This report introduces a new statistical model for time-resolved photon detection in a generic single-photon-sensitive sensor array. The model is validated by comparing modelled data with experimental data collected on a single-photon avalanche diode sensor array. Data produced by the model are used alongside corresponding experimental data to calculate, for the first time, the effective distance resolution of a pulsed direct time of flight 3D optical imaging system over a range of conditions using four peak-detection algorithms. The relative performance of the algorithms is compared. The model can be used to improve the system design process and inform selection of the optimal peak-detection algorithm.