Right now, the Celtics like to protect the paint by using aggressive on-ball perimeter defense to make it hard to penetrate. With a lack of rim protecting bigs to serve as a last line of defense, the scheme seems more focused on controlling real estate. Big men are called upon to be good help defenders and to protect against the pick and roll. The scheme may change a bit with a defensive anchor who is a shot-blocking threat, but I suspect that strong perimeter defenders will be preferred.
Above all, however, Stevens seems to want commitment to defense, so hard and consistent effort, combined with enough intelligence to be teachable as to where you are supposed to be on the floor at all times, seems to be what is needed to fit into the Celtics defense. If you can do that, Stevens will figure out how to use your talents on offense. If you can't do that, Stevens will probably not let you shoot your way into playing time.
If we go with the idea that talented offensive players who take defensive plays off and are lazy about rotations may not see the floor so the Celtics might as well not draft them, and that Stevens will prefer a player with average athleticism and good awareness over elite athleticism with poor awareness, who are the players most likely to display that "defensive DNA" that Stevens wants as central to the Celtics identity and who are the players that the Celtics should not draft if they are never going to play because they will fail to fit that identity?
I've really only looked at players who might be available for the Nets pick so I'd like to know about possibilities for the later picks who are very good or very bad on this criterion, even if you think the rest of their game is so bad that you do not want or so good that you covet them.