Here is a summary of Fred Hoiberg's tenure since the Bulls' vaunted, exhaustive, worldwide search -- a thing that never happened, and is now a punch line inside league circles -- unearthed him as Tom Thibodeau's replacement in the spring of 2015.

Year 1: Hoiberg inherits the remnants of Thibodeau's defensive grinder. Joakim Noah is in decline. A stray elbow busts Derrick Rose's orbital bone during a preseason practice, slowing his integration into Hoiberg's offense.

Jimmy Butler emerges as Chicago's best player (by far), and annoys teammates by flaunting his new alpha dog status. He clashes with Hoiberg. After a mid-December loss, Butler declares the Bulls need to "be coached harder at times," an early indication that Butler doesn't fully respect Hoiberg's authority. The organization was concerned about Hoiberg's hold over the team then, and never really stopped being concerned until Monday morning's announcement.

The Bulls are light on shooting, and heavy on ball-stoppers -- a poor fit for Hoiberg's preferred pace-and-space style. Holdover players urge Hoiberg to reinstall some of Thibodeau's old sets, sources tell ESPN in the winter of 2015. "Fred put in a lot of ball movement, but we have a lot of guys who hold the ball a lot," Noah tells ESPN.com then.

Year 2: The Bulls trade Rose and let Noah walk to New York, presumably opening a path to a roster more styled for Hoiberg's system. They sit out free agency in the summer of 2016 -- the summer of the cap spike, of Bismack Biyombo and Timofey Mozgov and Ian Mahinmi and Luol Deng and Kent Bazemore and, umm, Noah -- hoarding their space for future summers and/or in-season money dumps from teams about to feel intense buyer's remorse.

Smart! But as free agency lurches to a halt, the Bulls notice two decorated All-Star veterans remain available. They cannot resist the chance to add Rajon Rondo and Dwyane Wade on fat (partially guaranteed) two-year deals, vaporizing that carefully carved out space, and handing Hoiberg -- pace-and-space Hoiberg -- perhaps the worst 3-point shooting team in the league. To cap it off, they trade Tony Snell for Michael Carter-Williams.

They sneak into the playoffs, and lead the top-seeded Celtics 2-0 before Rondo injures his thumb. They lose the next four games. They also give us Three Alphas, maybe the worst nickname for any cluster of stars, ever, in any sport, and certainly the most absurd.

Year 3: The Bulls scrap everything and rebuild! They waive two alphas and trade the third, Butler (plus the No. 16 pick in the 2017 draft), to Minnesota for Zach LaVine, Lauri Markkanen, and Kris Dunn. Bobby Portis breaks Nikola Mirotic's face. Mirotic returns in December. He hits many 3-pointers. The Bulls win many games. The Bulls don't want to win many games. The Bulls trade Mirotic for Omer Asik, many buckets of Omer Asik's sweat, and what would become a late first-round pick (the very bouncy Chandler Hutchinson).

They are bad on purpose and select Wendell Carter Jr. with the No. 7 pick. Good!

Year 4: The Bulls sign Jabari Parker to a two-year, $40 million deal -- with the second season at their option -- instead of potentially using their space to rent Denver's bad contracts, and another first-round pick. (Brooklyn did this for the Nuggets instead.) OK, sure. As I wrote here, teams and the NBA media have perhaps fetishized those cap dump trades. Teams have paid a fortune in bad money for picks in the 20s, or worse. That includes the Bulls, who gave up a good player (Mirotic) and swallowed Asik's contract for that one Hutchinson pick.

But Parker plays the same position as Markkanen, the team's most important player, a reality with which no one seemed all that concerned. Parker would guard wings! The Bulls would switch a lot, anyway! (Markkanen's preseason elbow injury forestalled the positional fit questions until his return Saturday. It seems strange and cruel to fire Hoiberg upon Markkanen's return, unless the Bulls are trying to set up his replacement -- Jim Boylen -- for success.) Nor was anyone much concerned that pairing Parker and LaVine risked near-constant flammability on defense.

These Bulls were never going to be good. It was very, very unlikely they would even sniff the vague conversation for the No. 8 spot in the junior varsity conference. And that was before players got hurt, including Markkanen, Dunn, Portis, and Denzel Valentine. The team is starting freaking Ryan Arcidiacono at point guard and playing him 40-plus minutes in some games. They are giving many fewer minutes to Cameron Payne, for whom they ludicrously traded Taj Gibson, Doug McDermott, and a second-round pick in a deal that made so little sense at the time you almost wondered if there was another "C. Payne" in the league you had forgotten about. Payne is getting minutes now only because Hoiberg (and lots of League Pass viewers) tired of Antonio Blakeney shooting every single time he got the ball.

There were other detours involving Pau Gasol and Carmelo Anthony, and a landmark draft day trade gone bad in which the Bulls flipped the picks that became Jusuf Nurkic and Gary Harris for McDermott.

The bottom line is this: If you know after those three-plus seasons that Hoiberg is either a good or a bad NBA coach, I am both impressed and a little worried about the confidence you have in your convictions. I freely admit I have little idea. The Bulls have had zero on-court identity over that entire span, and a lot of that confusion -- likely most of it -- lays at the feet of Gar Forman and John Paxson above him.

Hoiberg wanted to shoot 3s; the Three Alphas Bulls ranked 28th in 3-point rate, and the team has been around league average since. The Three Alphas team crashed the hell out of the offensive glass. The last two iterations ranked near the bottom of the league in that category. (They are last right now.)

Their pace of play -- another alleged Hoiberg hallmark -- jumped all over the place. Hoiberg loves to shift the ball from side-to-side; the Bulls ranked 10th, 10th, 15th, and 13th in passes per game over his tenure, per NBA.com. Whatever. He talked before this season about installing the famed San Antonio "0.5" rule -- a command that no player hold the ball longer than half a second before shooting, passing, or driving. Shockingly, some players -- ones he did not pick -- had trouble with that.

Hoiberg talked about switching more; the Bulls switched at about the same league-average rate as last season, per Second Spectrum data. They lost several close games, including one against Detroit in which Hoiberg inexplicably left Parker on the floor for a crucial last-second defensive possession.

You could argue it is on the coach to install some sort of coherent identity -- at least one thing for which a team stands regardless of roster turmoil. There is truth in that. A Mike D'Antoni team is going to shoot 3s. An Alvin Gentry team is going to run. A Quin Snyder team is going to pass and cut a lot. A Gregg Popovich team is going to defend (at least until this season).

Hoiberg is not a forceful personality, and I have come to believe, after talking to lots of sources over lots of years now, that his tepid nature played some role in his inability to imprint any foundational belief upon any of his four Chicago teams. Had he done so, perhaps there would have been less roster upheaval.

But, my God, look at all that upheaval. That is a lot of upheaval. Hoiberg walked into an established team that didn't fit his principles, and then coached three wildly different rosters with wildly different goals. Any coach would have struggled to establish any core feature across two or three of those teams -- let alone all four of them.

Hoiberg's situation is similar to that of Scott Brooks in Washington: None of this is really his fault, but he might not have been the coach to galvanize this bad team or that mishmash roster.

The Bulls under Forman and Paxson had no discernible direction until dealing Butler in the summer of 2017. They would surely argue that they could not possibly have had such a direction until then -- that Rose's max contract imprisoned them until they offloaded him in 2016, and that Butler's presence on the roster then mandated they wait and evaluate. There is some truth in that, too.

But the moves outlined above speak for themselves. Even amid that Rose purgatory, the Bulls both forfeited some opportunities to build up their war chest and acquired players in an alarmingly haphazard fashion.

They are building, now. They made a bet that the Markkanen/Dunn/LaVine/Carter/2019 first-round pick nucleus represented a better chance at long-term title contention than a team built around Butler (potentially on a supermax contract), Mirotic, and all of Chicago's own (presumably midtier or below) first-round picks.

It is that bet that will determine how long Forman and Paxson stick around. It is not a closed case. Butler is awesome -- a borderline top-10 player. Forman and Paxson have had some hits late in the first round -- most notably, Butler. They cannot boast about those and then argue they would have had no chance to nail another pick in that range with Butler and Mirotic on the roster.

Parker may not be on the team next season. Dunn is almost 25, with no track record of anything close to average NBA starting point guard play.

LaVine's play on offense this season, and especially his hard-charging drives, has been largely promising even as his shooting has dropped off. The Bulls are also 29th in points per possession, and have scored at about that rate in LaVine's minutes, per NBA.com. He's still not efficient enough as a shooter, or enough of a playmaker, to work as the lead dog of an above-average NBA offense.

Markkanen's return will lighten LaVine's burden. That's good. LaVine is talented enough to do well on offense in a secondary role. Carter and Markkanen should prove a snug fit on the front line -- on both ends. The Bulls may have to cultivate an ace playmaker, or figure out whether they have enough other stuff to build a functional offense without one.

Maybe they will develop into a killer shooting team. Maybe Markkanen becomes a Dirk Nowitzki-esque sharpshooting screen-setter who warps opposing defenses to a degree that compensates for Chicago's lack of an "A"-level off-the-bounce orchestrator. Maybe the Markkanen-Carter duo brings so much shooting and passing that the Bulls get by that way.

We don't know. There is a ton of work left. Markkanen and Carter are promising enough that Chicago's long-term championship equity is probably a little higher now that it would be with Butler, Mirotic and all their own picks. (Butler is almost 30, and his next contract will be a doozy.) But if you simulated every outcome for both macro versions of the Bulls, the most likely end point for both would probably be the same: good but not great. There are worse plausible endpoints than that, too.

That is not to say these Bulls can never be great with Markkanen, Carter, and whatever cast joins them. It is to say the surrounding cast might have to look very different than it does now. That's fine. That's normal. Rosters turn over fast in the NBA.

That includes the coach. The Bulls -- Forman, Paxson, ownership -- did not put Hoiberg in a position to succeed. Chicago's failures post-Rose are more about their choices and franchise circumstances -- digging out from the Rose-Noah era -- than anything Hoiberg did in games or in practices.

It is on them now -- to get this hire right, whether it's Boylen or someone else, and to find the right surrounding pieces. The Bulls are far, far away, and dismissing Hoiberg doesn't change that.