Distributed beamforming in wireless ad hoc networks has the promise of greatly improving network throughput. However, unlike traditional beamforming from a fixed array, the random locations of the nodes collaborating to form the array lead to a random beam pattern. In particular, the position and size of side lobes can vary greatly and have a significant impact on the concurrent transmissions that are the source of much of the throughput gain realized from distributed beamforming. Here, we present a simple model that captures this randomness and then use the model to consider the average throughput of a large ad hoc wireless networks. Numerical results are compared to those obtained if one employs the oft-used pie-wedge approximation for a directed antenna beam, and the difference is shown to be significant in regions where the side lobe interference is non-negligible.