Histogram of the positional offset between an AGB star and its associated eRASS1 X-ray counterpart relative to the 1-σ positional uncertainty of the latter for most likely, possible, and spurious X-AGBs in Tables 1, 2, and D.1, respectively. The histogram of the possible X-AGBs (black histogram) was added together with that of the most likely X-AGBs (blue histogram and shade). The histogram and shade of the spurious X-AGBs are shown in purple. The spurious X-AGBs associated with diffuse X-ray sources or those superimposed on diffuse emission are not included.