a suitable radius (in our case 3) of each X-ray source, and K is the ratio $N_U/N_{tot}$ between the number of such putative counterparts $N_U$ and the total number $N_{tot}$ of all (also non-unique) objects in the band close to the X-ray sources within the same radius, i.e. inclusive of background objects.

We computed these estimators for each survey and band where a potential counterpart is present, and assigned the best value (highest LR) to the counterpart set. We then ordered the counterpart sets by decreasing LR, and also divided them into three broad groups: good, fair, and bad according to $LR>0.25$, $0.05<LR<0.25$, $LR<0.05$ using P as a cross-check.

We then assign a preliminary rank, rejecting most of the cases with bad scores. A *primary single counterpart* is either a physical solitary association, a single non-bad association, or exceptionally the best of the rejects, which is ‘recovered’. When several candidates above the thresholds exist, the one with best estimator is considered the *primary counterpart*, and all the others are *secondaries*. If the estimator ratio between the primary and the best secondary is above 10, the primary should be definitely preferred and the secondaries are just nominally included. Otherwise the primary 