National Research Assessments represent the principal policy used by countries with public university systems to improve the quality of their universities research. They typically employ expert panels of local academics to assess journal quality, and use such assessments to reward publications. We propose a model of how experts assess quality and test this model using data from the recent Australian assessment. Controlling for objective quality, we show that experts cognitive biases dominate their assessments. Consequently, such assessments exaggerate the quality of the experts research and understate that of their colleagues. Our model can explain 95 of the variation in assessments.