The dependence of stimulated polariton-polariton scattering in InGaAs/GaAs/AlGaAs microcavities on pump power, angle, and energy is investigated. We show that contrary to much previous belief there is no "magic angle" for stimulated scattering under continuous-wave conditions, the process being shown to be a rather general phenomenon, occurring over a wide range of pump angles. Close analogies with optical parametric oscillator behavior are found, but also aspects which can only be explained by inclusion of the polariton nature of the quasiparticles. The first physical explanation of why the optical parametric oscillator picture leads to the observed square root dependence of signal power on laser intensity is provided. The asymmetric nature of the tuning curve for excitation of the stimulated scattering process is explained in the framework of the renormalization of the lower polariton branch.