Rating-based human evaluation has become an essential tool to accurately evaluate the impressive performance of large language models (LLMs). However, current rating systems suffer from several important limitations: first, they fail to account for biases that significantly influence evaluation results, second, they require large and expensive preference datasets to obtain accurate ratings, and third, they do not facilitate meaningful comparisons of model ratings across different tasks. To address these issues, we introduce Polyrating, an expressive and flexible rating system based on maximum a posteriori estimation that enables a more nuanced and thorough analysis of model performance at lower costs. Polyrating can detect and quantify biases affecting human preferences, ensuring fairer model comparisons. Further, Polyrating can reduce the cost of human evaluations by up to $41\%$ for new models and up to $77\%$ for new tasks by leveraging existing benchmark scores. Lastly, Polyrating enables direct comparisons of ratings across different tasks, providing a comprehensive understanding of an LLMs' strengths, weaknesses, and relative performance across different applications.