Gale Sayers, the will-o’-the-wisp running back who in a short but brilliant career with the Chicago Bears left opponents, as they used to say, clutching at air, died on Tuesday at his home in Wakarusa, Ind. He was 77. His son Guy Bullard said the cause was complications of dementia and Alzheimer’s disease. In March 2017, his family revealed that Sayers had dementia after he had publicly displayed symptoms of it for four years. He joins a growing list of football players who developed dementia and died of brain damage while still young. Though his career was cut short by knee injuries, “Sayers is the greatest halfback I ever saw, ” Ernie Accorsi, who was general manager of three National Football League teams, wrote in an email in 2017. Jim Brown was the greatest running back of all time, he said, and some great fullbacks may have had more heft and power than Sayers — who was six feet tall and weighed 198 pounds — but nobody could cut corners like Sayers.“I never saw anyone who could be at full speed, stop on a dime and, in one step acceleration, be at top speed again, ” Accorsi said. “I saw runs he made that if it was one-handed touch football instead of tackle they couldn’t have caught him. ”As Sayers himself said of ability to elude tacklers in close quarters, “All I needed was 18 inches. ”Sayers’s fame reached beyond the football field in 1971 with the broadcast of the Emmy Award-winning television movie “Brian’s Song, ” based on his friendship with his teammate Brian Piccolo, who died of cancer at 26. A consensus all-American at the University of Kansas — where he was called “the Kansas Comet” — Sayers chose to play for the Bears of the established N. F. L. over the Kansas City Chiefs of the upstart American Football League in 1965. He went on to have one of the greatest rookie seasons ever. He led the league in all-purpose yards (rushing, receiving and runbacks) with 2, 272 yards; scored 22 touchdowns, six of them in one game; and was named to the all-league team for the first of five consecutive years. Sayers was already a legend in 1967 after two pro seasons, when Rick Volk, a safety from the University of Michigan, tried to defend against him while a college all-star team was training at the Bears’ camp.“He was amazing, ” Volk recalled in 2017.