Large storms make it difficult to extract the long-term trend of erosion or accretion from shoreline position data. Here we make storms part of the shoreline change model by means of a storm function. The data determine storm amplitudes and the rate at which the shoreline recovers from storms. Historical shoreline data are temporally sparse, and inclusion of all storms in one model over-fits the data, but a probability-weighted average model shows effects from all storms, illustrating how model averaging incorporates information from good models that might otherwise have been discarded as un-parsimonious. Data from Cotton Patch Hill, DE, yield a long-term shoreline loss rate of 0.49 ± 0.01 m/yr, about 16% less than published estimates. A minimum loss rate of 0.34 ± 0.01 m/yr is given by a model containing the 1929, 1962 and 1992 storms.