Olympic Medals vs. GDP: An Intriguing Inspection – RantAWeek
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Olympic Medals vs. GDP: An Intriguing Inspection

4 Comments
Posted by Tyler Miksanek on August 12, 2012 at 2:47 pm

The size of a nation’s economy naturally affects how well that country will do in the Olympics.  After all, larger and richer nations should generally be able to field bigger and stronger teams.  This explains why, as the world’s largest economy, the United States was able to win the most medals.  Second in the medal standings was China, the world’s second largest economy.

To truly analyze how well a country preformed in the Olympics, it is thus necessary to examine its medal count relative to the size of its economy.  Determining the size of a nation’s economy is simple: this analysis used 2011 estimates of gross domestic product from the CIA World Factbook¹.  Examining the medal count, however, forces a decision on how to weigh the differences between gold, silver and bronze.

It is fairly safe to say that all Olympic medals should not be counted equally.  Winning a gold carries more prestige than a silver, and silver carries more prestige than a bronze.  But how should we measure this?

Upon noticing that the United States Olympic Committee pays athletes $25,000 for a gold, $15,000 for a silver and $10,000 for a bronze, I decided to use these payouts as a weighing system for the medals.  A bronze medal is then 1 ‘medal point’, a silver 1.5, and a gold will be worth 2.5.  (It should be noted that Russia also awards payouts at similar ratios, another reason this weighing was chosen.)

Here are the results: calculated medal points vs. GDP for economies larger than $1 trillion.

 

Notice that even though the United States and China have the most medal points, their results are nothing special due to the extreme size of their economies.  The United States, in fact, is actually below the line of best fit.  More impressive are the feats of Russia and the United Kingdom.  Despite their much smaller economies, they are able to post impressive numbers of medal points.  On the other hand, even though Brazil and India are rapidly developing economies, their medal points are unimpressive, and they fall well under the line of best fit.

The three unlabeled countries above the line of best fit are France, Italy and South Korea, who join already labeled Germany as nations that slightly over-performed.  The six unlabeled (and thus under-performing) countries underneath the line are Mexico, Spain, Indonesia, Canada, Turkey and Iran.  Most surprising is Indonesia.  Even with one of the largest economies in the world, Indonesia only managed to win one silver and one bronze, worth a mere 2.5 medal points.  However, this can be explained by noticing that Indonesia only sent 22 athletes to the Olympics.  When compared to other nations of similar economic clout, Indonesia chose to send a tiny representation.

The case of Indonesia demonstrates that factors other than GDP affect Olympic results.  After all, some countries simply choose to become more competitive than others.  As the host nation, the U.K. was more driven towards success.  Thus, they significantly outperformed most of their peers.

Take this data with a grain of salt, as GDP is not alone in predicting Olympic success or failure.  However, also consider this data to be a new alternative to the more traditional and basic medal count.  After all, when it comes to the Olympics, athletics are important, but money plays a crucial role as well.

 

1 – CIA World Factbook – https://www.cia.gov/library/publications/the-world-factbook/fields/2001.html

(A note – these GDP estimates incorporate Purchasing Power Parity)

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4 Comments

  • On August 13, 2012 at 2:23 pm Adam Erickson said

    Interesting work, my friend. Hans Rosling (http://tinyurl.com/99rnmm) would be very proud.

    However, I have some inquiries. First, in order to avoid a non sequitur, why exactly do you think that larger economies would produce a better faring in the Olympics? It may seem like a silly question, but its important to understand what types of assumptions you are making before you look at this data. Will larger economies pay for better training equipment? Provide more incentives for athletes to chose a certain sport/career? In general, just have more people to select a team from? China and the US happen to have won the most medals, and they also happen to have the largest economies, but I think that they are outliers in several other fields that aren’t accounted for here. I’m not saying that you assume causaul elements from correlation, but at times you flirt with it. That being said, money does make the world go round and it probably does play a major role in producing successful olympic teams. What that role is specifically, though, would be an interesting topic to explore.

    I would argue that culture is more important at producing successful olympic teams. That is what influenced the UK, what seems to influence China, and is the only explanation I can see for Russian success.

    I’m also trying to understand why you chose a line of best fit for this data in order to compare. It is true that since this line has constant slope it compares the countries in a relative manner, but I think that y=x (adjusted for units of dollars vs. medal points, of course) would have been a suitable solution as well. I have one main reason for this. You use the line to say how impressive [or not] China and the US are in terms of their medals and economy, but without them the line wouldn’t exist in the first place. They are clearly “influential observations”, both in the X and Y direction, and should be treated as outliers. In fact, the line would be nearly vertical if you looked at the other countries without the US and China. So, I think you got lucky that these two superpowers flattened the slope of the line. All that being said, medal points are arbitrary and the exact line you use is arbitrary as well, as long as it has constant slope. I just don’t seem much evidence of a trend here to predict any type of best fit.

    I have to commend your medal point system. The “weights” in such an inner product space are arbitrary, but I think you found a very good solution based on judgement of larger organizations.

    You ought to do more of these.

    Reply

    • On August 13, 2012 at 5:27 pm Tyler Miksanek said

      As far as why larger economies do better at the Olympics, the assumption is that they should be able to draw from greater resources. Resources here can mean equipment, trainers and of course the athletes themselves. The culture point you make is also a good one, and I tried to bring this up at the end of the article, especially with my rationale for Indonesia’s performance.

      I understand that you may view China and the U.S. as mathematical outliers, and I will concede that the sheer size of their economies concerned me as well. However, since China and the U.S., through both their size and competitiveness, influence the level of competition for the rest of the world, I figured it would only be accurate to let them influence the trendline here as well. It should also be noted that the removal of China and the U.S. does not steepen the line, it actually lowers the slope from 11.2 medal points/trillion dollars to 8.4. And yes, the trend of my graph is far from perfect (R^2= .607), but for an admittedly simple fitting, R^2 is surprisingly high.

      – And yes, I ought to do more of these. Don’t worry, I plan on it!

      Reply

      • On August 14, 2012 at 5:26 pm Adam Erickson said

        Lowers the slope? Really? I wonder what kind of software you are using – I assume you are fitting a Least Squares Regression Line? I understand India’s poor performance has a flattening effect, but I wouldn’t guess that it would overcome Russian and the UK. Then again, I’m sure computers know how to fit the data properly better than I.

        As for the line itself – US and China would serve to make it fail as a predictive model. You never said that that was your goal, but if you were given a country with known [predicted] GDP and you wanted to know a good amount of medal points, then China and the US would serve to change that prediction greatly. This does seem fair in some respects, because those two large countries take away medals so that others can’t win them, but that also points out another difficulty with using a line – it assumes a continuous distribution over the interval, when in fact [medal points] is a finite, discrete set. We could go on like this . . . but it lost all practical importance a while back haha.

        So in other words, I was critiquing a use that you may not have intended. As far as comparative I think that your line has a slope close enough to 1 that it all works out. It all may be arbitrary in the end, anyways.

        Reply

        • On August 14, 2012 at 5:58 pm Tyler Miksanek said

          The line is simply Microsoft Excel’s linear regression.

          Yes, you are right in pointing out that the largest issue with this data is the lack of a continuous distribution. However, due to widely varying GDP sizes, it is near impossible to address this. As such, you are also right in saying that the fit works better for comparison than it does for a prediction. After all, the line of best fit has a y-intercept of ~19, and it would be near inconceivable to see a nation with a negligible economy win that many medals. Even North Korea, a nation with a devastated economy that tries very hard at the Olympics, only won 12 medal points. And North Korea is the exception, the rule is that most nations with micro-economies are lucky to even get a single medal. That being said, the line of best fit is only included here for a simple comparison, not a basis for future predictions.

          Reply

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