Models of human behavior for prediction and collaboration tend to fall into two categories: ones that learn from large amounts of data via imitation learning, and ones that assume human behavior to be noisily-optimal for some reward function. The former are very useful, but only when it is possible to gather a lot of human data in the target environment and distribution. The advantage of the latter type, which includes Boltzmann rationality, is the ability to make accurate predictions in new environments without extensive data when humans are actually close to optimal. However, these models fail when humans exhibit systematic suboptimality, i.e. when their deviations from optimal behavior are not independent, but instead consistent over time. Our key insight is that systematic suboptimality can be modeled by predicting policies, which couple action choices over time, instead of trajectories. We introduce the Boltzmann policy distribution (BPD), which serves as a prior over human policies and adapts via Bayesian inference to capture systematic deviations by observing human actions during a single episode. The BPD is difficult to compute and represent because policies lie in a high-dimensional continuous space, but we leverage tools from generative and sequence models to enable efficient sampling and inference. We show that the BPD enables prediction of human behavior and human-AI collaboration equally as well as imitation learning-based human models while using far less data.