Abstract River avulsions are commonly considered to be driven by the aggradation and growth of alluvial ridges, and the associated increase in cross-valley slope relative to either the down-channel slope or the down-valley slope (the latter is termed the slope ratio in the present paper). Therefore, spatial patterns of overbank aggradation rate over stratigraphically relevant time scales are critical in avulsion-dominated models of alluvial architecture. Detailed evidence on centennial- to millennial-scale floodplain deposition has, to date, been largely unavailable. New data on such long-term overbank aggradation rates from the Rhine–Meuse and Mississippi deltas demonstrate that the rate of decrease of overbank deposition away from the channel belt is much larger than has been supposed hitherto, and can be similar to observations for single overbank floods. This leads to more rapid growth of alluvial ridges and more rapid increase in slope ratios, potentially resulting in increased avulsion frequencies. A revised input parameter for overbank aggradation rate was used in a three-dimensional model of alluvial architecture to study its effect on avulsion frequency. Realistic patterns of avulsion and interavulsion periods (≈1000 years) were simulated with input data from the Holocene Rhine River, with avulsions occurring when the slope ratio is in the range 3–5. However, caution should be practised with respect to uncritical use of these numbers in different settings. Evidence from the two study areas suggests that the avulsion threshold cannot be represented by one single value, irrespective of whether critical slope ratios are used, as in the present study, or superelevation as has been proposed by other investigators.