Olympic Games – Small is not beautiful

Olympic-logoThe Olympic Games came to an end a little bit more than a week ago. Beyond the last-minute logistic annoyances, the United States showed the rest of the world that one more time they were dominant in the Olympic arena. Good surprise came from team GB, which benefited from years of investment and the partial ban of the Russian delegation to clinch the runner-up spot. On the other end of the rankings, almost 100 countries will fly back with no medal.

The question is what is the best predictor of a nation’s performance at the Olympics? First, we need to be clear about what we mean by ‘performance’. Limiting myself to countries which have managed to take a medal home, I have used the official medal table and I have allocated 5 points for a gold medal, 3 points for a silver medal and 1 point for a bronze medal – I could have used the gold medals only but this would have created an ‘edge effect’ as many countries have won no or very few gold medals. The official ranking (taking only gold medals into account) is largely preserved: only exceptions in the top 10 are France (with its famous ‘fear of winning’) and the Republic of Korea.

Points ranking according to our methodology.
Top 10 countries according to our methodology.

We can use a few macroeconomic indicators to assess whether they are correlated to the success of a given country. It is important to note here that a regression only enables us to conclude about the presence or absence of correlation and not about the presence of a causality effect. For instance, if we plot population on the X axis, we see that the bigger a country is, the more medals it tends to gather – with the notable exception of India, circled in red, whose poor performance has been largely documented throughout the event. So what we can conclude is that there is a correlation, but we cannot state that ‘a higher population leads to a higher number of medals’ (which is nonetheless probably true) or that ‘a higher number of medals leads to a higher population’ (if so we would have baby booms in the US every 4 years).

Regression log(population) (X) - log(points) (Y).
Regression log(population) (X) – log(points) (Y).

The Economist argues that the most significant driver is actually GDP. The correlation effect is also significant.

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Regression log(GDP) (X) – log(points) (Y).

What it means, interestingly, is that GDP per capita correlates poorly with the ultimate country performance – contrary to what the same Economist article may assert. The nominal sizes of the economy and of the population thus prevail. This is understandable: more money overall tends to mean more investment in infrastructures, training etc. However, we would need to dig further as wealth created is not evenly allocated to the development of sports in each country.

Log(GDP per capita) (X) - log(points) (Y)
Regression log(GDP per capita) (X) – log(points) (Y).

Goldman Sachs performed a forecasting exercise using its proprietary Growth Environment Score (GES), which captures “important features of the economic, political and institutional environment that affect productivity performance and growth across countries”. Simply said, Goldman Sachs uses a multi-variable correlation instead of relying on one macroeconomic driver as we have done so far. The algorithm grants extra points for the last two hosts (i.e. Brazil and the UK) to acknowledge the important investment and support of the crowd. The accuracy obtained is remarkable.

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Number of gold medals for top 10 countries: Goldman Sachs forecast vs. actual.

In its paper, Goldman Sachs states that “a country is more likely to produce world class athletes in a world class environment”. I took the statement seriously and checked for a correlation between the number of medals and the Human Development Index, which accounts for human well-being beyond economic considerations by including data on life expectancy and education, among other factors. A high correlation would be fantastic news: sports excellence would be a ‘by-product’ of the improvement in life standards. The result can be found below.

Regression HDI (X) - log(points) (Y)
Regression HDI (X) – log(points) (Y)

Although we could advocate for a slight correlation, the effect of human development remains limited compared with the one of money. This conclusion highlights a fact that is widely shared throughout the sporting world (including football, which we will deal with in a later post): human effort alone only returns sweat, but only with a wallet will it be worth its weight in gold.