You hear it now and then from team higher-ups: “Our village can raise one child.” Every team thinks its culture is the one strong enough to soothe a knucklehead player away from his bad habits and into a team-first approach.

The Cavaliers and Knicks gave up on three such problem children yesterday in hosting the NBA’s version of a key party with Oklahoma City — a three-way deal filled with high hair, insane shot selection, and players prone to audacious proclamations. Needless to say it broke Twitter — and not in the way anyone ever expected J.R. Smith to break Twitter.

And yet, get past the funky characters involved and you can see a three-way deal that makes some sense for each team. The Cavaliers get wing depth and a 3-and-D player without doing much further damage to their already damaged cap sheet; the Knicks get salary relief and rid themselves of two players they no longer wanted; and the Thunder enter uncharted tax territory by gambling on a wing talent with a season and a half left on his cost-controlled rookie deal. Win-win-win? Maybe. Let’s dig deeper.

Cleveland Cavaliers

Perhaps the league’s most depressing story so far. They’ve underachieved on both ends and sit just three games over .500, with a tiny positive point differential to match that middling record. That understates how good they’ve been offensively; they’ve hovered around the top five in points per possession when healthy and they’ve scored at a rate above the Mavs’ league-best offense when all three of LeBron James, Kevin Love, and Kyrie Irving are on the floor.

The offense is not the fluid passing machine we all envisioned. The Cavs sprinkle in some funky stuff, but this is basically a souped-up version of the stagnant LeBron-centric offense they ran during his first stint as a hometown hero — one LeBron high pick-and-roll after another, with shooters dotted around him.

And that’s fine. You can destroy defenses that way, even if they all know what’s coming. A LeBron–Tristan Thompson pick-and-roll with Kyrie Irving, Wing Shooter X, and Kevin Love spotting up is a powerful weapon.

But it’s not the sort of offense that David Blatt ran in Europe, and having Love toggle between token post-ups and begging for the ball in the corner doesn’t maximize his value. There is a space between running the offense through Love, like Minnesota did, and marginalizing him. It involves leveraging his shooting ability at power forward by having him screen and cut all over the floor — sucking defenders into his moving orbit, opening up things for teammates.

In a healthy, continuity-based offense, things like this can both start a possession and work as a second or third option if Plan A yields nothing:

Love said all the right things about committing to Cleveland, but we should all know by now that public proclamations after happy trades mean nothing. He’s a free agent this summer, and he will absolutely survey the market if things continue this way in Cleveland. LeBron’s on-court demeanor toward him has been icy; James will regularly glare back at Love after yet another enemy layup in Love’s grill.

The defense has been even worse than expected, and Anderson Varejao’s season-ending Achilles injury won’t help. Love talked a big game about washing away his warts on that end, but he hasn’t walked it yet. He still admires his 3-point shots while his defender happily leaks out in transition. Love will never be a rim protector, but just trying can help. Raise your arms, jump in the air, and cause at least some sort of distraction.

There are just too many possessions on which Love does nothing as a help defender. He watches the game happen to him.

The problems aren’t all on Love. The roster doesn’t contain a functional center. Cleveland wasted too many spots on Friends of LeBron who can’t play, and while Joe Harris and Matthew Dellavedova are charming sorts who have their moments, they shouldn’t play major rotation roles on a title contender.

LeBron has been coasting, sometimes to an embarrassing degree, on defense. Chill mode, everyone. Here’s the tell that reveals a defender isn’t working: When his man passes out of some action and cedes control to a teammate, the defender will relax. He’ll stand up straight, lower his arms, watch the rest of the possession, and perhaps even creep toward midcourt in anticipation of a fast-break chance.

With LeBron doing this all the time, it has hurt Cleveland. They’ll dial all of this up in the playoffs, but nearly halfway through the season, they did not appear a legitimate threat to any of the Western Conference powerhouses — even while piling up points with all three stars on the floor.

This trade may not change that, but it helps. Shumpert’s ambitions for ball-dominant stardom rankled the Knicks, but he’s exactly the sort of 3-and-D player Cleveland sorely needs; I mentioned him as a target for Cleveland’s bizarre Keith Bogans trade exception before the season — which they still have after using the Varejao injury exception in this deal.

Cleveland had zero such players beyond LeBron. Waiters is shooting just 26 percent from deep, and in a weird twist, he has struggled horribly on open catch-and-shoot 3s in each of the last two seasons, per SportVU data. Those are exactly the kinds of shots he needed to hit in a LeBron-centric offense.

Waiters occasionally tried on defense, but he has been mostly awful — slow, unwilling, unintuitive. Shumpert isn’t a blowaway defender, and he’s a (slightly) below-average 3-point shooter for his career. But he’s long-armed and tenacious, he can guard multiple positions, and he should grade out as quite good on that end if he can just avoid his bad tendencies — gambling for steals and losing focus off the ball as his man cuts backdoor.

Shumpert can hit enough open 3s on offense, and he has shown some secondary playmaking chops — especially earlier this season in the triangle. He can’t run an offense on his own, but if LeBron bends the defense away from Shumpert and then kicks the ball to him, Shumpert can create something off the dribble. He’s a willing and smart passer in tight spaces, and a decent enough pull-up shooter from midrange when the shot clock is running down. He’s been turnover-prone, and he barely gets to the line, but he should be able to keep things moving in a background role.

Alex Goodlett/Getty Images

Smith is the tax that Cleveland must pay for acquiring Shumpert and a first-round pick from the Thunder — a pick that will likely fall around no. 20 this season or toward the back end of the first round next season. That’s a nice asset. It is well documented now that Cleveland has trapped itself in a place where it will be very hard to improve the roster in the easiest ways.

Shumpert and Tristan Thompson, a LeBron buddy, are free agents this summer. Re-signing both would rocket Cleveland way over the luxury tax, and that’s before even accounting for the possibility that the Cavs flip Brendan Haywood’s nonguaranteed contract for another high-salaried guy. Retaining both Shumpert and Thompson long-term might even imperil their flexibility in the vaunted summer of 2016, when most team executives expect the cap to rise by nearly $20 million — to something around $90 million.

Market-value deals for Shump and Thompson would take Cleveland well over that mark, assuming max-level contracts for LeBron and Love. A few other moves could take Cleveland close enough to the tax that even executing a sign-and-trade or using the full midlevel exception would be dicey.

That was already going to be the case before this trade. The needless Varejao extension put them in cap hell. Smith’s deal expires after next season, so he doesn’t affect their 2016-17 cap picture, and they were already going to be shot this summer. Shumpert replaces Waiters in the long-term cap projection.

He’s a better fit around LeBron, and Cleveland did well to add another pick beside the Memphis first-rounder it snagged two seasons ago. It won’t be a great pick, but the Cavs are avoiding the classic superteam trap of dealing away every possible method of restocking the back of the roster with young and cost-controlled players. It’s a much better than 50-50 bet that Cleveland uses one of its extra first-rounders to deal for a center; the Cavs are in serious off-and-on talks with Denver and Memphis about Timofey Mozgov and Kosta Koufos, respectively, per several league sources. They could always sign Samuel Dalembert once he becomes a free agent, but Samuel Dalembert has never been the answer to any team’s questions.

Smith, by the way, is a live body with a track record of doing some useful things in the NBA — even on good teams. Both he and Shumpert have to get healthy, but Smith is a much better shooter than Waiters, and he gives the Cavaliers a decent athlete on the wing who can actually play. That doesn’t sound like much, but the Cavs need real wing depth. It allows them to play smaller, using LeBron at power forward, without forcing so many one-dimensional liabilities onto the court.

The Cavs will need that kind of lineup flexibility until they somehow get a full stock of big men. Smith is a head case prone to jacking even worse shots than Waiters, but he can make more of those shots, and the Cavs won’t need him to play major minutes.

Oklahoma City Thunder

The Thunder nearly traded their first-round pick in the last draft, no. 29, for Shumpert, and they’ve essentially made the same trade here for Waiters. The deal puts them nearly $2 million over the tax for now, but this may be a precursor to another move down the line. The Thunder don’t have enough minutes for all of their wing guys, and they’re staring hard at Reggie Jackson’s free agency.

Jackson has been clear about wanting to start, and though the point guard position is super-deep, it seems almost certain he’ll find an eight-figure contract in free agency from someone. Matching that kind of deal would take Oklahoma City close to the projected tax for next season, the last year remaining on Waiters’s rookie contract.

Devoting something like $25 million combined to Waiters and Jackson after 2015-16 would erase a lot of Oklahoma City’s cap maneuverability going forward — even amid a skyrocketing cap — as Kevin Durant, Russell Westbrook, and Serge Ibaka all come up for fat raises. One of Waiters and Jackson may have to go, and if it’s Jackson, you can expect a lot of shouting about how the Thunder have cheaped out on another Harden.

But Jackson isn’t Harden. He’s a nice player, but he’s shooting 27 percent from deep, and there are games when he looks reluctant to launch open 3s. Teams don’t guard him, and that can muck up the Thunder’s spacing. Jackson and Westbrook can make it work on both ends, but it’s not a clean fit, and the Thunder would be justified thinking they might be able to do better for less money.

In the meantime, Waiters is worth a gamble. I’ve joked before about being one of the last, lonely residents of Waiters Island. All that bad stuff about him — it’s all true. But the guy can just do some high-level NBA things. He’s a nifty ball handler on the pick-and-roll; he can get into space, make tough shots, and toss some smart interior passes.

He reminds a bit of Evan Turner in this sense: We all rip him to shreds, and then he’ll do something — a hard drive, a slick drop-off pass — that tells you he can do stuff not many NBA guys can manage. And here’s the difference: Waiters, in shooting 37 percent from deep last season on his delightful moonballs, flashed at least the possibility of being a workable NBA 3-point shooter from outside the corners. Turner has never done anything like that.

Look at Oklahoma City’s wing rotation. Andre Roberson cannot shoot at all. The dude airballs open 3-pointers. He’s a plus defender, but if you thought defenders ignored Thabo Sefolosha, wait until you see how they treat Roberson in the playoffs. Anthony Morrow is among the world’s greatest shooters, and he’ll feast once he gets to play sustained minutes alongside both Russell Westbrook and Kevin Durant. But he can’t defend a lick, and though he has developed something of a one- or two-dribble floater game, he’s not someone who can reliably create against good defenses. Jeremy Lamb has a nice week and then vanishes for months. Ditto for Perry Jones III, though he at least brings the flexibility of sliding to power forward.

In that context, I’d bet on Waiters — especially since he’s on an affordable contract through next season, unlike Jackson. But let’s go easy suggesting Waiters can play the Harden role. Harden was, like, good at basketball on a regular basis coming off the bench for OKC. Great, even. Waiters has no track record of doing that over any prolonged stretch. In an ideal world, Waiters would provide just enough defense and shooting to be a poor man’s amalgam of Morrow and Roberson. But it’d be shocking if Waiters developed enough on defense to fulfill that ideal.

Still: It’s a decent way to monetize Oklahoma City’s first-round pick. And by the way: Good work by Sam Presti protecting the pick the way he did. The pick is top-18 protected this season, meaning the Thunder keep it if they miss the playoffs or make it with a worse record than enough top Eastern Conference teams. It’s top-15 protected over the next two seasons, per Brian Windhorst of ESPN.com, meaning they keep it if they miss the playoffs in 2015-16 or 2016-17.

That’s key for two reasons: Durant’s future is uncertain, and the league will revisit lottery reform soon. Presti was perhaps the loudest voice outside Philly agitating against lottery reform, and he made sure to eliminate any chance of losing a pick that gets tossed in a revamped system featuring better odds for the “best” lottery teams. After 2017, the pick reverts to two second-rounders. That is smart hedging.

New York Knicks

The Knicks are in full-on tank mode, and they’re saving something like $20 million in salary and tax payments by dumping Smith and Shumpert for a second-round pick and two trade exceptions. Who knows if the Knicks will ever use those exceptions; Presti just used one to snag Waiters, but the Knicks won’t be in salary-adding mode unless they can snag a pick as the price of doing business.

That could change next season if New York hits a home run in free agency and this deal clears Smith’s poisonous $6.4 million option from its books. The Knicks could still have carved out max-level room this summer even with Smith onboard, but it would have been close, and Shumpert’s cap hold would have torpedoed any such scenario. The Knicks will now have something like $27 million in space — enough to add a superstar and a role player. We’ll see how they do. No team knows better the winner’s curse of signing the fourth- or fifth-best max-type free agent on the market.

The Knicks did not get enough for Shumpert in the end. They balked at taking a low first-rounder for him last season, and now they’ve lost him for tax relief and some flexibility they might not have needed. Yes, Shump’s appeal allowed them to offload Smith, but they got next to nothing for a solid young player, and they could have had $20 million in space this summer even with Smith around. That’s poor asset management, even if Shumpert had worn out his welcome in New York.

It’s all about this summer for the Knicks, though. They’re in the awkward spot of rebuilding around a 30-year-old maxed out star with knee issues. That’s not a situation in which patience is really an option.