Mean p_any distribution per eROSITA tile for real (top) and random (bottom row) eROSITA coordinates, using ancillary data from LS10 (left), GDR3 (middle) and CW2020 (right). The colour scale is consistent across all panels to facilitate comparison. While the p_any values for the real sources are generally higher than those for the random positions, they can approach similar levels in regions of high source density, indicating an increased risk of chance associations (see the main text for further discussions).