The utility of stochastic point kinetics theory has been demonstrated through the examination of a criticality excursion in a supercritical system. It has been found that a deterministic point kinetics model underpredicts the excursion maximum energy release by up to two orders of magnitude with respect to a counterpart stochastic model. This potentially large underprediction shows that neutron population fluctuations play an important role in the evolution of that system. This work provides a review of the formalism and approximations used to arrive at this conclusion. To broaden the result's applicability, we relax several approximations, leading to the construction of new, nonanalytical expressions. We compare the two sets of results using local sensitivity analysis, which also allows us to assess the impact of potential uncertainties in included model parameters or data. This comparison (presented also for a 235U system) also proves useful in assessing the validity of the approximations under consideration.