Jabari Parker doesn't want to hear how the Bulls, in Year 2 of a rebuild after a slapdash ending to the Derrick Rose and Jimmy Butler eras, will have problems finding touches for all their score-first young guys.

"Did I even have the ball a lot?" Parker asks about his final days in Milwaukee. "I had to learn to play off the ball. I don't mind now."

Parker is still salty about how it ended with the Bucks. He heard the rumblings that his complaints about postseason playing time fractured his relationship with the team. "I've never had an answer for why I didn't play," Parker says. "People say it's my attitude. But who would have a good attitude when you thought you should be in there?"

Chicago is hoping Parker channels his edge into the sort of all-around effort that could bring balance to a young roster light on defense, playmaking, and overall hoops IQ.

They already know the jewel of that core, Lauri Markkanen, plays with a swagger that frankly surprised them. Robin Lopez saw it in training camp. "He didn't back down from anyone," Lopez says. "He has such a wonderful mentality for a young guy."

The coaches saw it in how he seemed to delight in hanging 33 points on Kristaps Porzingis in Madison Square Garden. Three days later against the Pistons, Markkanen missed an open 3-pointer that would have given Chicago the lead with 1:10 to go; the rebound ricocheted out of bounds off a thicket of hands.

As referees reviewed which team should get the ball, Fred Hoiberg, Chicago's coach, drew up a play. He heard Markkanen apologizing to teammates: "I have to make that shot." Hoiberg erased his play, and drew up a new one for Markkanen. "Coach," Markkanen said, "I'm going to make it," the two recall. He nailed the game winner.

It didn't surprise Markkanen. Nothing about his All-Rookie season did. "Everyone thought I was just a shooter," he says. "I knew I could put the ball on the floor and do other stuff."

But Markkanen can really shoot, and the threat he presents off the ball gives him confidence Chicago can make it work with Zach LaVine, Kris Dunn, Parker, and Markkanen jostling for touches.

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The Bulls made a fascinating bet in trading Butler for Dunn, LaVine, and the right to move up nine spots in the draft to snag Markkanen. Part of the payoff involved being bad enough in 2017-18 to nab another blue-chipper. Nikola Mirotic tried to sabotage them with a month of preposterous shooting.

The Bulls still ended up with Wendell Carter Jr. at No. 7, and they are thrilled with his potential as an Al Horford-style fulcrum who makes plays in space -- a perfect frontcourt partner for Markkanen. The more Carter proves a capable middleman connecting Chicago's offense from Point A to Point B, the less it will matter if none of Dunn, LaVine and Parker grows into the sort of alpha dog who makes that connection himself.

"He's really good playing in the pocket," Hoiberg says of Carter. "We need that. We are going to have to string together a lot of simple plays -- to hit singles. When one guy tries for a home run, we get in trouble."

Butler is a borderline top-10 player. He's just 28. You tank, or rebuild, for the chance to get that sort of player. But the Bulls never found Butler a post-Rose co-star. They couldn't work a sign-and-trade for Carmelo Anthony in 2014 (whew!), and settled for Pau Gasol. They had no workable cap room the next summer.

They had a bunch in the summer of 2016. Everyone else did, too. Chicago was ahead of the curve understanding the $24 million spike in the cap would produce outrageous long-term contracts, and wisely stayed out of the bidding for middling guys chasing $15 million per year over three and four seasons. Their books are clean.

But they could have done something more productive with their space than splurging on short-term deals for Rajon Rondo and Dwyane Wade. They could have kept their room open, and absorbed dead money in exchange for draft picks. At least Chicago would have something -- even a pick in the 20s, or two seconds presuming they wouldn't sell them -- to show for the $37 million they spent on Rondo and Wade that season.

They could have gone forward with Butler, Mirotic, all their own picks, perhaps one extra first-rounder, and cap room to chase free agents in one or both of 2017 and 2018. (This is to say nothing about what could have been had they kept the picks who became Gary Harris and Jusuf Nurkic instead of swapping them for Doug McDermott. There are other missed opportunities -- Spencer Dinwiddie and Draymond Green, notably -- but every team misses on the fringes more than it hits.)

They didn't get that extra pick, or that second star. They couldn't bank on luring one. Butler and Hoiberg didn't gel. They decided Butler, Mirotic, and uncertainty around them would lead to long-term mediocrity -- especially with a potential Butler supermax contract soaking up 35 percent of their cap. They wagered that a whole bunch of uncertainty wrapped into a half-dozen prospects gave them a better chance at eventual title contention.

Jabari Parker, left, and Lauri Markkanen are now teammates on the Bulls, but will their games mesh? Tannen Maury/EPA

These Bulls are a blob of clay. No one knows how many of them will still be on the team when it becomes something. But the likeliest outcome (among many) is that this group hits a hard ceiling around the same place the franchise anticipated the alternative Butler-centric team would have. That sounds pessimistic, but it's just the reality of the NBA. Every half-decade rebuild, executed in whatever team-building style, is a slim-odds proposition if the criteria is championship contention.

The way to jolt those odds is for one of Dunn, LaVine, and Parker to become a more complete player, someone who can be trusted to run an efficient NBA offense.

Markkanen and Carter are young, but they have the outlines of an ideal modern NBA frontcourt. Markkanen is the surest thing on the roster. He showed the ability late last season to run unconventional big-big pick-and-rolls, and grew more comfortable dragging small defenders into the post on switches -- a must-have skill for any screen-setter.

"My personal goal is that whenever you switch, you will regret it," he says.

When Parker and Markkanen man the forward positions, lots of opponents will try to arrange things so that a wing defends Markkanen -- leaving a bulkier player on Parker. They will screen for each other, and for Dunn and LaVine in various combinations -- plays opponents will often switch. For the Markkanen-Parker tandem to work, both will have to exploit size mismatches.

Markkanen is adding weight in anticipation of playing more center -- a look Hoiberg likes, even though Chicago hemorrhaged points in that alignment last season. "I'm eating a lot more," Markkanen says, laughing. (As a frontcourt pairing, Markkanen and backup Bobby Portis make for an interesting fit.)

Dunn, LaVine, and Parker are more experienced than Markkanen, yet somehow more unknown -- due in part to ACL tears in the latter two cases. We do know Parker and LaVine have been among the league's very worst defenders. Parker is going to have to defend a lot of wings, and that will end badly unless he remakes his game. (Chicago will mitigate this some by staggering Markkanen and Parker, or shifting one to center.)

The Bulls profile as a bottom-five defense. That is the biggest reason to temper expectations that have some folks whispering about the playoffs.

It is not great (Bob) to devote $40 million per season to two guys with such poor track records on defense. Sacramento's offer sheet for LaVine probably came in higher than Chicago would have liked, and the sunk cost fallacy surely played some role in their matching; LaVine was the most coveted piece in the Butler trade at the time. Walking away would have hurt.

With LaVine locked into one wing spot, most rival executives would have recommended Chicago shift away from Parker -- and use his slot to take unwanted salary from Denver, along with the Nuggets' 2019 first-round pick. (The two teams discussed general parameters of such a deal, sources say; the Nuggets eventually made it with Brooklyn.)

That makes theoretical sense. If Parker disappoints, the Bulls can decline their option on him for 2019-20. If he plays pretty well, he will torpedo their tanking efforts a bit, and demand a salary after 2020 that could be both fair and an overpay -- a deal that would be difficult to trade. NBA free agency and trades! Here's the latest on another thrilling summer in the NBA: • Offseason grades: Best in the West

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It would be nice to turn that salary slot into an asset that sustains longer. Given Denver's competition in the West, there's a chance the Bulls could have received a pick at the bottom of the lottery (depending on how Denver protected it).

But we have all been guilty of fetishizing those kinds of dump deals. Most dumps since 2013 have been meh for dumpees.

The Nets paid $31 million (DeMarre Carroll's salary over two seasons) for the No. 29 pick. The Bulls ate about $20 million in Omer Asik salary -- and gave up a good player in Mirotic -- for what became the No. 22 pick (Chandler Hutchison).

In that context, having already acquired an extra pick in the Asik deal, taking a shot on Parker is fine. I would bet against him breaking out into a star worth $20 million-plus, but not everything can be about artful cap work. Sometimes you have to chase talent.

Parker even showed flashes of competence on defense starting in Game 3 against Boston. He tried, and wouldn't you know it, trying helped! He even (kind of) walked back recent comments from a radio interview in which he seemed to dismiss the importance of defense in saying, "They don't pay players to play defense."

"Obviously it's a two-way sport," Parker says now. "To be effective, you gotta be able to attain both offense and defense. I'm not saying one is more important than the other. But at the end of the day, you gotta outscore the other team. That's all I was saying."

Chicago is hoping to simplify things by switching more. Dunn and Carter are capable bookends. Markkanen is ahead of expectations. LaVine tries, and has the speed to guard three positions. Parker has the speed and size to guard almost everyone. Alas, Parker and LaVine have spent most of their time on defense two steps behind the action.

The Bulls' switched everything in summer league -- a philosophical shift for an organization that has regarded switching as a form of surrender. "It's not really how the Bulls have played," Hoiberg says.

Regardless of scheme, the Bulls will be bad on defense. That doesn't really matter. This season should not be about winning. It should be about discovering how the young players fit, and whom to keep long term.

And for that dilemma, how Dunn, LaVine, and Parker look on offense is paramount. Right now, none are close to good enough to run a top-shelf scoring outfit. Dunn had the ball most last season, and probably will again, if only because his bricky jumper makes him a liability off the ball; Dunn is just 34-of-125 (27 percent) on catch-and-shoot 3s for his career, per NBA.com. (Forget about off-the-bounce triples that are becoming almost mandatory for lead ball handlers.)

Dunn has some explosion and craft off the bounce, including a snazzy in-and-out dribble; he uses fakes to ram defenders into picks, or get them leaning in that direction before bolting the other way:

He knows the basic reads coming around a screen. Surround him with better talent and spacing, and Dunn should make another mini-leap.

But it's hard to see much exciting upside. Dunn is already 24. Defenders duck under picks on him anytime they can manage. He has made about half his shots at the rim -- well below average for a guard. "Finishing is the biggest thing Kris has to improve," Hoiberg says.

His vision and feel meet minimum standards for the position. They aren't special. He's not operating one step ahead of defenses, or conjuring passes other guards can't. He misses some open shooters:

Dunn is a hair too predictable. He loves to dart around a pick, and then zigzag back into the path of his screener -- known as "snaking" -- before pogo-sticking into a floater:

He snakes all the time. Do not make a drinking game out of it.

LaVine failed horribly when the Wolves experimented with him as lead guard. Hoiberg used him mostly as a secondary ball handler last season; Dunn would down break the defense and kick the ball to LaVine on the opposite wing with a head start. LaVine can be effective that way. He is a very good 3-point shooter.

But he is addicted to contested jumpers. When things go badly, the combined lack of plus playmaking leads to this:

The ship has sailed on LaVine as lead dog. I'm not ready to pigeonhole him as a sixth man quite yet -- he's too good a shooter -- but that would be a sensible endgame.

Parker has been scattershot as a creator. His off-the-bounce game is jagged, arrhythmic. It doesn't seem to make sense to teammates. He'll take one long dribble forward, pull back, and then pitter-pat the ball three times in rapid succession while standing almost in place. He throws passes too early ...

... or sees them too late:

He approaches picks so fast, with such hunger to score, that he is often gone before the pick arrives.

You can see in that last play why Parker tantalizes. He gets deep into the paint against Horford, and kicks to President Malcolm Brogdon with an advantage. Parker can blow by bigger guys on switches when he doesn't waste time:

He can bully smaller guys on the block. He is a solid passer when not afflicted by tunnel vision:

That is a smart dish, delivered early. That play starts with Parker spotting up as Giannis Antetokounmpo does the heavy lifting. Parker has been better in that sort of role -- more finisher than starter. He is dangerous on catch-and-shoot 3s. But a team of finishers won't work at the highest level.

A total of 225 players used at least 100 ball screens last season, per Second Spectrum tracking data. Markkanen (first), LaVine (37th), Parker (48th), and Dunn (90th) all ranked among well above league average in how likely they were to attempt a shot after dribbling around a pick.

That speaks to the possibility that there isn't an alpha dog creator on this roster -- a drive-and-kick hub. If the Bulls are bad enough, maybe the player is coming in the 2019 draft. Perhaps they can churn non-Markkanen assets into something better, though right now, that seems unlikely given the collective trade value of Parker, LaVine, and Dunn.

Chicago will be decent on offense anyway -- probably around league average. They will have good spacing. They have enough guys who can generate shots for themselves, so no possession will totally bog down. Hoiberg hopes to compensate for playmaking deficiencies by running like hell.

In the half court, the Bulls will have to pass and cut their way into the sort of open looks a superstar generates on his own. This is what Hoiberg means by "hitting singles." He has instituted San Antonio's rule that no one is allowed to hold the ball for longer than half a second before shooting, passing or driving. Hoiberg runs a lot of prelude screening action to loosen the defense before the real action starts.

Mastering that sort of system basketball requires repetition, experience, and a collective feel that is probably above this roster's head for now. And if none of Dunn, LaVine, or Parker emerges as a reliable every-possession initiator, Chicago's rebuild will remain bereft of the single most important piece any contending team needs.

They don't have to find that player now. They have time to see what this group is, whether it meshes better than expected. Perhaps Markkanen can grow into such a multifaceted screen-setter -- deadly on pick-and-pops and in the post -- that Chicago won't need a perimeter superstar when Markkanen hits his prime.

It will be years before we know. But that ceiling still looms.