Using a large set of ab initio molecular dynamics trajectories we demonstrate that the mechanistic details of aqueous proton diffusion are insensitive to finite size effects. Furthermore, we show how correlation in the proton hopping direction is related to the presolvation of the hydronium ion. Specifically, we observe a dependence of the probability for the excess proton to return to its previous hydronium ion on whether that hydronium ion was accepting a hydrogen bond from a fourth water molecule at the time the excess proton left. The dynamics of this fourth water molecule was previously linked to the net displacement of the proton, and our analysis shows that this connection is due to the changes in the hopping probability that we calculate. Additionally, we show how our simulated dynamics with correlations that imply a faster time scale are compatible with recent spectroscopy results that point to a slower hopping time scale by looking closely at which proton transitions are being taken into consideration. Finally, we show that the correlation in proton hopping directions is not strongly influenced by interactions among hydronium ions.