Most natural ecosystems contain animals feeding on many different types of food, but it is difficult to predict what will be eaten when food availabilities change. We present a method that estimates food preference over many study sites, even when number of food types vary widely from site to site. Sampling variation is estimated using bootstrapping. We test the precision and accuracy of this method using computer simulations that show the effects of overall number of food types, number of sites, and proportion of missing prey items per site. Accuracy is greater with fewer missing prey types, more prey types and more sites, and is affected by the number of sites more than the number of prey types. We present a case study using lion (Panthera leo) feeding data and show that preference vs prey size follows a bell-curve. Using just two estimated parameters, this curve can be used as a general way to describe predator feeding patterns. Our method can be used to: test hypotheses about what factors affect prey selection, predict preferences in new sites, and estimate overall prey consumed in new sites.