Uncertainty quantification (UQ) is a field of endeavour that aims to analyse the interplay between simulation inputs and outputs for the purpose of determining the uncertainty associated to obtained results. In the present study, we are particularly interested in quantifying the aleatoric output uncertainty that is controlled by the initial random velocity seed. A series of our studies have presented robust evidence that simulation outcomes are strongly controlled by the initial random seed, and that averaging over a set of simulations all starting with different random seeds consistently reduces the uncertainty of obtained results. Indeed, this aleatoric uncertainty completely dominates the epistemic uncertainty arising from the way in which the model is parameterised and set up. A crucial feature of performing ensembles of simulations, which allows us to conduct uncertainty quantification, is that the distribution of properties of interest can be obtained. Here, we apply UQ to multiple properties of spontaneous ligand-protein binding simulations, namely, the protein-ligand residue contact frequency distribution and the computed binding free energy of the ligand with a protein target.