We present a general probabilistic framework for predicting the outcome of pairwise matchups (e.g. two-player sport matches) and pairwise preferences (e.g. product preferences), both of which have widespread applications ranging from matchmaking in computer games to recommendation in e-commerce. Unlike existing models for these tasks, our model not only learns representations of the items in a more expressive latent vector space, but also models how context modifies matchup and preference outcomes. For example, the context “weather” may alter the winning probability in a tennis match, or the fact that the user is on a mobile device may alter his preferences among restaurants. More generally, the model is capable of handling any symmetric game/comparison problem that can be described by vectorized player/item and game/context features. We provide a comprehensive evaluation of its predictive performance with real datasets from both domains to show its ability to predict preference and game outcomes more accurately than existing models. Furthermore, we demonstrate on synthetic datasets the expressiveness of the model when compared against theoretical limits.