Rain runs off in two main ways: saturation excess when soil is full, and infiltration excess when rain exceeds infiltration. They often occur simultaneously in a watershed, but most models treat them separately. We introduce a new theory that captures both processes within a single framework, tracking their shift over space and time. Tested over 181 U.S. watersheds, the theory well predicts streamflow in most watersheds and improves understanding of runoff under diverse climates.