Abstract For effective fishery management, estimated stock sizes, along with their uncertainties, should be accurate, precise, and unbiased. Atlantic salmon Salmo salar stock assessment in England and Wales (and elsewhere across the Atlantic) estimate returning salmon stocks by applying a measure of rod exploitation rate (RER), derived from less abundant fishery-independent stock estimates, to abundant fishery-dependent data. Currently, RER estimates are generated for individual principal salmon rivers based on available local data and assumptions. We propose a single, consistent, transparent, and statistically robust method to estimate salmon stocks that transfers strength of information from “data-rich” rivers, i.e. those with fisheries-independent data, to “data-poor” rivers without such data. We proposed, fitted, simplified, and then validated a Beta–Binomial model of RER, including covariates representing angler and fish behaviours, river flow, and random effects to control for nuisance effects. Our “best” model revealed covariate effects in line with our hypotheses and generalized to data not used to train it. We used this model to extrapolate stock estimates from 12 data-rich to 52 data-poor rivers, together with their uncertainties. The resulting river-specific salmon stock estimates were judged to be useful and can be used as key inputs to river-specific, national, and international salmon stock assessments.