The music business is all about the next big act, the next big performer. Who’s going to break out. Who’s going to be the next household name. The Grammys, over the years and to varying degrees of success, has delivered that prediction with its Best New Artist prize.

Starting with Bobby Darin in 1960, the award has been the harbinger of who’s going to be topping the music world … some of the time. Darin didn’t do too bad in his long music and acting career. In 1965, a little combo from the UK made the cut and The Beatles went on to become one of the greatest bands ever.

Some other highlights of the Best New Artist roster. In 1962, Peter Nero was the first jazz musician to win. Bobbie Gentry was the first woman to win in 1968. The Carpenters, Richard and Karen, was the first duo to win...