As the NFL Draft gets under way, one of the hot topics inside the league is the growing number of top prospects who have admitted smoking pot or have been caught doing so.

Based on information obtained from NFL team executives, agents, scouts and trainers, just under one-third of the 327 players who attended this year's NFL pre-draft scouting camp, or combine, had some incident involving marijuana turn up in interviews or background checks—which NFL teams collect and share before and during the event. This number represents...