The EMD taken between the random and simulated systems supports the observations that can be made from the histogram. The distribution of n-TM sites becomes increasingly similar to a random distribution as a function of the number of transition metals in the simulation and supports the hypothesis that increasing cation configurational entropy leads to a more homogeneous distribution of cations in lithium transition metal oxide disordered rock salts. However, there is a decrease in the rate at which the EMD value decreases as the number of transition metals increases, indicating that the distribution becomes more similar to a random distribution at a slower rate. "Diminishing returns" are observed in the short-range order suppression with respect to the number of transition metals. This indicates that increased cation configurational entropy can improve mixing to an extent, but is unlikely to fully overcome the electrostatic and elastic effects that drive cation short-range ordering in lithium transition metal oxides . This implies that moderate entropy systems will see most of the short-range order suppression benefit of the many-transition-metal systems.