It is a classic excuse mostly heard by small(er) countries: Brazil (or USA, Spain, France – pick your favorite adversary) is a very big country and it is much easier to find 20 very good players in a population of 100 million that it is to find 20 equally good players in 10 million.
It is possible but is it likely?
Based on the data available at the CIA Factbook per country participating in the World Cup and the corresponding FIFA Rank the following bar graph can be created (with Excel 2007 and Adobe Photoshop Elements.)
It seems that population is not a significant factor. Two out of the top 5 countries have populations under 20 million and one of them (Portugal) is barely over 10 million. In the Top 20 there are 3 countries under 9 million (Switzerland, Serbia, Uruguay – though not expected to do very well) and one more country (Greece) that is listed as close to 11 million. Between 21 and 32 there are 6 more countries with populations under 10 million. Not to mention that the top 2 countries by population (China and India) are not participating.
However, if you look at the data in some more detail there is a bit of a pattern that seem to favor the more populous countries.
Plot population vs. Rank and fit a first order polynomial:
Though the polynomial fit indicates that, in general, higher population translates to higher performance in national team soccer, the correlation coefficient (R = -0.225) is such that the two quantities are very weakly correlated. That is:
It is not likely that population is a significant factor in the success of a country’s national team in world soccer!
Some population statistics for the WC2010 countries:
N = 32
Mean: 49.5 millions
Median: 22 millions
Intercept: 75.8
Slope: –1.6
Residual std. deviation: 64.7 millions
Correlation = -0.225
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