The present study approaches the subject of spontaneous protein-ligand binding simulations from the perspective of chaos theory and uncertainty quantification. In this section, we describe how the chaotic nature of molecular dynamics simulations causes individual simulations to be non-reproducible, no matter their length. We also describe how running ensembles of simulations remedies this by allowing for expectation values to be subjected to rigorous uncertainty quantification and convergence analysis. By presenting this theory, we make clear that running an ensemble of simulations which sum to a certain time is not equivalent to simply running a single simulation of the same aggregate time. The novel point which we explicitly demonstrate is that, contrary to the current consensus, the level of certainty of a simulation derived expectation value does not increase with simulation time. This necessitates the use of ensembles when reporting macroscopic expectation values for all long-timescale simulations. Not only is such a prescription required by the tenets of statistical mechanics, it is also essential in order to quantify the uncertainty of the calculated properties.