At the Scouting Combine, former Michigan State linebacker Max Bullough said his suspension from this year’s Rose Bowl for violating team rules was “not going to affect my draft stock whatsoever.” But it did: Bullough has undeniable NFL talent, but he went undrafted.

That’s a common trait among many of the most talented players who weren’t selected in this year’s NFL draft. Teams may like your talent, but if they don’t like your character, they don’t want you in their locker rooms.

LSU defensive tackle Anthony Johnson is the kind of powerful 300-pound athlete NFL teams are looking for on their defensive fronts, but he reportedly failed a drug test at the Scouting Combine, and he wasn’t drafted.

Florida had two cornerbacks who were passed over despite being good enough to be drafted, Loucheiz Purifoy and Marcus Roberson. Purifoy reportedly was caught with drugs last month and avoided arrest by agreeing to work as a police informant. Roberson served a suspension during his career with the Gators.

Colt Lyerla was once viewed as one of the top tight ends in college football during his career at Oregon, but Lyerla had a string of off-field issues that resulted in him leaving the team during the 2013 season. Lyerla was also arrested on a drug charge shortly after he left the Ducks, and those issues resulted in Lyerla going undrafted.

All those players still have a chance to sign on as undrafted free agents and prove they belong in the NFL. But teams are wary of players with off-field red-flags, no matter who talented those players are.