IN THE SUMMER of 2019, Connor Pardoe was trying to persuade Life Time, Inc., a health-club chain and the largest private operator of tennis courts in the U.S., to embrace a different game. Pardoe, then 26, was peddling pickleball: a racquet sport similar to tennis but played on a much smaller surface, over a slightly lower net, with a squarish paddle and a perforated plastic ball. The year before, Pardoe had left his family’s real-estate business to build the Professional Pickleball Association. As he hunted for tournament venues, he went straight for the flashiest sites in pro tennis. “We started big, reaching out to the Miami Open, the Lindner Family Tennis Center, where they play Western & Southern. A lot of those guys weren’t too interested,” he says. After all,…