The high substitution regimes (Mn-0.75/Zn-0.75) in Figure a and b tend to find the ground state structure more often than the lower substitution regimes (Mn-0.25/Zn-0.25) when starting from the normal spinel configuration. This is understood from the normal spinel starting structure being the ground state for all compositions. The higher substitution regime is much more likely to attempt a substitution event at a given step, and therefore the high substitution runs accept many steps in a row finding the normal ground state structures at each composition. The consistent high acceptance rates of swapping (Table ) implies that, in general, directed swaps either decrease the energy of the structure or increase the energy by only a small amount.