One of the most dramatic events in river environments is the natural diversion, or avulsion, of a channel across its floodplain. Though rarely witnessed, avulsions can cause massive floods, and over geologic time they create most of the fluvial stratigraphic record. Avulsions exhibit behavior ranging from reoccupying abandoned channels to constructing new channels and splay complexes. To quantify avulsion behavior, or style, we measure avulsion-related floodplain disturbance in modern environments. We show that for 63 avulsions from Andean, Himalayan, and New Guinean basins, avulsion style correlates with channel morphology and changes systematically downstream. Avulsions in braided rivers reoccupy abandoned channels, whereas avulsions in meandering rivers often produce flooding and sediment deposition during channel construction. These downstream changes in avulsion style can explain the abrupt transition from channel-dominated to floodplain-dominated facies commonly observed in foreland basin stratigraphy. These dynamics also explain why some avulsions are more hazardous than others.