“The obvious one sometimes is the power forward position,” Toronto Raptors GM Masai Ujiri said when asked at his season-ending press conference about off-season priorities. “With the way the NBA is going, and also the emergence of [Jonas] Valanciunas and [Bismack] Biyombo, it’s a position where we really have to kind of get creative and figure out what’s going to work.”

The position has been in flux since Amir Johnson left summer, and was a big topic around the trade deadline as well. But it’s proven difficult to address.

Luis Scola was added in July and played well in a starting role particularly in the early going, hitting a career-high 40.4-percent of his threes in 76 regular-season games as a starter. But his lack of defence contributed to a lot of poor first quarters for the Raptors, and reduced him to limited minutes in the playoffs. Patrick Patterson, meanwhile, provided defensive intensity and shooting on the league’s best bench unit throughout the season, but wasn’t able to raise his game when thrust into the starting lineup in the playoffs.

Patterson, playoffs Reserve Starter MIN 26.7 32.3 FG% 0.444 0.370 3P% 0.324 0.273 TRB 3.2 4.7 PTS 7.2 8.2

What’s more, Scola is a free agent and at this point seems unlikely to return. So the Raps will make a move this summer, and ostensibly for a starter.

While Ujiri said at the same press conference he might keep both first-round picks Toronto owns in the coming draft (ninth and 27th), he also said he’d be open to moving one of them. And given the immense value placed on lottery picks now (they’re not tied to the cap, so will be even cheaper assets the next couple of years as other salaries skyrocket), moving No. 9 as part of a package would open up a lot of deals, whether in two- or multiple-team swaps.

The only question remains: Which potentially available players fit the bill of what the Raptors are looking for? Given the strengths and weaknesses of the pieces they already have in place, they need a guy who can defend out to the perimeter, clean up the boards at a decent rate and space the floor at the other end with shooting at least out to the three-point line if not beyond it.

Doesn’t sound like the tallest order in the world (is that a pun? I mean, we’re talking about basketball players here. If we’re calling it a pun, then pun intended), but looking at the starters for the league’s other 29 teams doesn’t reveal a ton of obvious fits. Many offer one of the items on the checklist, but then completely fail everything else. And among the guys who check off every box, several are sure to be untouchable.

Let’s break them down, category by category:

NOT ENOUGH DEFENCE

Starting PFs, 2015-16 Age PER 3PAr DRB% BLK% DBPM VORP Kevin Love, CLE 27 19.0 0.449 28.4 1.4 0.9 2.8 Tobias Harris, DET 23 16.2 0.269 18.6 1.3 0.4 1.9 Mirza Teletovic, PHO 30 16.2 0.592 16.3 1.0 -2.7 0.7 Zach Randolph, MEM 34 18.3 0.029 20.7 0.6 -1.1 0.6 Jabari Parker, MIL 20 14.8 0.039 12.8 1.0 -1.5 -0.2 Donatas Motiejunas, HOU 25 11.3 0.278 14.6 0.8 -1.9 -0.3 Noah Vonleh, POR 20 8.6 0.165 19.8 1.7 0.0 -0.6 Julius Randle, LAL 21 13.9 0.043 32.0 1.0 0.0 -0.9

The main reason Scola has been labeled a poor fit is his inability to defend, so getting a guy with a similar weakness is just not going to happen. While Love’s multi-faceted offensive game would make him a clear upgrade on that end, he doesn’t provide value on defence beyond cleaning the glass. And also, as we’re seeing in the finals, he isn’t his most productive self when relegated mainly to the perimeter.

NOT ENOUGH SHOOTING

Starting PFs, 2015-16 Age PER 3PAr DRB% BLK% DBPM VORP Amir Johnson, BOS 28 16.0 0.101 19.6 3.6 3.2 2.3 Nerlens Noel, PHI 21 16.2 0.003 22.2 3.9 3.4 1.3 Thaddeus Young, BRK 27 17.5 0.031 23.0 1.2 0.6 1.3 Kenneth Faried, DEN 26 21.0 0.003 23.0 2.9 -0.1 1.2 Willie Cauley-Stein, SAC 22 15.3 0.006 16.6 3.8 1.5 1.0 Markieff Morris, WAS 26 12.2 0.216 19.3 1.7 0.1 -0.3

While I like Cauley-Stein and Noel as centre prospects, Randle is the most interesting power forward name to me here because he has the potential to turn into something despite a so-so rookie season. That said, the whole point of this exercise is to find someone ready to contribute in the starting lineup this November. And, judging by this shot chart, Randle still needs a little seasoning:

Some room to improve there.

NOT GOING ANYWHERE

Starting PFs, 2015-16 Age PER 3PAr DRB% BLK% DBPM VORP Draymond Green, GSW 25 19.3 0.315 23.0 3.0 3.9 5.5 Karl-Anthony Towns, MIN 20 22.5 0.076 27.5 4.3 1.2 3.1 Anthony Davis, NOP 22 25.0 0.095 26.4 4.7 1.2 2.3 Derrick Favors, UTA 24 21.6 0.005 19.6 3.9 2.3 2.3 LaMarcus Aldridge, SAS 30 22.4 0.015 22.2 2.8 1.1 2.2 Chris Bosh, MIA 31 20.2 0.289 21.1 1.5 -0.3 1.8 Aaron Gordon, ORL 20 17.0 0.245 21.3 2.4 1.2 1.8 Dirk Nowitzki, DAL 37 19.0 0.308 20.3 1.8 -0.3 1.7 Blake Griffin, LAC 26 22.1 0.030 22.3 1.1 1.6 1.6 Kristaps Porzingis, NYK 20 17.7 0.274 20.7 5.0 0.9 1.1 Myles Turner, IND 19 15.4 0.026 21.0 5.1 1.4 -0.1

For various reasons (franchise player on a contending team, too tied to a team’s past, too tied to a team’s future, health status up in the air, their coach/GM has stated emphatically he’s not trading them, etc.), these guys aren’t getting traded—anywhere—this summer.

And so, once all those guys are taken off the table, we’re left with the following:

TARGETS

Starting PFs, 2015-16 Age PER 3PAr DRB% BLK% DBPM VORP Paul Millsap, ATL 30 21.3 0.218 21.5 4.1 4.2 4.9 Marvin Williams, CHO 29 16.8 0.506 18.6 2.7 1.0 2.7 Nikola Mirotic, CHI 24 15.6 0.568 19.1 2.0 0.1 1.3 Serge Ibaka, OKC 26 13.9 0.212 16.2 4.5 1.0 1.2

And here we go. I could see any of these four moved from their current situations for the right deal.

If I’m Ujiri (I’m not; I’m much, much worse), and if Atlanta pulls off that rumoured Nerlens Noel-for-Jeff Teague trade signalling a major rebuild, I’m going hard after Millsap. Not only does he check off every box—he rebounds, he shoots, he might be the most underrated defender in the league after being the only guy in 2015–16 to appear in the top five in defensive rating, defensive win shares and defensive box plus-minus—but he’s exactly the type of character guy the team is looking for.

As for the other guys on the list: Not too long ago Ibaka probably would’ve been among the untouchables above, but he’s seen a dip in production in each of the last two seasons, and his PER sat below league average in 2015–16. That said, he still represents an upgrade for the Raptors. Plus, OKC has a habit of selling on pieces before they hit free agency, and with big paydays on the way for Kevin Durant and Russell Westbrook they could (could, mind you) be looking to trade him this summer for a cost-effective asset not unlike the No. 9 pick.

Williams, the only player among these five not under contract for next season, is interesting to me, too, though it would take some financial wizardry to even offer him a contract. (Despite what you’ve heard about every team having a large amount of space due to the rising cap, the Raps won’t be among them unless they dump salary in a trade with a team that can absorb the incoming contract while remaining below said cap.)

Still, though, Williams has rounded into a productive player as a full-time power forward, and he’s managed to outlive the “bust” label he got when the Hawks took him over Chris Paul and Deron Williams in the 2005 draft. And he definitely provides both high-volume (.506 three-point attempt rate) and efficient (40.2 percent) three-point shooting:

Last on the list, Mirotic is certainly not known for his defence (in fact, putting him in here kind of breaks the rule about getting an upgrade on D…), and he spent the season bouncing in and out of Fred Hoiberg’s starting rotation in Chicago. But the Bulls will likely lose both Pau Gasol and Joakim Noah this summer—meaning the entire frontcourt could get a makeover.

Mirotic is just 24, was nearly Rookie of the Year in 2014–15 and still has upside. Given the lack of even remotely likely options, that might be all the Raptors can ask for.

Correction: An earlier version of this story listed DeMar DeRozan’s cap hold this summer as $10 million. Should he opt out of the final year of his contract as expected, his cap hold will actually be $15,075,000.