As another edition of March Madness looms, the NCAA is accelerating the search for new cutting-edge data tools to better measure which teams should be invited to the annual college-basketball extravaganza and which ones should stay home.

When the selection committee convenes next month to pick teams for this year’s tournament, it will again lean heavily on a 36-year-old formula called Rating Percentage Index. Used since 1981, it attempts to take 351 Division I teams that play vastly different schedules and rank them based...