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Tuesday, August 12, 2008

Beijing 2008: The cost of gold

What price for an Olympic Gold? How much would you pay?

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How much is an Olympic Gold medal worth?
I guess that depends who is answering the question...to an athlete, it's a lifetime of achievement, or perhaps endorsement deals worth millions, a lifetime of fame and contentment. If you're a national government like that of China, then every gold medal represents your "statement" of superiority to the world.

But can it be quantified financially? Is there a price tag associated with an Olympic medal? It turns out that while difficult to quantify, it can in fact be done in some cases. The graph below shows the number of medals won by Australia at the Olympic Games between 1980 and 1996, with a projection on the number of medals that would be won in 2000. The x-axis is the money spent in each four-year cycle leading up to the Games. This analysis was presented at an IOC Congress in the months leading up to the Sydney Games of 2000.

What you will see immediately is a nice, linear relationship between the number of medals won and the money spent during a four-year cycle between Olympic Games. The bronze medals lie on a slightly different 'line' to that of the gold and silver, but it's possible to work out, using the slope of the line, the approximate cost PER MEDAL. It turns out that each bronze medal will set you back a cool Aus $15 million, while gold and silver will cost you about Aus $40 million!

I must stress that this price is "context-specific", and depends on the nation and how that money is spent. Money can be wasted, or it can be invested wisely, and the return on spending depends on the system in which the money is spent. Some nations invest little and win a great deal, but it's because their resources and sporting structures are entirely different.

So this cost is the Australian-price. In Cuba, for example, Olympic medals cost a lot less, and if you reshuffle the Olympic Medal table, then Cuba tends to win the most medals per dollar (though this is expressed per $ GDP). Other countries that win "cheaper" Olympic medals include the Eastern Bloc nations, like Hungary, Bulgaria, Belarus. For the USA, it's almost impossible to quantify the cost, because there is no state-controlled spending on sport development during the four-year cycle - the system is "privatised".

But the point is, there is a relationship between money invested and medals won. If you want 20 gold medals, then spend Aus $800 million every four years. The graph above was used to project how many medals Australia would win in Sydney - the dashed line in the graph. It turns out it was pretty accurate, because as hosts, Australia won 16 GOLD, 25 SILVER and 17 BRONZE medals, for a total of 63 medals (projection was 14 GOLD, 14 SILVER and 35 BRONZE, a total of 58 medals). They exceeded themselves by winning more silvers than anticipated - home-town advantage perhaps?

What does this information mean? Well, it means that China, who have spared no expense in their question to be the dominant nation of the Olympics, are set for great things, not just in Beijing, but beyond. Anyone who saw the Opening Ceremony will recognize the investment by China into a "vision" of superiority and dominance. They reportedly had between 20,000 and 50,000 athletes in elite training camps leading into the Beijing Games. The cost associated with running these facilities, providing coaches and medical/scientific support is enormous. Yet it's been done, in the name of "super-power" status. China will therefore be able to produce a graph much the same as the one above, and it will be interesting to see just how the rest of the world responds to the onslaught by a nation of a billion people throwing massive money into sport.

As for my country, South Africa...well, let's just say that we would probably not even make it onto the graph above, both in terms of spending and medals won! I doubt whether we spend enough to win even one single medal in the Australian model. Luckily for us, we have a "back-up" plan, which sees our best swimmers leave South Africa to go to the USA and train there. That is our best shot for a medal. It is a sad state of affairs that in order to achieve success in SA sport, your best chance is to leave the country. But that is the reality. And for the simple reason that we fail to invest, either in people or financially, I would pick that we'll win 2 medals in Beijing.

But then you get what you pay for, even when it comes to Olympic medals...



Ashish M said...

Even more interesting than the input "cost" might be calculating the "value" of an Olympic medal, either to the individual recipient (lifetime income increase), or to the country (GDP increase).

I realize we're looking at correlation, not causation.

Anonymous said...

You mixed up your numbers - they won 58 and the projection was 63.

Anonymous said...

1) With every Olympics, more medals have been given out. How is this accounted for?

1980 - 631
1984 - 688
1988 - 739
1992 - 815
1996 - 842
2000 - 922

2) What happens if all countries increase their spending to $500 million or whatever? It is impossible for the medal count for each country to increase.

Anonymous said...

I think you would have to analyzye ratios of spending for this to be relevant. If all countries increased spending, but relative share remained constant, one might expect for medals to remain constant unless there were more to it. It would be neat to see what say $10,000 did in say Ethiopia vs what it does in China or the US...

What about the larger economy? If one must struggle to feed one's family, winning a heavweight boxing title is a bit unlikely. I like the fact that there is such diverse representation. It bodes well for the world.

Another thought is that of cross-over funding. US collegiate athletics are the driving force behind many small countries earning metals. Likewise, immigration to the US has brought many great athletes who should have been elsewhere. The water is muddy, and it makes the whole event more interesting, dramatic and personal.

tim said...

i know you guys didnt write this article...so excuse me when i post that i think it is ridiculous.
surely it's contextual reference is critical- perhaps is relative to the lease amount of money spent by any country to achieve a bronze medal?- or perhaps it's the most?...
from my perspective there's a number of variables which surely must be included in order to arrive at such a conclusion?- such as talent pool and total pool..and GDP surely has an impact (?).
i note that some have asked the question if each country spends more...then what. That answer would have to be that the cost of medals increases, as the base standard increases.

I wouldve thought that rather than a linear relationship, attaining gold would be logarithmic representing a virtual limit of infinite $ spent and still not achieving gold for some countries.

Ross Tucker and Jonathan Dugas said...

Hi Tim

No, you're quite right. And we did write the article, hopefully not too ridiculous. But I did emphasize this point in the article. I wrote the following paragraph in the post:

I must stress that this price is "context-specific", and depends on the nation and how that money is spent. Money can be wasted, or it can be invested wisely, and the return on spending depends on the system in which the money is spent. Some nations invest little and win a great deal, but it's because their resources and sporting structures are entirely different.

So I was very careful to emphasize that the context of the spending is crucial. That's why the gene pool (which are the human resources) are important.

As for what happens if every country starts to spend more, that's quite obvious - the cost goes up. This is nothing more than a supply and demand curve for economics. If the demand rises and the supply remains the same, then the cost per medal goes up. That's why the Beijing Games will skew the cost - China and Britain have spent much more than usual and the Australian model has been altered.

So you're right, but it's all accounted for in the model. and it remains linear, just like supply and demand - all that happens is that the curves jump up to reflect the increased demand.