The trajectory of an entire sports league can turn on random things. If you gave Heat officials truth serum three weeks ago, after they had vanquished an imploding Indiana team, they’d have told you they preferred Oklahoma City as a Finals opponent.

The Thunder have three overwhelming athletes, but even a wheezing Heat team has a fighting chance against elite athleticism, provided it comes without a sophisticated offensive scheme. The Heat might not have beaten the Thunder, but they’d have had a better chance than they did against San Antonio. The Thunder might not have beaten the Spurs had Serge Ibaka been healthy for the whole conference finals, but they’d have had a better chance.

In other words: You don’t have to squint too hard to see a scenario in which the Heat three-peat, or at least emerge from the Finals without having been disemboweled — a scenario in which the world is not wondering whether the Heatles era is over.

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But the Spurs broke Miami. They demoralized the Heat, and Dwyane Wade’s second straight depressing Finals performance hammered home the notion that Miami must prepare as if he will end every season that way. This Heat team is in decline. If all three stars opt in for next season, or just return at similar salaries, Miami will have limited means to improve the supporting cast.

The Heat have a first-round pick in this draft, and during a Thursday press conference that was mostly a bombastic monologue, Pat Riley mentioned that James Ennis, a 2013 second-rounder whom the Heat acquired in a draft-day trade, might join next season, after a year playing overseas. Toss in Udonis Haslem’s $4.6 million player option and Norris Cole, and the Heat would have about $70.5 million committed to eight players if all three stars opt in next season. That would make it difficult, and perhaps even impossible, for the Heat to use the full midlevel exception; Riley hinted Thursday that the Heat may have to use the smaller one for tax teams in order to duck both the tax and the hard salary ceiling that comes for any team using the bigger midlevel.

Dodging the tax might be a must for Miami. The Heat have paid it in all three seasons since the lockout, meaning that if they pay again next year, they’ll be the first team to suffer the extra-harsh repeater penalties reserved for teams that fly into the tax four times in a five-year span. Riley said Thursday he would not ask any of his three stars to take a pay cut — that he would leave it to them to volunteer. But Miami will be hamstrung in team-building, again, unless it cuts projected salary somehow — by coaxing a cut from someone, or striking a wink-wink deal with Haslem to opt out in exchange for a guarantee of a front-office job.

LeBron could look at this roster and plausibly conclude it no longer represents his best chance at long-term championship contention. But where else would he find that? LeBron can in theory force his way to any team, especially if he’s willing to take a larger pay cut than most would have expected possible even a year ago. LeBron could go anywhere, without any cap gymnastics, if he’s willing to shock the world by accepting only the midlevel exception.

He could also opt in for just one more season in Miami, suss out the franchise’s plans, and see what the free-agency landscape looks like a year from now. James is sensitive about his legacy, and surely understands that jumping teams again would brand him a mercenary.

But let’s assume LeBron opts out and considers some suitors who can contend immediately and offer a reasonable salary without any complex cap machinations. Any fits?

Chicago Bulls

The Bulls could open up about $13 million of cap room if they use the amnesty provision on Carlos Boozer, though the precise figure would depend on what Chicago does with its two first-round picks, and whether they want to bring Nikola Mirotic over from Europe. They could crack open $5 million more by finding a landing spot for Mike Dunleavy and using one of their two first-rounders on an international draft-and-stash guy. That gets them in range.

That is exactly what Chicago would do in order to sign Carmelo Anthony in straight free agency, and if you’re chasing Anthony, you might as well at least call LeBron. A core of Derrick Rose, LeBron, Joakim Noah, Jimmy Butler, and Taj Gibson would be an overwhelming favorite to get out of the Eastern Conference. If LeBron cared only about winning, this is a better option than Miami.

And not to restate the obvious, but the East-West split is huge. If your no. 1 goal is to win a title, you should absolutely get yourself into the NBA’s minor league. Critics want to discredit the Heat’s “runner-up” status by pointing out they merely had to prance through the East, and there’s some validity to that. But the Big Three didn’t choose Miami by accident.

The fit would also be appealing. James can share ballhandling duties with Rose, which would allow Rose to ease back into stardom after two lost seasons. Noah is a skilled high-post passer, meaning LeBron could own the low block when optimal. Working from there would be easier if the Bulls could separate the Noah-Gibson duo a bit; they’ve rarely played small over the past two seasons, but LeBron is the ultimate enabler of lineup flexibility. He’s an elite defender when motivated, and he could adapt to Tom Thibodeau’s conservative scheme — a system that would be a bit kinder to his legs as he ages.

Winning isn’t the only factor, of course. There is some legitimate bad blood between Chicago and Miami, and joining a Central Division team would mean slamming another nut-shot into the city of Cleveland.

Houston Rockets

The same general principle holds true here: If Houston has a series of transactions lined up that would free it to chase Melo, the identical domino effect would allow it to chase James. The fit here might be a bit more awkward, though Houston, unlike Chicago, has embraced small-ball lineups over the past two seasons.

Dwight Howard is strictly a paint player, and it’s harder for LeBron to find maneuvering room on the block if there’s another behemoth standing (along with his defender) just across the paint. That’s especially so because James loves to turn toward the middle, draw defenders, and kick to open shooters.

Howard soaks up a lot of possessions with his own post-ups, and James Harden loves to jab-step away before and after running high pick-and-rolls. But greatness eventually trumps fit issues. We ranted and raved about the skill overlap between James and Wade in their first season together, but they came within two wins of a championship.

By the way: Note the number of teams that would have to dump salaries to chase the league’s elite free agents. This would seem to present a nice opportunity for teams with cap room to extort the desperate dumpers. But there are so many teams with cap room, the extortion process might not yield more than a second-rounder or two. We’ll see.

Phoenix Suns

There’s a near-zero chance of this happening, but Phoenix should be a viable landing spot if LeBron wants to earn his actual max on an up-and-coming team with a smart new head coach who favors an exciting style of play.

The Suns have so much cap flexibility, they might be able to sign LeBron to the max, re-sign Eric Bledsoe at close to his (lower) max, and still have max-level cap room in the summer of 2015. They’re flush with extra first-round picks, meaning they’d have weapons to land another star player over the next couple of years.

In the short term, LeBron can take some of the ballhandling duties from Bledsoe and Goran Dragic, give the team the killer low-post threat it lacks on nights Markieff Morris’s midranger isn’t falling, and seal up a below-average defense. The Suns’ two most important rotation big men, Morris and Channing Frye, can shoot from the outside, giving LeBron free rein to occupy the post when he wants.

Having full access to one of the league’s best training staffs is a nice bonus for any player approaching 30 with nearly 28,000 minutes under his belt.

This is one of those ideas that won’t happen simply because it’s too far out of the box. Players don’t have a ton of affection for Robert Sarver, the team’s owner, a lockout hard-liner who went through a draft pick–selling spree in the mid-2000s. (In fairness, the Suns also paid a bit of tax during three separate seasons late in the Nash era.) But wouldn’t this be fun?

Atlanta Hawks

Go ahead, laugh it up. The Hawks might be the most consistently successful punch line in sports. People mock their dead crowds, their hallowed tradition of playing first-round games on NBA TV, and their uncanny ability to peak at “pretty good” during high times.

But Atlanta could clear about $17 million for LeBron if it salary-dumps Lou Williams onto one of many, many teams slated to have enough space to soak up his deal. That’s not LeBron’s max, but it’s close. If LeBron is willing to take a haircut, he’s going to do it in Miami, but this is a fun roster to contemplate.

Good freaking luck trying to guard a starting lineup of Jeff Teague, LeBron, Kyle Korver, Paul Millsap, and Al Horford. That is a ton of shooting and creativity, and if you play stretches with Pero Antic in Horford’s spot, the degree of 3-point shooting reaches scary levels. There’s enough defense among the LeBron-Millsap-Horford trio for the Hawks to survive on that end, and Mike Budenholzer would have them playing a sound system.

The Hawks under Budenholzer and Danny Ferry are trying to build the Spurs East, only with more 3-point shooting. (Budenholzer is a shooting zealot, and was known as Matt Bonner’s strongest backer on the Spurs’ coaching staff.) They want high-IQ players who keep the machine moving, share the ball, and shoot from range. Ball-stoppers need not apply. You think LeBron fits that vision? Duh.

Atlanta’s cap sheet is lean enough that it could ink LeBron to a big long-term deal and still have plenty of flexibility to continue building the roster around him.

LeBron could even bike to games with Harry the Hawk.

You could make arguments for a few other cap-room teams, including Dallas and LeBron’s hometown Cavaliers, but neither team would be quite as deep as the above four — unless the Cavs do something nutty in trading the No. 1 overall pick for a veteran star. And this is all probably a pipe dream anyway, because …

Miami Heat

Miami made the Finals even though just about every rotation player beyond LeBron and Chris Bosh broke down at some point in the last two rounds. The East will be stronger next season, but it’s still the league’s weak sister. The Big Three have grown together, and LeBron has tangible evidence this group can make the Finals, provided the front office helps along the fringes.

Its record in that regard is spotty, which is what happens when you sign old guys. Two of those old guys — Shane Battier and Chris Andersen — made huge contributions to Miami’s title teams before aging in dog years in 2014. The team’s pursuit of glittery names over unknown vigor blew up when Greg Oden and Michael Beasley proved unable to crack the rotation in meaningful games.

Ray Allen remains a contributor, but Miami cannot overtax him if he re-signs. And if Allen does return, that eats even more into the little flexibility the Heat will have. Miami has passed up loads of younger, cheap contributors with boring names in favor of fogies and big dudes who could barely move (Erick Dampier, Zydrunas Ilgauskas, Juwan Howard). Hell, this team had Patrick Beverley and waived him.

It also had Mike Miller, and Riley attempted some Twister-level gyrations Thursday in trying to convince an audience of sentient humans that the team’s decision to ax Miller via the amnesty provision had nothing to do with Micky Arison’s desire to cut his tax payment. Riley said the team cut Miller and dealt Joel Anthony because it didn’t want their contracts on the books for the 2014-15 season.

And that’s accurate. Miami will enter this offseason with real breathing room under the tax. But Riley also said the team didn’t have any urgent need for Miller this season because the roster featured heavy “duplication” of Miller’s skill set.

This is the part where you call B.S. Miller was crucial in the 2013 Finals. Battier’s decline robbed Miami of a key 3-and-D player and vaporized much of the phony “duplication” that Riley referenced Thursday. Rashard Lewis emerged late in the playoffs, but defenses didn’t really guard him. Miller would have unlocked different sorts of small and hybrid lineups, and provided an alternative to Wade as he ambled around for the last half of the Finals.

Anthony was a nonentity, but Miller’s absence hurt. Period. So did attaching what will likely become two second-round picks as the sweetener in Anthony’s salary dump. The rate of return on second-rounders is low, but it’s better than zero, and the Heat need upside assets.

The Heat need a hit in supporting-cast free agency, and they may have to do so with a very limited tool set. But it’s a better set than they had last summer, and the franchise understands it needs to be more creative. There will be some interesting names in Miami’s price range. Darren Collison had the best 3-point shooting season of his career with the Clippers (considering shot volume), and he can thrive as an option lower down on the totem pole. He plays a position of clear need for the Heat, though he’s a bad defender who will command a large portion of the mini midlevel — if not all of it.

Marvin Williams is a strong locker-room guy who served as a stretch power forward last season in Utah and would be a nice fit as Miami’s new Battier. He can get more money elsewhere, but Miami might have a shot at him if it offers nearly the full mini midlevel. Anthony Tolliver could work in this role on a minimum salary, and he did surprisingly well spotting time at small forward last season when injuries on the wing in Charlotte forced him there.

Shaun Livingston is a popular name, but his complete lack of long-range shooting makes for a shaky fit alongside Wade. Xavier Henry and Wesley Johnson have useful, discrete skills, and yet probably didn’t do quite enough with the Lakers last season to nudge their fair-market salaries much higher than the minimum. Thabo Sefolosha’s shooting ability is a complete mystery at this point, which is a weird thing for a 30-year-old player.

All three of Jordan Hamilton, Reggie Williams (remember him?), and C.J. Miles deserve a look on the wing. If Miami opts for rim protection, it might be able to get someone like Ekpe Udoh or Kris Humphries on the cheap. No one quite knows the market for those guys, especially with Humphries possibly being willing to exchange cash for happiness after banking an insane $24 million in salary over the last two seasons.

There are other names. Veterans especially will take a discount to chase a ring in Miami. This was always the most likely scenario: bring back the stars and do a better job filling out the back of the rotation. The boring salary particulars are crucial here. The Heat will have a much tougher job if everyone comes back at their full 2014-15 salaries. Let the fun begin.