CHICAGO — Dwyane Wade already has a Hall of Fame portfolio, with three rings, five trips to the Finals and much of the credit for pulling together the NBA's most famous Big Three in recent memory down in Miami.

Rajon Rondo has led the league in assists three times, gone to four All-Star Games, earned one championship ring and got to Game 7 in a bid for another, all the while quarterbacking the league's previous biggest three (Kevin Garnett,Paul Pierce, Ray Allen) in Boston.

Both have brought their games and their resumes to the Chicago Bulls this season. And from the moment of their offseason arrivals, both have demurred that the Bulls "are Jimmy Butler's team."

What the three of them will begin sorting out with the start of training camp Tuesday is whether that's a good thing, a bad thing or just an NBA dumb thing that doesn't loom nearly as large in other major team sports.

Already referred to by some as "The Three Alphas" -- as in alpha dogs, as in pecking order and supremacy and other animal-kingdom psycho-babble about who gets to eat first (or something like that) -- Wade, Rondo and Butler are going to mesh in some manner, like it or not. They're going to develop a three-headed working relationship, ranging from copacetic to fractious, and the Bulls likely will rise or fall at least partly due it.

As the older guys, Wade, 34, and Rondo, 30, sound as if they're taking one for the team -- and for the younger guy, Butler, 27, whose star still is rising. A self-made basketball success, Butler is a two-time All-Star who picked up an Olympic gold medal in Rio last month with the rest of Team USA.

He's also the guy who was Chicago's oil to Derrick Rose's water last season, the two of them undermining any claims their talents seemed to make about premier NBA backcourts. It's a story familiar in sports as much as in Hollywood -- a star drops from the sky for some period of time, in this case Rose's protracted injury comebacks, and another one ascends. When the former returns, the latter isn't inclined to relinquish.

And so it went for a Bulls team that underperformed. Butler grabbed at the leadership reins, Rose and a few other teammates recoiled and there was no order at the trough at all.

Rondo and Wade have tried to defuse that, even though it's only at the words stage.

"It's important because all egos have to go out the window," Rondo toldNBA.com Monday at media day. "I wanted to play with a competitor, a warrior beside me. Based on the years I played against Jimmy, I felt like he was the best fit."

Wade, when he signed with Chicago in July, joked when he initially was asked the question. "I think it's Jerry Reinsdorf's team," he said, mentioning the Bulls chairman.

But soon enough he got to the heart of the matter, at least as it relates to the NBA, where strong personalities on short rosters wield impact.

"I think, you know, it's funny to be sitting in this seat," Wade said then. "I remember when Shaquille O'Neal came to Miami. Coming from the Lakers, three championships, came to Miami, we had no championships at the time. And I remember his press conference ... Shaq said, 'We're not going to go through this all year.' He said, 'It's Dwyane Wade's team.' So we're not going to go through this all year. This is Jimmy Butler's team. Myself and Rondo are here to bring what we bring as athletes to this team and to this city."

Butler is the guy on the right side of 30, the player whose past two seasons as a 20-point scorer layered on top of his lockdown individual defense suggest more of the same or better.

Coincidentally, Wade and Rondo are catching Butler at a point when he might not be as driven to shine individually if it comes at the expense of group success. That was one of the obvious lessons he took away from his USA Basketball stint, where all 12 players were stars and even the biggest names -- Carmelo Anthony,Kevin Durant, Kyrie Irving -- did some of the dirty work. And the sitting.

"Just how hard everybody worked," Butler said of another takeaway. "Whether it was KD or Carmelo. Or whether it could have been [Bulls youngsters] Doug McDermott or Denzel Valentine. If the best players in the world are constantly working, everybody should be constantly working. That's what I got from that event."

Butler's approach to this season is no different from his previous ones: It's all about winning and his game needs improvement across the board. There's no one move he has grooved, no specific new wrinkle. And even before he climbed a few status rungs as a player, he never really identified or talked about them, even though they clearly mattered.

"I don't think the individual stuff means too much to me," Butler said Monday. "I still want to win a championship, I still want to win it as a team. So I'm not going to halt on getting better. That's the main reason I am who I am, all the hard work, all that good stuff. Individual stuff, it sounds fine and dandy, but I think winning would be more than any individual stuff."

But geez, having your own NBA team -- as in, "It's Jimmy's team" -- sounds especially fine and particularly dandy.

"I don't think it's that important at all," Butler said. "I just think [Wade and Rondo] get just as tired of having to answer that question as I do. So they just threw out a name and it happened to be mine.

"It doesn't matter, because I can tell you right now, I can't beat any NBA team 1-on-5. I need at least four other guys out there with me. If they want to put five other guys with me, I'm pretty sure we'd get a technical foul and get in trouble for it."

Steve Aschburner has written about the NBA since 1980. You can e-mail himhere and follow him on Twitter.

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