A pair of power players on the North American sports scene are looking to their in-house staff to help address scandals related to their core operations.

Nike Inc., which in October shuttered its Nike Oregon Project, has said publicly it will investigate abuse claims brought by athlete Mary Cain in a New York Times op-ed last week against the long-distance running program’s former coach.

Major League Baseball also confirmed this week that it would investigate allegations that the Houston Astros stole pitching signs from opposing teams in 2017, a season that resulted in the franchise’s World Series victory over the...