Similar to Fig. 5 but comparing results that involve the simplest adjustments to the XMM position errors. For reference, the black histogram is based on using the unadjusted XMM position errors while the expected Rayleigh distribution is overlaid (grey). The blue histogram represents the simplest adjustment to the XMM position errors, involving the addition of a systematic in quadrature, b(=0.37), while the red histogram involves both a scaling of the XMM position error by a factor a(=1.12) and addition of a systematic, b(=0.27), in quadrature. These histograms are based on slightly different filtering compared to Fig. 5, as explained in the text