Auroral substorms are often associated with optical ray or bead structures during initial brightening (substorm auroral onset waves). Occurrence probabilities and properties of substorm onset waves have been characterized using 112 substorm events identified in Time History of Events and Macroscale Interactions during Substorms (THEMIS) all-sky imager data and compared to Rice Convection Model–Equilibrium (RCM-E) and kinetic instability properties. All substorm onsets were found to be associated with optical waves, and thus, optical waves are a common feature of substorm onset. Eastward propagating wave events are more frequent than westward propagating wave events and tend to occur during lower-latitude substorms (stronger solar wind driving). The wave propagation directions are organized by orientation of initial brightening arcs. We also identified notable differences in wave propagation speed, wavelength (wave number), period, and duration between westward and eastward propagating waves. In contrast, the wave growth rate does not depend on the propagation direction or substorm strength but is inversely proportional to the wave duration. This suggests that the waves evolve to poleward expansion at a certain intensity threshold and that the wave properties do not directly relate to substorm strengths. However, waves are still important for mediating the transition between the substorm growth phase and poleward expansion. The relation to arc orientation can be explained by magnetotail structures in the RCM-E, indicating that substorm onset location relative to the pressure peak determines the wave propagation direction. The measured wave properties agree well with kinetic ballooning interchange instability, while cross-field current instability and electromagnetic ion cyclotron instability give much larger propagation speed and smaller wave period.