CLEVELAND -- The Atlanta Hawks' history doesn't contain a catalog of deep heartbreaks or cosmic tragedies. The Hawks have never been victimized by "a shot," nor have they suffered any epic meltdowns.

There was no "Dominique's elbow" game and no Sacramento 2002. In the final possession of a closeout game at home against Boston in 1988, Cliff Levingston got the ball when he shouldn't have. But by and large, the Hawks' body of work in Atlanta has been every bit as devoid of drama as it has been of glory.

Tuesday's formality, a 118-88 loss to the Cleveland Cavaliers in Game 4 of the East finals that ejected top-seeded Atlanta unceremoniously from the 2015 postseason, won't go down as a defining moment. It will be wielded like a blunt object by those who tagged the Hawks as a finesse team and paper tiger and superstar-less novelty that owed its 19-game winning streak as much to randomness as rigor.

But the Hawks have already chalked up 2014-15 as the most important advancement in franchise history.

After the shellacking, Hawks players mulled over the full breadth of the season. One commonality in their reflections is that "this was only our second year together," as Jeff Teague said from the podium. "You can really say it was our first year because Al [Horford] didn't really play half of last year," DeMarre Carroll said down the hallway in front of his locker.

Paul Millsap will be a free agent this summer and is expected to command the max, which projects to be between $18 million and $19 million a season. Jesse D. Garrabrant/NBAE/Getty Images

It's an interesting observation, especially for Teague, who has now spent six seasons in Atlanta. But this is how this Hawks team interprets events: The arrival in 2013 of Mike Budenholzer, the acquisitions of Carroll and Paul Millsap that summer and the formation of Teague-Kyle Korver-Carroll-Millsap-Horford as the starting unit that fall represented Year Zero in Atlanta basketball.

The Hawks would demure if you called them romantic, but there's something very aspirational about what they're trying to do as a team and a basketball organization. Korver talks about it most willingly when he describes the satisfaction of building something, and Carroll does, too, when he gets going about "Hawks basketball."

This is the idea that an NBA team can put structure before talent, that culture and system and trust can be the basis for success. Of course, a team needs talent to win, and few things annoy Budenholzer more than a nation of basketball pundits declaring his team isn't talented. But the notion that you take the best talent on the board in free agency and the draft, then worry about sculpting it into something cohesive doesn't wash with the Hawks.

Being annihilated by Cleveland doesn't help their case. As the celebrations commenced at Quicken Loans Arena just outside the Hawks' locker room, the superstar model was looking mighty good. Meanwhile, over in the Western Conference, the top two finishers in the MVP race are battling it out to face LeBron James.

Was the Hawks-Cavs series a referendum on talent vs. structure? It's hard to say. But Atlanta didn't lose this series because it was lacking a superstar. It lost it because it was less devoted to its game plan than Cleveland was and because it hit 31 percent of its uncontested 3-pointers and 20 percent of its catch-and-shoot triples -- half its regular-season rate. Defensively, its big men were slow to get up early on ball screens, something it normally excels at. And an interior-oriented defense that must be quick to close to the perimeter was too slow to react.

So when the Hawks say, "This is only our second year," there's a tacit recognition that they haven't yet proven their structure-over-talent thesis. Teague insisted after the game that the Hawks' system could beat a superstar in a seven-game series. After all, the Spurs have done so. But the Hawks are engaged in a much trickier exercise, and they know it. Three Hall of Famers reside in San Antonio, so while usage and opportunity might be distributed equitably, the skills are transcendent.

Yet the Hawks believe in their project, and they not only want to win the title, but the argument. They maintain that you can win in the NBA without compromising, that if you build the structure, then populate it with trustworthy competitors who can shoot, defend and like to come to work with each other, you can win big.

The Hawks have declared continuity as a guiding principle -- again, "we're only in our second year" -- and now comes the challenge of keeping their core intact in what's shaped up as a very big summer for Atlanta. One of the cruel ironies of the maintenance of any team is the complications that accompany success. When players outperform expectations, hefty raises usually follow. For a team managing its roster within the confines of the NBA's salary cap, that means tough choices.

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Millsap and Carroll are free agents, and if the Hawks want to retain them, both will need to be signed under the salary cap. Right now, the Hawks are set to be about $23 million and change under the cap after factoring in some cap holds, including the No. 15 pick in next month's draft. Once the accounting is done, that's unlikely to be enough to sign both Millsap and Carroll, and the Hawks probably will have to perform some spreadsheet gymnastics.

Though Millsap is reportedly very fond of his situation in Atlanta, the All-Star will have plenty of suitors on the open market. With gobs of cap space around the league and the reality that a max deal signed in 2015 will look like a lot less once the salary-cap number explodes in 2016, Millsap is expected to command the max -- or close to it -- which for 2015 projects to be somewhere between $18 million and $19 million for a player with eight years of service.

Carroll has a bit more elasticity in the marketplace, largely because he isn't a max player. There might not be a player in the league who drove up his price more than Carroll this season -- and postseason. League sources say that the high appraisal on Carroll is four years and $50 million, with the regular caveat these days (see above) that the combination of a league brimming with cap space and a salary-cap number one year away from an historic explosion could compel a single team to go even higher.

The Hawks like Carroll a ton, but they're also a pragmatic and unemotional front office that doesn't have a single player on their roster under a contract that's unfavorable to the team. That's unlikely to change going forward, whether or not Carroll gets an outsized offer from one of 29 other teams. And as much as Carroll treasures the opportunity and trust he's been given in Atlanta, he's worked his whole life for the contract he'll sign this summer. He's boosted his value and now intends to cash in on it.

The likely scenario is that if the Hawks want to keep both Millsap and Carroll, they'll need to clear a bit more cap space to do it. That means moving some existing contracts, with candidates being Mike Scott and Shelvin Mack. Doing so would generate another $5.8 million in space, which could be enough to secure a Year 3.

With two years and $16 million remaining, Jeff Teague's deal is too affordable to make a change. Mike Zarrilli/Getty Images

When it's time to speculate about the future, Teague might be the most intriguing member of the core. Millsap, Korver and Carroll were hand-picked, and if you went into a laboratory and designed a five-man for Budenholzer with the right skills and temperament, it would look something like Horford.

But Teague is a different breed, and he's in a system and culture that requires a very specific combination of competitiveness and self-awareness. The point guard position in Atlanta these days demands a complete devotion to the system, a willingness to read at all times, a commitment to play hard off the ball. Teague, a product of AAU, a loopy Wake Forest team and the Iso-Joe Hawks, has deprogrammed himself admirably.

But the Hawks are as ardent an identity team as exists in the league outside of San Antonio. They're not exactly clannish -- not yet, at least -- but there's little tolerance for anything less than a full buy-in on both sides of the ball. Remember, Popovich-Parker is the relationship prototype here, which means Teague is ridden hard in Atlanta. That can wear on a player's confidence unless he's truly special -- and therein lies the question. Is Teague sufficiently special for a team on the Hawks' mission, and does he have the confidence to lead?

For now, Atlanta's fortunes will ride with Teague. At two more years and $16 million, his deal is too affordable to forfeit, and whatever deficiencies exist, he's still a very nice point guard. The organization loves second-year backup point Dennis Schroder. If Schroder were reasonably mature -- and he isn't -- there could be a basis for a more serious debate about the point guard slot, but for a little while longer, the platoon makes sense for Atlanta, even if it isn't ideal.

Following the game, Budenholzer wasn't ready to reflect on the totality of the season. Too soon. But after the dull pain of this sweep recedes, the Hawks will appreciate the sum of their season, how they filled a dormant building in a sleepy market, how they closed ranks after a tumultuous September of leaked emails and conference calls and the loss of Thabo Sefolosha in a bizarre altercation in New York.

Most of all, the Hawks will contemplate the future, which is still a steep climb in a superstar league. The very nature of a system is its reliance on precision, all the pieces working together in function. As we've learned in the past week or two, a system allows for the thinnest margin of error -- otherwise it wouldn't be a system. Absent a superstar, the Hawks have chosen to go this way, with the loftiest expectations. This is why, come October, they'll still be the NBA's most interesting experiment.