On his best days, when his team is thriving and the mood is right, Kyrie Irving won’t just dazzle you with deft ball-handling and expert marksmanship—he’ll disarm you with self-awareness and humility.

Yes, Irving will concede, I could bring that defensive intensity more often. I could make those scoring passes more consistently. I could drop 10 assists if necessary. I could do more. I know I need to do more.

His coaches have heard it. His teammates have seen it.

It is in these rare moments, when the cool facade drops, the ego hibernates and his better angels emerge, that the swaggering 25-year-old offers a hopeful glimpse of what he might yet become: a complete player, a true superstar, a leader.

That’s the player the Boston Celtics hope they just obtained in their finally completed blockbuster trade with the Cleveland Cavaliers. It’s just not clear if that’s the player they actually got.

As a scorer, Irving is certifiably elite—strong, quick, shifty, with an uncanny ability to create (and convert) any shot, anywhere, from all sorts of ridiculous angles.

“Probably the best one-on-one player in the league,” says one veteran scout.

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Yet the evidence suggests Irving is a flawed star—flaky on defense, indifferent to passing and consumed with a desire to score. (And on his worst days: moody, non-communicative and passive-aggressive.)

The key assets surrendered by Boston—star point guard Isaiah Thomas, defensive ace Jae Crowder and the Brooklyn Nets’ unprotected first-round draft pick in 2018—are worthy of a franchise player. So there’s only one question that matters:

Is Kyrie Irving a franchise player?

Celtics president Danny Ainge clearly believes so, because after months of zealously guarding his best assets (to the point where he could have starred in his own reality show, Hoarders: NBA Edition), he finally parted with a few to snare Irving.

The Nets pick should be in the top five next June. Crowder, one of the league’s best three-and-D wings, is also one of the NBA’s best bargains, earning an average of $7.3 million over the next three years. Thomas, of course, made the All-NBA second team last season.

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The Cavaliers are also receiving Ante Zizic, a promising 20-year-old center, plus a 2020 second-round draft pick (via Miami).

Ainge was roundly crushed when the deal was first announced Aug. 23. (It was finally completed Wednesday with the addition of the second-round pick to allay concerns over Thomas’ injured right hip.) Critics—and there were many—called it an overpay made all the more puzzling by Ainge’s reticence to include that Nets pick in potential deals for Paul George and Jimmy Butler, both of whom are significantly better than Irving.

A week later, the deal should be seen in a slightly more charitable light. The Cavs’ concerns over Thomas’ health are significant, and he’s hitting free agency next July. If he misses a significant part of the season—or worse, never returns to All-NBA form—then the deal really boils down to the Nets pick and Crowder, which seems like a reasonable price, no matter how you view Irving.

But that’s the thing. Ultimately, this trade is not about Ainge and his assets. It’s not about LeBron James’ big shadow (the reported cause of Irving’s trade demand) or the chaos created by Cavs owner Dan Gilbert (another speculated motive). It’s not about Thomas’ balky hip.

No, the Kyrie Irving trade is about Kyrie Irving. How history judges the deal will depend solely on what Irving does next.

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Can he evolve? Does he want to? Will he play the brand of defense the Celtics demand? Will he embrace coach Brad Stevens’ move-the-ball philosophy? Can he suppress his worst tendencies for the greater good? Can he be a galvanizing force instead of a one-man show?

“Franchise player” is a term with many definitions, but the most meaningful is this: best player on a championship contender. The Celtics are flush with complementary stars, in Al Horford and Gordon Hayward, but they need a leading man, a dominant force who pulls it all together. Is that Irving?

“I have my doubts,” says the longtime scout, a view echoed by numerous coaches, executives and scouts around the league.

“I think it’s fairly clear he’s not,” says one team’s analytics director, pointing to the surprisingly soft trade market for Irving. “The league as a whole agrees he’s not.”

To wit: No other team appeared willing to part with an All-Star or a high lottery pick to get Irving. The New York Knicks would not part with third-year big man Kristaps Porzingis. The Phoenix Suns refused to include rookie forward Josh Jackson or scoring whiz Devin Booker.

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Irving was among the NBA’s leading scorers last season, averaging 25.2 points per game, and with great efficiency (40 percent on three-pointers, 50 percent inside the arc). The scout calls him “as good as anybody in the league at getting his own shot and creating for himself.”

But creating for others? Not so much. Last season, Irving ranked 21st in the NBA in assists per game (5.8), and though that’s partially a consequence of playing with James, it’s not the whole story.

The scout calls Irving’s playmaking skills “plain vanilla” and “average for a starting point guard.” He says he would be surprised if Irving raised his assist average much in Boston. (And he might not need to since Horford and Hayward are both skilled passers.)

And Irving is positively awful defensively, according to just about every available defensive metric—“a train wreck,” in the words of one Cavs official. He ranked 28th among starting point guards last season, per one team’s proprietary metrics. (The only point guards worse? Thomas and his new Cavs teammate, Derrick Rose.)

The most damning stat is the most basic: The Cavaliers went 4-23 over the last three seasons when James didn’t play. If Irving were truly a franchise star, shouldn’t they have won more? That’s the question everyone around the league asks.

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Except, interestingly, those who have worked closest with Irving. Despite his blemishes—the ball domination, the defensive lapses, the moodiness and all of those damning stats—people associated with the Cavs remain Irving’s biggest believers.

They have seen him at his best. They have seen him effortlessly collect 10 assists in a half. They saw him lock down Stephen Curry for long stretches in the 2016 Finals. They know he’s capable of so much more. They have heard him, in his softer moments, admit as much.

All stats aside, they believe Irving would be a better player, and a better leader, if not for James’ heavy presence.

“He’s evolved more the last three years than anyone else on our team,” says one Cavs official, who declared himself “really bullish” on Irving’s future in Boston. “He’s just scratching the surface of who he can be, and he’s not going to find out playing with [James].”

The Celtics will demand a higher degree of accountability, the official says. Stevens’ slick offense, predicated on ball and player movement, will require Irving to break old, bad habits. Horford and Hayward’s selflessness will set the right tone. Irving has “utmost respect” for Stevens, the official says, and a strong connection to Hayward, whom he actively recruited in 2014 (just before James returned).

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“He’s in a space mentally where he thinks he’s ready for this challenge,” says another person who knows Irving well. “I think he’s going to be the best version of himself that we’ve seen.”

The record is the record. It’s checkered, wholly unflattering in places. It’s reasonable to wonder how much any star, especially one as prideful as Irving, can change after six years in the league. Even Irving’s most optimistic supporters say the doubts are justified.

But the elements are in place for Irving, still just 25, to make that evolutionary leap.

“I know he’s gifted enough to do it,” the Cavs official says. “I’ve seen him in isolated situations do everything he needs to do.

“Will he choose to do that?” the person asks rhetorically. “Nobody knows the answer.”

Howard Beck covers the NBA for Bleacher Report and BR Mag. He also co-hosts the Full 48 podcast, available on iTunes. Follow him on Twitter, @HowardBeck.