The field of fixation prediction is heavily model-driven, with dozens of new models published every year. However, progress in the field can be difficult to judge because models are compared using a variety of inconsistent metrics. As soon as a saliency map is optimized for a certain metric, it is penalized by other metrics. Here we propose a principled approach to solve the benchmarking problem: we separate the notions of saliency models and saliency maps. We define a saliency model to be a probabilistic model of fixation density prediction and, inspired by Bayesian decision theory, a saliency map to be a metric-specific prediction derived from the model density which maximizes the expected performance on that metric. We derive the optimal saliency map for the most commonly used saliency metrics (AUC, sAUC, NSS, CC, SIM, KL-Div) and show that they can be computed analytically or approximated with high precision using the model density. We show that this leads to consistent rankings in all metrics and avoids the penalties of using one saliency map for all metrics. Under this framework, good models will perform well in all metrics.