We tested for equality of the population medians of the gradient distributions for independent runs using the Kruskal-Wallis H-test. Figure shows that the proportion of windows showing significant differences at the 95 % confidence level is always above 70 % for the bound vanish and bound discharge stages. However, for the free legs, the fraction increases with ligand size from around 0 for T4L to similar to the bound fractions for MDM2-Nutlin. Because these replicate runs produce different distributions of gradients on this timescale, none of our calculations are strictly converged, even after 30 ns sampling time per window. This confirms that replicate runs are essential for reliable free energy estimates and uncertainty quantification for the bound leg runs, and many free leg runs, at least without improved sampling. In accordance with Wan et al., this suggests that the optimal number of replicates for a given sampling time is likely to be the maximum number of replicates which remain long enough to achieve sufficient equilibration. We note that averaging results from multiple replicate runs which become trapped in separate regions of configuration space is not theoretically rigorous, 128 because there is no guarantee that the distribution among these conformational regions is not biased by the starting conformations.