Example of the original and the resulting AFs, after the matching procedure is applied, in order to obtain a mass-independent comparison of the dynamical parameters between two isolation bins, 1 < R_isol/r_vir < 4 (red) and 4 < R_isol/r_vir < 7 (black). On the vertical axis, N is the number of halos. The solid lines correspond to the original AFs and the dashed lines to the AFs derived by the matching procedure. We note that a common shape of the AF between any two isolation bins is obtained and not the same overall number of halos.