The unique properties of dark matter are revealed during collisions between clusters of galaxies, such as the bullet cluster (1E 0657-56) and baby bullet (MACS J0025-12). These systems provide evidence for an additional, invisible mass in the separation between the distributions of their total mass, measured via gravitational lensing, and their ordinary 'baryonic' matter, measured via its X-ray emission. Unfortunately, the information available from these systems is limited by their rarity. Constraints on the properties of dark matter, such as its interaction cross-section, are therefore restricted by uncertainties in the individual systems' impact velocity, impact parameter and orientation with respect to the line of sight. Here we develop a complementary, statistical measurement in which every piece of substructure falling into every massive cluster is treated as a bullet. We define 'bulleticity' as the mean separation between dark matter and ordinary matter, and we measure the signal in hydrodynamical simulations. The phase space of substructure orbits also exhibits symmetries that provide an equivalent control test. Any detection of bulleticity in real data would indicate a difference in the interaction cross-sections of baryonic and dark matter that may rule out hypotheses of non-particulate dark matter that are otherwise able to model individual systems. A subsequent measurement of bulleticity could constrain the dark matter cross-section. Even with conservative estimates, the existing Hubble Space Telescope archive should yield an independent constraint tighter than that from the bullet cluster. This technique is then trivially extendable to and benefits enormously from larger, future surveys.