We perform a superposed epoch analysis of the evolution of the Birkeland currents (field-aligned currents) observed by the Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) during substorms. The study is composed of 2900 substorms provided by the SuperMAG experiment. We find that the current ovals expand and contract over the course of a substorm cycle and that currents increase in magnitude approaching substorm onset and are further enhanced in the expansion phase. Subsequently, we categorize the substorms by their onset latitude, a proxy for the amount of open magnetic flux in the magnetosphere, and find that Birkeland currents are significantly higher throughout the epoch for low-latitude substorms. Our results agree with previous studies which indicate that substorms are more intense and close more open magnetic flux when the amount of open flux is larger at onset. We place these findings in the context of previous work linking dayside and nightside reconnection rate to Birkeland current strengths and locations.