Question about pair sampling in MSD calculations from KMC simulations

[tfhughes]

I found your article on calculating MSDs from KMC simulations with variable time steps extremely useful. There I think you are sampling N_pairs pairs of sites where N_pairs = N_history * (N_simulation - N_history), where N_simulation is the number of frames in the simulation (for example 1,000,000) and N_history is the number of frames to sample prior to the current frame (for example in your article you use 38 and 380). To be specific for example for frame 9000 you would include (9000, 8999), (9000, 8998), ..., (9000, 9000 - N_history) pairs in the histogram. Due to computational expense we know N_history can't be too large. But I am curious why you choose pairs like this rather than sampling N_history previous frames from a uniform distribution of all previous frames going back to time zero?