Goodness-of-fit (GOF) parameter plotted against the excess noise, with the inset showing a zoomed-in version. At the extreme end is Polaris with ɛ_i = 7.5 and GOF = 270 (top panel). For clarity a randomly Gaussian distributed number is added to the excess noise when it is below 0.02 mas in the inset. In the middle panel the histogram of the GOF parameter is shown with a Gaussian distribution (with mean 4.0 and σ = 1.8) overplotted in blue. In the bottom panel the GOF statistic has been recomputed by multiplying the astrometric_chi2_al statistic by 0.7 for all sources to force a peak in the histogram at about zero. The σ of the Gaussian is 1.7. The abscissa has been shifted by ten units compared to the plot in the middle panel.