Median GGSL probability as a function of lens redshift for galaxy clusters with primary Einstein radii θ_E, p in the range of the observational dataset. From left to right, the three panels refer to source redshifts z_S = 1, z_S = 3, and z_S = 6. The results for the GIZMO-SIMBA and GADGET-X runs are shown as solid orange and dashed blue lines. The colored bands show the 99.9% confidence intervals for each dataset. The θ_E, p selection limits are reported in each panel and correspond to the range between the minimum and maximum of the primary Einstein radii of the observed clusters for a given source redshift. The number of cluster projections satisfying the selection criteria in the two simulation datasets (n_{Gizmo − Simba} and n_{Gadget − X}) are also reported in each panel. The black stars show the GGSL probability of the clusters in the observational dataset with associated 99.9% confidence limits derived from the posterior distributions of the lens model parameters. The insets in the upper right corners show the distributions of primary Einstein radii in the selected simulation samples, limited to the redshift range 0.3 < z_L < 0.45. The vertical black dashed lines show the measured values in the observational dataset.