The Philadelphia 76ers’ practice facility is one of the largest and most expensive in the NBA—an $82 million, 125,000-square-foot behemoth that boasts a hydrotherapy room, a recording studio and a full-service restaurant. It’s the morning of a home game versus the Miami Heat, and the 76ers have just finished a light practice on one of two regulation-size basketball courts.

Meanwhile, in the strength and conditioning center next door, five women ages 22 to 27 are stretching their wrists. If not for their team-sponsor Buffalo...