The big caveat is that it's trivial to measure the AIC, BIC and other quality of fit measurements for a distribution. If you think it's so and so distribution, go for it. In my experience in this specific case of chess rankings and in the broader case of test scores, skew-normal and log-normal have worse fits than plain Guassian.

I have no idea why you would believe increasing the population would make this Gaussian distribution look Pareto, when the exact opposite is true - increasing populations make things look more Gaussian - in all natural circumstances.

I was conjecturing that the distribution would be closer to Pareto for everyone (including people who've never learned how to play chess), hence why I said that "active players" is a big caveat.

> increasing populations make things look more Gaussian - in all natural circumstances.

This is just not the case, there's plenty of "natural circumstances" where populations have non-Gaussian distributions.

Perhaps you meant a specific type of population, like chess ratings? I'd be interested in seeing what you find there, but all I've found shows significantly distorted tails (not to mention a skew from 1500).