Cumulative distribution of the fraction of X-ray sources with an r-band counterpart above R_crit as a function of distance between the X-ray and SDSS positions (﹩{r}_{{\rm{sep}}};﹩ red solid line) and between the randomized X-ray positions and SDSS sources (blue dashed line). The top panels are for the matches from single-epoch imaging (1852 X-ray/SDSS counterparts and 41 random matches) while the bottom panels show the matches to the coadded Jiang et al. (2014) catalog (1652 X-ray/coadded counterparts with 61 spurious associations). The number of spurious matches occurs at r_sep distances similar to that as the un-shifted X-ray catalog, indicating that MLE helps to mitigate unassociated sources compared to nearest neighbor matching by using magnitude and astrometric precision information in the calculation.