MIAMI — For Ted Herring, who has spent 32 years on Florida’s death row for murdering a store clerk, signs of intellectual disability arose early and piled up quickly: He repeated first grade and got D’s and F’s through fourth grade. He read like a fourth grader at 14 and did not know that summer followed spring.

By then, a psychologist in New York City, his hometown, had declared him “undoubtedly functionally retarded.” Life was no less trying in his late teens; he could not hold down a job, and something as simple as transferring buses posed a challenge.

His intellectual disability was even obvious to a Florida judge, who found him “mentally retarded” and took him off death row 18 years after his original sentence. At 19, in 1981, Mr. Herring murdered a Daytona Beach 7-Eleven clerk, robbed the store and walked away with $23.84. But because Mr. Herring’s I.Q. scores were 72 and 74, just over the “bright line” cutoff of 70 used by Florida to determine intellectual aptitude, the Florida Supreme Court returned him to death row.

When the Supreme Court ruled this week that states can no longer rely on a fixed I.Q. score cutoff to decide intellectual competency, it increased the likelihood that Mr. Herring and other death row inmates like him will have a chance to avoid execution. Fewer defendants are also less likely to wind up on death row in the future because their claims of intellectual disabilities will be not be as readily discounted by the courts.