. Being an American living in Norway, I would argue that the greatest advantage of the American system is school and university sport. This is a stable driving force, independent of surges in national funding often associated with becomeing a host nation. USA has taken 36 gold in each of the last 3 Olympics for example. The host nation effect for the US was tiny compared to other recent hosts. Australia has built up a fantastic top sport program by combining some school sport with a very strong national talent development program. Norwegian success is built up completely around the club system and a national development program. There is zero school sport here.
Cuba remains impressive by being the tiny island nation that wins in numerous sports with extremely limited economic investment or physical infrastructure. And finally, GERMANY is the big loser in the medal race. This one time sports super power has shown a linear decline in golds and total medals since 1992 when they first competed as a unified team.

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Anonymous said...

Hi Ross

How many medals would the former USSR have won?

If the former Soviet Union did not break up, it would have dominated the medal count in the 2008 Beijing Olympics.

As of 2008, there are 15 countries that were once part of the former Soviet Union. The USSR was an Olympics powerhouse frequently winning more medals than any other country.

In the 2008 Olympics in Beijing, the United States won the overall medal count with 110 total medals. China, however, won significantly more gold medals (51 vs. 36 for the U.S.). Russia came in a distant third with 72 total medals.

If the USSR did not shatter into 15 different countries in the early 1990s, their medal count in Beijing would be staggering. As you can see in the chart below, the countries that made up the former Soviet Union won an amazing 171 medals. They did not win more gold medals than China, but their total medal haul was nearly 50% more than the next-place finisher — the United States!


Food for thought!

Maybe South Africa should split up into provinces.