It had been one month without football for Myron Rolle, an N.F.L. safety, and he was foundering. Mr. Rolle was just 25, and his pro football career looked grim: He was released in 2011 after three unremarkable seasons with the Tennessee Titans and had failed in his attempt to make the Pittsburgh Steelers’ roster. Without the structure and rigor of a football career, he struggled to make sense of what would come next.

Mr. Rolle had always had a Plan B. He had been a hot-tempered kid, but at 11, his older brother, Marshawn, gave him a copy of “Gifted Hands,” Dr. Ben Carson’s popular 1990 memoir that detailed how Dr. Carson went from being an inner-city youth with poor grades to the director of pediatric neurosurgery at Johns Hopkins University Hospital.