Young, skilled, strong and savvy, the 24-year-old is a unique player in a league littered with larger-than-life specimens.
But the "Moose" stands out for the wrong reasons. A throwback force on the low block, he's alone in the supply column yet still outweighing the demand. Teams can recognize both his talent and production, but no one is buying ground-bound, defensively deficient bigs at the moment.
Not even the Detroit Pistons, the only NBA employer Monroe has ever known.
It's not that the Pistons want Monroe to leave. In fact, the news coming out of the Motor City suggests the opposite.
"Greg Monroe is a very important piece of the puzzle in Detroit and we want him back very, very much," coach-president Stan Van Gundy said, per the team's official website. "We’ll see what happens over the next weeks, months, whatever it takes."
The problem for the Pistons, and more so for Monroe, is that their pivot is an awkward fit—for them and every other team pushing further out to the perimeter.
"Monroe is a tricky player around which to build," Grantland's Zach Lowe wrote. "An ideal roster would surround him with at least one big man who can both shoot from range and protect the basket, and there are maybe a half-dozen guys who can do both of those things at an elite level."
The Pistons don't have one who can do both at even a passable level.
Andre Drummond is an explosive 6'10" shot-blocking terror, but his offensive range doesn't extend past the restricted area. Of his 479 made field goals last season, more than 91 percent were either dunks (183), layups (177) or tip-ins (78), per Basketball-Reference.com.
Josh Smith has a shooter's trigger but not a shooter's touch. His career 27.9 three-point percentage hasn't stopped him from launching 729 triples over the past four seasons. Outside of perhaps preparing for life-after-basketball work as a bricklayer, his perimeter shooting serves no purpose.
Considering Monroe is a career 31.7 percent shooter from beyond 10 feet, it's hard to imagine less complementary players with which to pair him. It's as if deposed general manager Joe Dumars built his frontcourt outfit for an ugly sweater party, not an NBA season.
The trio looked as bad in practice as it did on paper.
The Pistons were outscored by eight points per 100 possessions during the triad's 1,361 minutes together, per NBA.com. Of Detroit's 11 three-man lineups that played at least 800 minutes, none was less efficient.
That's why the Pistons are rightfully proceeding with caution in Monroe's contract negotiations.
Even an offensive mind as sharp as Van Gundy's can't manufacture space without shooting. And without room to operate on the low block or high post, Monroe's offensive talents are wasted.
At the opposite end, there are holes in his game wherever he plays. He's either a power forward with limited mobility or a center who offers no rim protection.
"Monroe has neither the feel for coverage nor the vertical lift to really challenge opponents at the basket, making it all the more important that he be flanked by a player who can," wrote Sports Illustrated's Rob Mahoney. "At the same time, Monroe's minutes at power forward have illustrated his troubles in recovering out to perimeter threats."
He requires careful planning for his production to be maximized.
When he gets the time and space needed to work, he's an impact player on the offensive end. He punishes post defenders with power and finesse, and he's a crafty player on the elbow whether attacking the basket or hitting an open teammate.
Even in Detroit's round-peg-square-hole setup last season, Monroe still managed to become one of 12 players to post at least 15 points and nine rebounds. He has reached those marks in each of the last three seasons, a claim only five other players can make.
But, again, his quiet reception on the free-agent market isn't a reflection of his talent. It's the simple result of teams having less interest in what he brings to the table.
So, what does that mean for his future and that of the Pistons?
For starters, it's pretty clear that his max-contract bubble has burst. If any team ever had the desire to pay that type of premium, it has since invested its funds elsewhere.
If Monroe finds an offer sheet outside of Detroit at this point, it's hard to imagine the Pistons balking at the lower price.
"No one has cap space or motivation to offer him a deal now because the Pistons will just match," CBS Sports' Matt Moore noted. "That leaves Monroe with the hanging threat of signing his qualifying offer and risking injury to hit unrestricted free agency next season."
Monroe, along with the rest of the hoops world, apparently recognizes his poor fit with the Pistons.
As Yahoo Sports' Adrian Wojnarowski told Aime Mukendi Jr. of the AIMEzing Words podcast, "Monroe doesn't really have a great interest in going back and playing with these Pistons" (h/t Sean Corp of Detroit Bad Boys).
Surely, the Pistons can see it, too.
But, at the moment, these two need each other.
Monroe isn't likely to find more money elsewhere this summer. And, despite the clumsy fit, he's still one of the most talented players on Detroit's roster and all of 24 years old. The Pistons need to get something of value from this, either via trade or figuring out a way to make this work.
What is the best move the Pistons can make with Greg Monroe?
An ideal conclusion for both sides might be a one-year deal. Not for Monroe's $5.5 million qualifying offer—that's an insulting rate if the Pistons want to keep him around—but rather something that gives him a low-end eight-figure salary.
That way, Monroe doesn't leave the summer completely disappointed, and he still has the option of improving his situation next year. Van Gundy gets 12 months to attempt to offload Smith and the $40.5 million left on his deal, which would give the Pistons the best-case outcome of retaining their top two bigs.
However Monroe pictured the free-agent market, surely he didn't envision his situation playing out like this. But a one-year reunion with Detroit is far from a disastrous outcome for either side.
It might be the best move he and the Pistons can make at this stage of the game.