Distribution of the ﹩\mathrm{log}({\mathrm{LR}}_{i,j})﹩ for the crossmatches between WIBRaLS and 4FGL (G_real) is shown in blue; the average distribution for the crosmatches between WIBRaLS and the fake γ-ray catalogs (﹩\langle {G}_{\mathrm{fake}}\rangle ﹩) is shown in green. The hatched histograms represent the same distributions when taking angular separation, r, into account with the exponential behavior shown in Equation (1).