The equilibration and relaxation times of the physical properties of time correlation functions have historically been of fundamental importance in terms of molecular simulation. An efficient algorithm for the acceleration of equilibration, termed the ‘event-chain Monte Carlo’ has been investigated over the past decade. Recently, by adding the collision rule often used in event-driven molecular dynamics, a Newtonian event-chain Monte Carlo was developed. In this event-chain Monte Carlo and variants thereof, optimal performance strongly depends on chain length, physical properties, and system size; the microscopic mechanism in play remains elusive. To identify key factors affecting equilibration, we investigated the diffusional characteristics per event (collision) for each algorithm, focusing systematically on the diffusion coefficients and pair dispersions in two-dimensional hard disk systems.