Consistency of the sub-halo mass function. We count the number of mass halos inside one virial radii of the cluster and show their mass distribution here. Assuming a minimum particle number of 100 particles for a halo, we show the mass resolution limit of each simulation where BAHAMAS is roughly equal to levels 10-10, intermediate corresponds to levels 10-11, and target corresponds to levels 10-12. The bottom panel shows the ratio between the mass function and the highest resolution, non-super-sampled run (12-12). We find that the sub-halo mass functions for the target resolution is moderately suppressed below M₂₀₀ < 2 × 10¹⁰ M_⊙.