Mars is dry today, but numerous precipitation-fed paleo-rivers are found across the planet's surface. These rivers' existence is a challenge to models of planetary climate evolution. We report results indicating that, for a given catchment area, rivers on Mars were wider than rivers on Earth today. We use the scale (width and wavelength) of Mars paleo-rivers as a proxy for past runoff production. Using multiple methods, we infer that intense runoff production of >(3-20) kg/m2 per day persisted until <3 billion years (Ga) ago and probably <1 Ga ago, and was globally distributed. Therefore, the intense runoff production inferred from the results of the Mars Science Laboratory rover was not a short-lived or local anomaly. Rather, precipitation-fed runoff production was globally distributed, was intense, and persisted intermittently over >1 Ga. Our improved history of Mars' river runoff places new constraints on the unknown mechanism that caused wet climates on Mars.