Ranking can support risk management by prioritising entities of interest based on rates of relevant events, such as bycatch rates for fleets, failure rates of targeting species, or catch rates across different fisheries. We consider the situation where the entities exposure to risk is heterogeneous as might arise when, for example, number of fishing trips varies between fleets, or fishing effort varies between different fleets.  We develop an empirical Bayes inference method (a two stage hierarchical model) for the estimation of event rates.  We demonstrate an application of the proposed method for seabird bycatch data comprising the varying efforts for a pool of fleets over a given time horizon.  We show how our empirical Bayes inference for the rates of Poisson count data can provide management insights about the worst and best performing fleets in terms of bycatch.