And as far as the distribution of chessplayer ratings is concerned, that is neither Gaussian nor logistic, it instead is more like a Gompertz extreme value distribution. My paper #20 explains how to derive such from a model, and my 1984 BS thesis performed a fit to the actual US Chess Federation rating distribution. The histogram of internet chess ratings Baker linked to, is a different data set, which also looks to my eye like it would be fit well by Gompertz, anyhow obviously better than any Gaussian or logistic could fit it. If Baker has the energy he might want to try such fits himself. In 1984 I had great difficulty doing the fits because this was 1984 and I was a math undergrad at MIT, which meant my access to computers was total dogshit. Some physicist who had a computer with commercial data fitting software agreed to help me in a halfassed way which just barely enabled me to do the job. Nowadays this sort of job should be far easier. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)