We address the stochastic characteristics of a recently proposed greedy routing scheme. The behavior of individual hop advancements is examined, and asymptotic expressions for the hop length moments are obtained. The change of the hop distribution as the sink distance is varied is quantified with a Kullback–Leibler analysis. We discuss the effects of the assumptions made, the inherent dependencies of the model, and the influence of a sleep scheme. We propose a renewal process model for multiple hop advancements and justify its suitability under our assumptions. We obtain the renewal process distributions via fast Fourier transform convolutions. We conclude by giving future research tasks and directions.