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Predicting outcomes in sports is important for teams, leagues, bettors, media, and fans. Given the growing amount of player tracking data, sports analytics models are increasingly utilizing spatially-derived features built upon player tracking data. However, player-specific information, such as location, cannot readily be included as features themselves, since common modeling techniques rely on vector input. Accordingly, spatially-derived features are commonly constructed in relation to anchor objects, such as the distance to a ball or goal, through global feature aggregations, or via role-assignment schemes, where players are designated a distinct role in the game. In doing so, we sacrifice inter-player and local relationships in favor of global ones. To address this issue, we introduce a sport-agnostic graph-based representation of game states. We then use our proposed graph representation as input to graph neural networks to predict sports outcomes. Our approach preserves permutation invariance and allows for flexible player interaction weights. We demonstrate how our method provides statistically significant improvements over the state of the art for prediction tasks in both American football and esports, reducing test set loss by 9% and 20%, respectively. Additionally, we show how our model can be used to answer "what if" questions in sports and to visualize relationships between players.