Warren raised some interesting points about the various distributions and scoring methods. Since we're talking about _models_ here, let's assume that: 1. The Elo chess system "works" & is "faithful", i.e., a. the eventually stationary scores actually imply the correct probabilities for wins; and b. the logistic pdf so produced actually matches the statistics of real chess players. (Some of the literature seems to indicate that the standard chess updating rule is slow to converge, but I only care that it does converge for my 1a. Warren will quibble with 1b, but here I'm simply assuming it.) 2. We further assume that the population size is large enough to be able to approximate well with continuous pdf's & cdf's. Let pdf_normal(x) and cdf_normal(x) be the gaussian pdf and its integral function, respectively. Let quantile_normal(q) be the inverse function to cdf_normal(x); i.e., quantile_normal(cdf_normal(x))=x. Let pdf_logistic(y) and cdf_logistic(y) by the logistic pdf and its integral function, respectively. Let quantile_logistic(q) be the inverse function to cdf_logistic(y); i.e., quantile_logistic(cdf_logistic(y))=y. Since cdf_normal and cdf_logistic are both monotonic with image [0,1), we can relate x,y by a 1-1 coorespondence: cdf_normal(x)=cdf_logistic(y) Thus, we can "transform" from "logistic coordinates" to "Gaussian coordinates" via the function quantile_normal(cdf_normal(x))=x=quantile_normal(cdr_logistic(y)) Furthermore, this "transform" preserves ordering, and enables us to relate more traditional statistical terminology to this problem. We can also scale our Gaussian coordinates so that the mean is 100 and the standard deviation is 15 (i.e., IQ-type scaling). We can also scale our logistic scoring so that the mean is 100 and the logistic score 115 is the same quantile as the Gaussian value 115 (= 1 standard deviation for the Gaussian distribution). Of course, none of the other integral standard deviations will match, but a least we tried. Perhaps Warren has already gone through this thought process?