The manner in which an earthquake rupture propagates across a fault reflects both the initial properties of the fault and the dynamical stresses produced by the rupture. We quantify the propagation of an earthquake rupture using the second moments of the earthquake space-time distribution. In particular, the second moments provide a simple way to differentiate between approximately bilateral and predominantly unilateral ruptures. We determined the second moments for a catalog of Mw ≥7 earthquakes that have occurred since 1994. The results show that approximately 80% of large shallow ruptures are predominantly unilateral. Our result agrees well with strong-motion inversions from previous studies on moderate and large earthquakes. The predominance of unilateral propagation in large earthquakes is explained by a simple characteristic earthquake model in which large events rupture an entire structurally defined fault segment and nucleation points are uniformly distributed along the fault. The predominance of unilateral rupture may also be enhanced by the dynamic stress field produced by contrasts in the elastic properties between the two sides of plate boundary faults.