All fans really root for is possibility. Hope for wins and rings, or at least the promise of them down the line. Reassurance the team’s drive for success matches their loyalty, so that faith isn’t spent in vain.

It’s why Cleveland burned LeBron James jerseys, only to embrace him again, because he robbed them of expectation once and returned with it years later. It’s why anticipation peaks on draft night, during free agency, at the trade deadline and with each rumored deal. Because possibility can walk through that door at any moment, making every heartbreaking loss and gut-wrenching season worth the wait.

No deal in NBA history embodied and consummated that possibility over the course of a single season quite like Boston’s trade for Kevin Garnett on July 31, 2007, exactly a decade ago today.

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“It was before KG ever arrived. Word that KG was coming gave great hope to everybody,” Celtics president of basketball operations Danny Ainge recalled in a conversation with Yahoo Sports last week. “There’s this hopefulness and excitement in expectations that permeates through the entire city of Boston, and obviously the closer you are to it, the more it filters through the organization.”

In the NBA, few teams have any real shot at the title, and in recent years it feels more like just two. Half the league is chasing the playoffs, believing anything can happen so long as you make it; a handful more teams feature young rosters on the rise; and the rest are left with no hope, rooting for losses and pingpong balls, so another 19-year-old can carry the expectations that may never be fulfilled.

The Celtics were one such desperate team in 2007, enduring a franchise-worst 18-game losing streak amidst a Boston winter that also claimed Paul Pierce’s All-Star status for the first time in six years. As his 30th birthday loomed, Pierce missed 35 games with foot and elbow injuries that were exacerbated when he was trampled by a tank the Celtics drove to the league’s second-worst record that season.

“I think that the greatest thing is just how we were at the bottom the year before, losing so many games, and how challenging that is on players and coaches and fans and everybody that’s involved,” Ainge said of that miserable 24-win 2006-07 campaign. “And then to make that quick of a change.”

The lottery dashed Ainge’s plan of selecting Kevin Durant, and Pierce all but lost hope. “That was the bottom of the barrel right there,” he said recently. In 2005, Pierce had publicly expressed frustration with the Celtics spinning their wheels in mediocrity, and Ainge nearly traded him for Chris Paul’s draft rights. By 2007, Pierce conducted candid conversations with the Boston brass about the team’s direction, and he was prepared to demand a trade if Ainge didn’t make a draft-night deal for a veteran.

Ainge appeased Pierce with a trade for Ray Allen. Even then, fans wondered what the Celtics were doing, because a Big Two of Pierce and Allen still didn’t make them a contender, and that’s the whole point of rooting for basketball in Boston.

Little did anyone know, possibility was lurking in Minnesota.

“If we don’t make the Ray trade, then KG doesn’t even decide to come to Boston,” Ainge told Yahoo Sports. “The idea of playing with Paul was intriguing to him, but not enough to sign a long contract extension, and then all of a sudden when Paul and Ray were in the fold, then KG was very energetic and enthusiastic and hoping for an opportunity to come to Boston.”

Garnett essentially owned a no-trade clause in the form of a contract set to expire in 2008, and he had previously rejected trades to Boston by refusing to sign an extension. That all changed when Allen joined Pierce. And on July 31, 2007, the C’s simultaneously announced the Garnett trade — the largest in NBA history for any one player — and signed him to an extension.

“It gives us hope,” then-Celtics coach Doc Rivers told reporters at Garnett’s introductory press conference 10 years ago to the day. “That’s what we want. From low expectations to high expectations, that’s what we want. That’s exactly what we want, and I can’t wait to get started.”

“I’m excited,” added Garnett, sitting between Pierce and Allen on the dais, all three beaming from ear to ear. “It’s like being in a Lamborghini doing 200 with your head stuck out the window.”

“On paper, this team looks good,” Ainge warned at the time. “These guys have a lot to do. These guys have to get the chemistry right. They have to make the sacrifices to win. I know there’s been a lot of comparisons already of the Big Three. These guys will never be the Big Three until they win, and I think they know that. I’ve heard these guys talk. I’ve talked with each of them, and they know that. Nothing has been accomplished by this team at all. We have a chance.”

Behind Ainge’s beats, KG could be heard repeating: “Yup.”

Thus, the next element of a trade that resurrected a once-proud franchise that was going on 20 years and a decade in the lottery since Larry Bird last delivered a title: Kevin Garnett was no false prophet.

“I’m a very passionate player, but the one thing that hurts more than anything is losing,” Garnett vented a decade ago. “Knowing you’re going into a game with a slight chance of winning is pretty difficult. I’m a very confident person. I try to instill confidence in everybody around me, and sometimes it gets hard, to be honest be with you, but what’s refreshing about this whole panel up here is knowing that each and every night I have an above-average chance to win. … I don’t know, man, it just feels good. It feels good to have two big guns on the side of me. It feels real good.”

“Paul and KG and Ray were all coming from lottery teams,” Ainge told Yahoo Sports last week, “so of course the excitement of all of them to have a chance to really compete for a championship was inspiring to every one of those guys, and all three of them, we don’t win it without any one of them playing at their very best. And they did for six seasons.”

Garnett cared about winning more than anyone, even Bostonians, and that passion was infectious. Over the years, everyone from ballboys to ownership described KG’s arrival as “a culture change.”

“We aren’t able to quantify much of it, but let’s forget about his personality for a second and his approach to life and the game,” Ainge said. “KG’s talent alone and what he brought to the table from a defensive presence and an offensive talent was very, very exciting for Paul and Ray, and I think it transformed those two players and Doc Rivers and the whole city of Boston. They could see on paper that, man, these three Hall of Fame players with still a lot of basketball left in them are coming together, and there was such an enthusiasm and excitement that elevated the preparation, effort and expectations immediately of the entire city of Boston.

“Then, you add KG’s energy, enthusiasm, unselfishness, work ethic and those characteristics that he exemplified on top of just the sheer talent. Those carry our franchise to this day.”

Garnett’s intensity was legendary. On bus rides, as teammates slept under the blanket of night, he sat in the rear, staring from beneath a hoodie, an emperor on his throne. In practice, he showed no mercy on the young. Only the strong survived the school of KG. He went silent an hour before games, only to erupt at the tip, whipping the TD Garden crowd into a frenzy, smashing his head on the stanchion.

That fire raged on the court. There was chest-pounding, trash-talk and knuckle push-ups, all to root out the weak. “If you’re going to be anything in this league, you’ve got to have an edge,” KG said in 2011. “There’s no room for soft. There’s no room for a person who’s going to give ground. Hell, yeah, I’m trying to gain an advantage out here. If you’re not, then you’re in some trouble. If you can’t handle it, get off the court. My job is to stop you, so I don’t anticipate you liking me. I don’t anticipate you trying to be my friend, because I’m not trying to be your friend.”

Behind it all, though, was a rare blend of talent and technique. Garnett was the Kevin Durant prototype, a 7-footer who refused to be listed as such, for fear he would be labeled a big, when in actuality he was a Swiss Army knife of skill. Offensively, there was that sweet mid-range jumper and those post moves he now teaches All-Star mentees, all developed through years of honing what KG called “my craft.” And if the Celtics’ defense was on a string, then he was the puppeteer.

“There’s a lot made of all the intangibles KG brings — the unselfishness and relentless energy — but ultimately it’s his amazing talent,” said Ainge. “I know a lot of enthusiastic people with lots of energy, but they’re not 7 feet tall, shooting long jump shots, getting every rebound, passing, defending, and everything else, so KG’s talent, first and foremost, was spectacular, and his energy and enthusiasm and unselfishness were just great added elements and remarkable.”

What followed was an era forged by “Ubuntu” and sealed with “grit and balls.” The 2007-08 season alone brought 66 wins, one of the largest average margins of victory ever, and, of course, a ring. His Celtics came within six minutes of another title and fell a quarter short of a third Finals appearance.

“When you look at the body of work we’ve done in the six years that I was here, no one can ever take that away from us,” Garnett said following his Boston homecoming in January 2014. “That was our era. That’s what we embedded in history, and that’s forever. We take that to our grave with us.”

More might’ve been had, if not for injuries to Garnett in 2009, Kendrick Perkins in 2010, Rajon Rondo in 2011 and Avery Bradley in 2012. But it was enough, because at least there was always possibility.

“Winning in 2008 brought back the respectability of the Celtics for this generation of young kids coming into the NBA who grew up in that era of KG winning a championship with Pierce and Ray,” Ainge told Yahoo Sports, “so that still carries us today, because that’s just a reminder of the great history that we’ve had and hadn’t had for a long time. KG’s presence is still felt, as is Paul’s and Ray’s.”

Garnett’s was a masters class in NBA culture, and graduates received undying loyalty. Rondo enjoyed his best seasons under KG, who breathed fire into the young point guard and helped him harness it.

“We’ll always bleed green as long as we’re playing basketball and as long as we’re living,” KG said upon his return to Boston in 2014. “Even when they bury us six feet, this is what it’s gonna be.”

The school of KG didn’t suffer dropouts, though. So, when Allen left the Celtics for LeBron’s Miami Heat in 2012, Garnett burned their relationship to the ground, and the ashes are still smoldering.

Ainge is more forgiving. “I have a great deal of respect for Ray Allen and know that we don’t have the success that we had over a five-year period without him,” he told Yahoo Sports, “and I’ll always be grateful for him and his talent and character and work ethic and example of professionalism to the Celtics that’s also carried on to the next generation. And I’m hoping that someday we’ll have a reunion of our 2008 championship and that Ray will be front and center like he should be.”

This season, Gordon Hayward will become the first player since Allen to wear No. 20 for the Celtics, but Garnett’s No. 5 and Pierce’s 34 will hang from the Garden rafters someday. Both could be raised in 2017-18, the 10th anniversary of their title campaign, but Ainge has bigger things to worry about than party planning. “I’m too busy trying to get our 2017 team together,” said the Celtics president.

Because the Garnett trade is still paying dividends a decade later. By the end of 2011-12, when KG gutted out a throwback playoff run to Game 7 of the conference finals, his age in basketball years was starting to show. By then, there was nothing left for him to give the Celtics. “I have no life at this point,” he said in 2012. “I go home, I get treatment, come back in here, study tape, film — no life at all.”

The following year, he and Pierce were dealt to the Brooklyn Nets in a trade that, in one way or another, yielded current Celtics Isaiah Thomas, Jaylen Brown, Jayson Tatum and Abdel Nader, as well as likely lottery picks from the Nets and Los Angeles Lakers next summer. Meanwhile, Hayward and Al Horford, arguably the two biggest free-agent signings in franchise history, both cited the so-called Celtics mystique — that aura Garnett restored in six short years — as reasons for signing with Boston.

“The KG, Paul Pierce, Ray Allen era speaks for itself,” Ainge told Yahoo Sports. “When those great teams were playing, it was just a reminder of the Celtics. For 19- to 30-year-olds today, that is the Celtics history to them. They know KG, Paul Pierce and Ray Allen, and they don’t remember Bailey Howell. Of course they all know who Larry Bird is, but they don’t really remember Robert Parish or Dennis Johnson or some of the great Celtics. They remember Paul Pierce and KG.”

Ainge is still chasing those memories. Bradley, an unfortunate salary cap casualty earlier this month, was the final bridge from Garnett’s era to the team that reached the conference finals last season, but possibility remains. Gone is the desperation of a franchise mired in a decades-long title drought, and in its place is the same blueprint of hoarding assets that landed Garnett and the prospect that the next draft pick, the next signing, the next trade will produce the player who changes everything.

Asked what from KG’s time in Boston stays with him, Ainge paused and said, “All of us had great anticipation for the 2008 season, and then you add KG’s personality on top of that, and I think both of those things were just very memorable. It had an impact on the team through that whole era — and not just the players who played with them, but the players who grew up watching them.”

Ainge has done well to identify players who personify Garnett’s mettle. When Thomas fought through tragedy and injury during these past playoffs, KG left an inspirational voicemail that the point guard played in the locker room during the conference semifinals. “A whole lot of cussing and words that I can’t repeat,” said Gerald Green, once packaged in the Garnett trade, only to return to Boston in 2016. “It was phenomenal, and it showed us the fire KG played with. We had to play with that same fire.”

As hard as a 5-foot-9 player can try, few can alter a franchise’s fortunes so drastically, so quickly, as Garnett. Russell and Magic delivered titles as rookies. Wilt, Bird, Shaq and LeBron all represented that same possibility and delivered championships within their first few seasons for their franchises. These are the greats — recognizable by first, last or nicknames — and KG belongs among them.

A decade before Garnett arrived in Boston, then-Celtics coach and GM Rick Pitino had already dubbed Boston fans “the fellowship of the miserable.” Pitino pushed Red Auerbach to the side, reaching a new franchise low, and then he reminded the city, “Larry Bird is not walking through that door, fans. Kevin McHale is not walking through that door, and Robert Parish is not walking through that door.”

But Kevin Garnett did on July 31, 2007. Ten years and nine playoff appearances later, hope is still alive for the Boston Celtics. Thanks to KG, anything is possible. That’s how you quantify a culture change.

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Ben Rohrbach is a contributor for Ball Don’t Lie and Shutdown Corner on Yahoo Sports. Have a tip? Email him at rohrbach_ben@yahoo.com or follow him on Twitter! Follow @brohrbach