In Atkins v. Virginia, the U.S. Supreme Court held that the Eighth Amendment ban on cruel and unusual punishment precludes capital punishment for intellectually disabled offenders. Death penalty states responded with laws defining intellectual disability in various ways. In Hall v. Florida, the Court narrowly struck down the use of a measured IQ of 70 to mark the upper limit of intellectual disability because it created ‘an unacceptable risk that persons with intellectual disability will be executed’. But the Court was unclear if not inconsistent in its description of an upper limit that would be acceptable. Four dissenting Justices accused the majority not only of misconstruing the Eighth Amendment, but also of misunderstanding elementary statistics and psychometrics. This article uses more complete statistical reasoning to explicate the Court’s concept of unacceptable risk. It describes better ways to control the risk of error than the Court’s confidence intervals, and it argues that, to the extent that the Eighth Amendment allows any quantitative cut-score in determining an offender’s intellectual disability, these more technically appropriate methods are constitutionally permissible.