Multiplayer Online Battle Arena (MOBA) games have received increasing worldwide popularity recently. In such games, players compete in teams against each other by controlling selected game avatars, each of which is designed with different strengths and weaknesses. Intuitively, putting together game avatars that complement each other (synergy) and suppress those of opponents (opposition) would result in a stronger team. In-depth understanding of synergy and opposition relationships among game avatars benefits player in making decisions in game avatar drafting and gaining better prediction of match events. However, due to intricate design and complex interactions between game avatars, thorough understanding of their relationships is not a trivial task. In this paper, we propose a latent variable model, namely Game Avatar Embedding (GAE), to learn avatars' numerical representations which encode synergy and opposition relationships between pairs of avatars. The merits of our model are twofold: (1) the captured synergy and opposition relationships are sensible to experienced human players' perception; (2) the learned numerical representations of game avatars allow many important downstream tasks, such as similar avatar search, match outcome prediction, and avatar pick recommender. To our best knowledge, no previous model is able to simultaneously support both features. Our quantitative and qualitative evaluations on real match data from three commercial MOBA games illustrate the benefits of our model.