In identifying whether universities provide opportunities for low-income students, there is a measurement challenge: different institutions face students with different incomes and preparation. We show how a hypothetical university's "relevant pool"--the students from whom it could plausibly draw--affects popular measures: the Pell share, Bottom Quintile share, and Intergenerational Mobility. Using a proof by contradiction, we demonstrate that universities ranked highly on the popular measures can actually serve disproportionately few low-income students. We also show the reverse: universities slated for penalties on the popular measures can actually serve disproportionately many low-income students. Furthermore, the Intergenerational Mobility measure penalizes universities that face relatively equal income distributions, which are probably good for low-income students, and rewards universities that face very unequal income distributions. In short, by confounding differences in university effort with differences in circumstances, the popular measures could distort university decision making and produce unintended consequences. We demonstrate that, with well-thought-out data analysis, it is possible to create benchmarks that actually measure what they are intended to measure. In particular, we present a measure that overcomes the deficiencies of the popular measures and is informative about all, not just low-income, students.