On the surface, the Supreme Court's death penalty holding today seems like a win for rationality and smart statistics. The 5-4 decision in Hall v. Florida said the state may not use an absolute cutoff of 70 on the IQ test as its measure of intellectual disability, below which a murderer cannot be executed -- because the standard error of measurement on the test is five points plus or minus. Freddie Lee Hall, the defendant, had scored 71, 72, 73 and 80 on his tests. The Florida Supreme Court said he wasn't intellectually disabled because he'd broken 70. Justice Anthony Kennedy, with the four liberals on his side, overturned the capital sentence.

On closer examination, though, the decision is less satisfying than it appears. Standard error is itself determined with reference to the degree of confidence we seek in the measurements we're making. It is thus, in an important sense, based on convention -- and the Supreme Court was relying not on its own statistical analysis of IQ scores, or Florida's, but on a medical consensus. The decision therefore embraces a kind of outsourced rationality, which has the unfortunate effect of making the death penalty seem rational.

If statistics aren't your preferred mode of expression, don't worry: The ones in this case are actually pretty simple, and so is the law. In 2002, the Supreme Court in Atkins v. Virginia held it unconstitutional to execute people with intellectual disability -- and left it to the states to define the term. Florida defined it as "significantly subaverage general intellectual functioning" alongside deficits in adaptive behavior. The same statute measures "subaverage" as an IQ of 70, two standard deviations below the mean of 100. The Florida Supreme Court interpreted the number 70 as an absolute cutoff: If you score above 70 on the test, no other evidence of intellectual disability matters.

Kennedy's opinion rejects the idea of considering only IQ evidence, then condemns the Florida court's "refusing to recognize that the score is, on its own terms, imprecise." Kennedy points out that "the professionals who design, administer, and interpret IQ tests have agreed, for years now, that IQ test scores should be read not as a single fixed number but as a range."

The range is, according to Kennedy, the same as the standard error, which he calls "a statistical fact, a reflection of the inherent imprecision of the test itself." The core of his argument is that when a defendant's score is under 75, the state needs to allow other evidence of disability. As Kennedy puts it, "a State that ignores the inherent imprecision of these tests risks executing a person who suffers from intellectual disability."

What could possibly be wrong with this analysis, which may reduce executions of the intellectually disabled, and achieves this worthy goal through a correct, rational statement of the nature of standard error? Should it not be welcomed as another incremental limitation of the death penalty?

The trouble is, each time the Supreme Court limits the death penalty, it offers an implicit justification for preserving it in most cases. The decision in this case accepts the argument that it's inhumane to execute people who don't fully comprehend what they've done or why they're being punished. In so doing, it implies that a murderer who does comprehend his crimes deserves to die.

The court presumably also allied itself with statistical rationality. But as Justice Samuel Alito points out in his dissent, some IQ tests have a standard error lower than 5. Of course, the very definition of "standard" error depends the level of confidence we want to have. Some common confidence intervals are 68 percent, 90 percent and 95 percent -- but strictly speaking, these are all based on consensus. While it's true that the error can be standardized, a standardization isn't "a statistical fact," as Kennedy puts it. It's a statistical convention.

The upshot is that although the majority presents itself as driven by professional, statistical rationality, it's in fact driven by medical consensus on the definition of disability. Yet that definition was developed to understand and, if possible, help the intellectually disabled -- not to determine who deserves to be executed. Kennedy borrows the authority of medicine to justify executions.

The death penalty is neither nice nor rational. But with this superficially liberal decision, it just got a little more entrenched in the court's jurisprudence.

Contact Noah Feldman at feldman@harvard.edu.