General methods for the analysis of step-current measurements on intercalation devices are applied to an aqueous, protonic, tungsten oxide-based device. Plots of the built-in potential as a function of the passed charge, V-bi(Delta Q), are generated. Methods are demonstrated for extracting a useful indicator of the intercalation level from Delta Q and for relating V-bi to the applied potential. An intercalation efficiency, zeta, is defined, and zeta(V-bi) plots are generated. With proper accounting for extraneous contributions, zeta(V-bi) provides a measure of the effective site energy distribution and of the instantaneous efficiency (or capacity) of the intercalation process. A nonfaradaic spontaneous deintercalation process has been observed which acts to deintercalate the film without contributing to the measured current. Methods for including this effect in the analysis are presented in terms of a virtual current.