Phosphorescent organic light-emitting devices (OLEDs) can suffer a significant reduction in device efficiency under high current density excitation. This steady-state efficiency roll-off is frequently modeled by including losses from exciton-exciton and exciton-polaron quenching. Despite success in modeling the steady-state efficiency roll-off, the corresponding transient electroluminescence behavior has not been modeled as effectively using the same quenching processes. In this work, both the steady-state and transient electroluminescence behavior of phosphorescent OLEDs based on tris[2-phenylpyridinato-C2,N]Iridium(III) (Ir(ppy)3) are successfully reproduced by considering a dynamic polaron population. Within this model, polarons are able to either form excitons or leak through the device emissive layer, reducing the overall efficiency. This formalism permits a natural and rigorous connection between exciton and polaron dynamics and device charge balance, with the charge balance cast as the efficiency of exciton formation. The full dynamics model reproduces both the rise and decay of transient electroluminescence, as well as the full dependence of the external quantum efficiency on current density. Fit parameters are independently verified using separate studies of transient and steady-state photoluminescence. The model provides a complete picture for the dynamics present during the electrical operation of phosphorescent OLEDs, while also offering a direct route to elucidate exciton formation.