Mention pair models that predict whether or not two mentions are coreferent have historically been very effective for coreference resolution, but do not make use of entity-level information. However, we show that the scores produced by such models can be aggregated to define powerful entity-level features between clusters of mentions. Using these features, we train an entity-centric coreference system that learns an effective policy for building up coreference chains incrementally. The mention pair scores are also used to prune the search space the system works in, allowing for efficient training with an exact loss function. We evaluate our system on the English portion of the 2012 CoNLL Shared Task dataset and show that it improves over the current state of the art.