Tokyo 2020

The United States topped the tables, both on count of gold medals (39) and total medals (113) at Tokyo 2020. China took the second place (38, 88). One is the richest country, the other is the most populous. Bigger countries, by population, or by GDP, or both, can be expected to win more medals than a smaller country. What if we refined the metrics to rationalize (normalize) for size? The mathematics for this is not too daunting.

Let the number of total medals won be M.  This is a measure of quantity of performance. Population, P or Gross Domestic Product, GDP are two possible measures of size. Then, medals per million of population, M/P, or medals per trillion dollars of GDP, M/GDP are two meaningful size-independent measures of performance at the Olympic Games. These indicators, M/P (medals per million of population) and M/GDP (medals per trillion US dollars of GDP) are “quality” measures of performance. From this, the numbers X(P) = M/P × M and  X(GDP) = M/GDP × M  become higher-order performance measures which change and challenge our understanding of how the participating countries have performed at Tokyo.

At Tokyo 2016 the number of countries that earned at least one medal was 93.  The remaining countries that took part drew a blank. We shall group these together as the Rest of the World. 

Table 1. On a medals per million of population basis, San Marino was the best performing country at Tokyo 2020.    

In Table 1, we see how some selected countries fared. On a medals per million of population basis, San Marino outperformed the rest.  As in 2012 and in 2016, India was now last, i.e. 93rd, among the 93 countries that earned at least one medal in 2020, with 7 medals for 1.38 billion people.

It is fairer to assess performance on a GDP basis than on a population basis; richer countries can be expected to dedicate greater resources to sports than poorer nations. Table 2 reports the performance on a nominal GDP basis. San Marino remained at the top even on this criterion. India has some consolation in that it is Saudi Arabia which takes the bottom most position. 

Table 2. On a medals per trillion US dollars basis, San Marino was the best performing country at Tokyo 2020.

In Tables 1 and 2, the indicators M/P (medals per million of population) and M/GDP (medals per trillion US dollars of GDP) are “quality” measures. The size measures in each case are P (millions of population) and GDP (in trillions of US dollars). The last columns in Tables 3 and 4 are these curious numbers X(P) = M/P × M and  X(GDP) = M/GDP × M. This second-order indicator is a product of a quality and a quantity term and perhaps best represents the “performance” of a country. San Marino continues right at the top. 

These results are different from the usual rankings that appear in the media. China occupies a middling position throughout. 

Table 3. Rankings using a second-order indicator X(P) based on a medals per million of population basis. San Marino remains at the top.

Table 4. Rankings using a second-order indicator X(GDP) based on a medals per trillion US dollars of GDP basis. San Marino continues at the top.