Late one recent night on Bible Street in Cos Cob, Conn., in the carpeted basement apartment of a gray bungalow, Mike Sandlock, 97, had a dream that he was in Yankee Stadium.

A tall, white-haired great-grandfather, he stood at the plate, under pressure to hit a home run. “I says: ‘That’s not me! I’m not a home run hitter!’ ” Sandlock protested. Nonetheless, he crushed one into the right-field stands, then woke up.

“I have crazy dreams anyway,” Sandlock said dismissively.

About 82 years earlier, when Sandlock lived about three miles from where he does now, he took the train one day to the Bronx with his older brother. It was his first time in Yankee Stadium, and Babe Ruth was in his prime. Sandlock sat in the right-field bleachers, and Ruth hit a towering drive well over the teenager’s head....