Before he won the Masters last month, Danny Willett had limited experience at Augusta National Golf Club. He had played in the tournament only once before, and was among the last players to arrive for practice rounds this year. But Willett also knew something many of his competitors did not.

His caddie had received an email from a London analytics firm with data that offered a hidden insight about Augusta’s par-5 holes. The numbers showed that when players lay up—leaving their ball short of the green to avoid a water hazard—they...