The Bulls still have no idea what they have in new forward Jabari Parker

Bulls forward Jabari Parker is still an enigma.

The former Simeon standout, who played at Duke before being drafted by the Bucks, now is back home and playing for the team he grew up idolizing. But with the preseason set to tip off Sunday, few in the Bulls’ organization know exactly what to expect.

The 6-8 Parker is coming off a second anterior cruciate ligament surgery on his left knee and played in only 31 regular-season games last season. He’ll be playing an unfamiliar position (small forward) once Lauri Markkanen returns from an elbow injury, and his defense is suspect.

Since being selected No. 2 overall in the 2014 NBA Draft, Parker’s career best can be summed up as glimpses of hope too often eclipsed by disappointment.

But it’s those glimpses of hope that motivated general manager Gar Forman and vice president John Paxson to invest $20 million in Parker this season, with a team option for 2019-20. The preseason will start the process of examining that investment.

‘‘He has looked great [so far],’’ teammate Zach LaVine said of Parker. ‘‘He was trying to dunk everything and stuff like that. He’s as explosive as ever.’’

But that has been in controlled team scrimmages. Will the Bulls get the Parker who at times looked uninterested in his role with the Bucks or the Parker who averaged 19.5 points and 8.2 rebounds in his last six regular-season games last season?

More important, how will coach Fred Hoiberg make sure Parker, LaVine, Markkanen and Kris Dunn all get their touches and establish a pecking order for late-game situations?

‘‘I think it just takes time,’’ Parker said of establishing those roles. ‘‘I can’t put a date on it. But once we figure out each other and start to jell, then we’ll see the results. As far as the results go, then we’ll know if we’re jelling or not.’’

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Hoiberg offered a more detailed answer.

‘‘We had multiple occasions when we were going through our really good stretch last year where Lauri would take the last shot,’’ Hoiberg said. ‘‘Or Kris Dunn really developed into a closer in a lot of those wins that we had. Zach had a couple of games where we put the ball in his hands late in games.

‘‘Obviously, Jabari is capable of making a big play, especially at [small forward], when you can put him on the block and take advantage of the mismatch.

‘‘That will develop as we go along. We’ll understand who has the makeup to be that guy that we put the ball in their hands late in games.’’

That means sacrifices will have to be made and feelings might get hurt at times. That’s why LaVine said egos need to be checked at the door.

‘‘We’re not going to start this thing on who is the alpha and things like that,’’ LaVine said. ‘‘We’re going to need more than one alpha on the team; that’s how teams are now.

‘‘There’s going to be some games where one of us doesn’t get as many shots as we did the game before or get as many points as we did the game before. But I think as long as we win, we’ll be OK.’’

But what if they’re not winning and things aren’t OK?

‘‘Then something’s got to change,’’ LaVine said. ‘‘I think we’re all unselfish. We all understand each other’s game and where the ball is supposed to go. I think we’ll be OK.’’