Interpreting how populations will change in response to exploitation is essential to the sound management of fish stocks. While deterministic models can be of use in evaluating sustainable fishing rates, the inherent variability of fish populations limits their value. In this paper a probabilistic approach is investigated which avoids having to make strong assumptions about the functional relationship between spawning stock size and the annual number of young fish (recruits) produced. Empirical probability distributions for recruits are derived, conditioned on stock size, and used to indicate likely stock changes under different fishing mortality rates. The method is applied to cod (Gadus morhua) in the North Sea to illustrate how population change can be inferred and used by fishery managers to choose fishing mortality rates which are likely to achieve sustainable exploitation.