Streamer discharges are the primary mode of electric breakdown of air in lightning and high voltage technology. Streamer channels branch many times, which determines the developing tree-like discharge structure. We simulate branching of positive streamers in air using a 3D fluid model with stochastic photoionization. The distributions of branching angles and branching locations agree quantitatively with dedicated experiments. The simulated branching is remarkably sensitive to the photoionization coefficients, which confirms the validity of the classical photoionization model.