Left: histogram of the mode of the EDSD prior (i.e. twice the exponential length scale L = L(l, b)) used by Bailer-Jones et al. (2018) for their Bayesian distance estimations of Gaia DR2 sources. Right: distribution of the first significant digit of the EDSD prior mode, together with the theoretical prediction of Benford’s law. The data have vertical error bars to reflect Poisson statistics, but the error bars are much smaller than the symbol sizes.