We study the origin of efficiency roll-off (also called ``efficiency droop'') in colloidal quantum-dot light-emitting diodes through the comparison of quantum-dot (QD) electroluminescence and photoluminescence. We find that an electric-field-induced decrease in QD luminescence efficiency---and not charge leakage or QD charging (Auger recombination)---is responsible for the roll-off behavior, and use the quantum confined Stark effect to accurately predict the external quantum efficiency roll-off of QD light-emitting diodes.