Left: histogram of the Gaia DR2 Bayesian distance estimates from Bailer-Jones et al. (2018) for the sample of one million objects with the highest RUWE values, i.e. the objects with the poorest astrometric quality. Right: distribution of the first significant digit of the Bayesian distance estimates, 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. Compare with Fig. 7 for a sample of one million random stars that meet all astrometric (and photometric) quality criteria.