It's because going from 1 to 2 changes the expected worst case load from an asymptotic log to an asymptotic log log, and further increases just change a constan

It's because going from 1 to 2 changes the expected worst case load from an asymptotic log to an asymptotic log log, and further increases just change a constant. See https://en.wikipedia.org/wiki/Balls_into_bins_problem https://en.wikipedia.org/wiki/Balls_into_bins_problem