Collisionless magnetic reconnection requires the violation of ideal MHD by various kinetic-scale effects whose relative importance is uncertain. Recent research has highlighted the potential importance of wave-particle interactions by showing that Vlasov simulations of unstable ion-acoustic waves predict an anomalous resistivity that can be at least an order of magnitude higher than a popular analytical quasi-linear estimate. Here, we investigate the nonlinear evolution of the ion-acoustic instability and its resulting anomalous resistivity by examining the properties of a statistical ensemble of Vlasov simulations. The simulations differ in their initial electric noise field but are otherwise identical with a Maxwellian electron-ion plasma of low number density and low electron to ion temperature ratio, appropriate to collisionless space plasmas. By studying the evolution of an ensemble of 104 Vlasov simulations with reduced mass ratio m _i /m _e = 25, we show that (1) the probability distribution of anomalous resistivity values produced during the linear, quasi-linear, and nonlinear evolution of the ion-acoustic instability is approximately Gaussian, (2) the ensemble mean of the ion-acoustic resistivity during the nonlinear regime is higher than estimates at quasi-linear saturation, and (3) the ensemble standard deviation is comparable to the ensemble mean. We argue that the large variability during the nonlinear phase is due to electron and ion bounce motion which is sensitive to the initial conditions. We demonstrate that the results are essentially similar for a real mass ratio simulation.