How far back are results of matches relevant for Elo purposes? If a player wins a few early matches then they will earn less points for later wins than if they'd lost those early matches. In the end there comes a point at which older results simply don't affect today's rating.
Matches with higher K factor will erase earlier history faster. I think that K factor has a linear effect on change in rating, so for the purpose of this calculation we can just assume constant K.