Offensively, we know what he brings to the table. His development on the offensive side of the floor has been impressive. We can recall the times where a fair amount of his shots were blocked in his rookie year, to him demonstrating a bevy of post moves on the block. His hook could use some work, and he still doesn't have much of an outside shot, but he's becoming a stud to say the least.
Defensively, he's the polar opposite. Synergy ranks him 81st in picking up his man on the P&R, as his assignments shoot 53% from the floor. However, this statistic does not illustrate the entire picture. The video clips that they show for every single possession can't highlight how many times the defense collapses because Monroe struggles picking up either the guard or the roll/pop man. Also forget about him even closing out on open shooters altogether. In a league that's becoming smaller & faster, Monroe's slow feet is really damaging, especially for a potentially max-contract guy.
Grantland went even further on his off-ball defense:
His off-ball defense is similarly unintuitive. Monroe wants to help and has a rudimentary sense of where he should be as the chess pieces move around the floor, but he’s unsure of himself and prone to fatal hesitations and bouts of confusion. He has struggled to develop any chemistry with his big-man partners, so that a lot of Detroit possessions end with late help rotations or both bigs chasing one opposing big man — each under the impression the other would be elsewhere on the floor. Watching film of Detroit’s defense basically amounts to sitting through an hours-long reel of dunks, shrugged shoulders, and inattentive help; only eight teams allowed more shots at the rim last season, and only three allowed opponents to shoot a higher percentage than the ghastly 61.1 percent Detroit allowed.
To use one example of a simple play with which Detroit and Monroe had depressingly chronic issues: Monroe in the below photo (standing at the right edge of the paint) is only just realizing Nicolas Batum, having caught the ball after flying around a Joel Freeland screen and drawing Freeland’s man onto him, is about to hit Freeland for an easy dunk.
Josh Smith is unique in which he can pick up both the guards and the roll man if he has to with efficiency. That level of versatility is worth using more often at the power forward position. He'll always be an enigma offensively, but he has historically found great success at the 4. I know it sounds crazy, but Monroe just isn't a power forward defensively. The paring of him and Drummond will never work when almost every team can stretch the floor with relative ease.
Detroit should just bite the bullet and let him walk, but that'll never happen. Smith will be the one shopped out, and Detroit will still be in the basement as far as defensive rebounding and opponent's FG%'s are concerned.