Minimizing the reverse bias dark current while retaining external quantum efficiency is crucial if the light detection sensitivity of organic photodiodes (OPDs) is to compete with inorganic photodetectors. However, a quantitative relationship between the magnitude of the dark current density under reverse bias (Jd) and the properties of the bulk heterojunction (BHJ) active layer has so far not been established. Here, a systematic analysis of Jd in state-of-the-art BHJ OPDs using five polymers with a range of energy levels and charge transport characteristics is presented. The magnitude and activation energy of Jd are explained using a model that assumes charge injection from the metal contacts into an energetically disordered semiconductor. By relating Jd to material parameters, insights into the origin of Jd are obtained that enable the future selection of successful OPD materials.