Frames Per Second (FPS) significantly affects the gaming experience. Providing players with accurate FPS estimates prior to purchase benefits both players and game developers. However, we have a limited understanding of how to predict a game's FPS performance on a specific device. In this paper, we first conduct a comprehensive analysis of a wide range of factors that may affect game FPS on a global-scale dataset to identify the determinants of FPS. This includes player-side and game-side characteristics, as well as country-level socio-economic statistics. Furthermore, recognizing that accurate FPS predictions require extensive user data, which raises privacy concerns, we propose a federated learning-based model to ensure user privacy. Each player and game is assigned a unique learnable knowledge kernel that gradually extracts latent features for improved accuracy. We also introduce a novel training and prediction scheme that allows these kernels to be dynamically plug-and-play, effectively addressing cold start issues. To train this model with minimal bias, we collected a large telemetry dataset from 224 countries and regions, 100,000 users, and 835 games. Our model achieved a mean Wasserstein distance of 0.469 between predicted and ground truth FPS distributions, outperforming all baseline methods.