FIFA World Ranking Per Capita

This guy came up with a formula to skew the FIFA world rankings to account for countries with large or small populations. This punishes teams like China, USA and Brazil for being bad, mediocre and great (respectively) while having a larger pool of potential athletes to draw from and rewards teams like Croatia, Northern Ireland and Mozambique for doing well despite small populaces.

The natural logarithm of population is used to compensate for the non-linear scale of FIFA ranking. The difference between actual and compensated rank will then show how much each country punches above or below their weight.

That’s great, but I hate not understanding methodology and where my math skills have always been lacking is the natural log region. Can someone explain natural log to me in basic terms? Why does this approach make sense?