When the Los Angeles Lakers hired Darvin Ham as their head coach, they arguably tasked him with the toughest gig in the Association.

The roster reads like a collection of pieces from different puzzles, and Ham is already working against the clock to form it into a complete, cohesive picture. LeBron James' 37th birthday is behind him. His NBA championship window could close at any moment.

Some—including the stat sheet—would argue the presence of Russell Westbrook is a hindrance to those hopes. That's why the working assumption entering this offseason was that L.A. would put its high-priced point guard on the first flight out of town.

Apparently, the Lakers had other ideas.

While a Westbrook trade shouldn't be ruled out, L.A. doesn't seem desperate to deal him. The Lakers "have no intention of using a first-round pick to facilitate a Westbrook trade," The Athletic's Jovan Buha reported Friday. It's virtually impossible to picture a Westbrook trade happening without a first-rounder to sweeten the pot.

Now, could this be posturing on the part of the Purple and Gold? No question. However, Buha addressed that issue in the report, too, calling the early refusal "not merely a bluff or tactic to try to regain leverage in trade talks." Buha then added, "there is a sentiment among some within the franchise that the right coach and a better supporting cast could smooth over Westbrook's awkward fit with James and [Anthony] Davis."

Could Ham be that coach?

The simple answer is: It's complicated.

On one hand, there are reasons to believe the Lakers are in great hands with their new skipper. The 48-year-old played nearly a decade in the league (suiting up for the 2003-04 Detroit Pistons that knocked off the superteam Lakers in the Finals) and has since coached in it for a decade. He has coached stars like Kobe Bryant and Giannis Antetokounmpo and emerged from the fruitful Gregg Popovich-Mike Budenholzer coaching tree.

Ham's experience and ability to relate to players could help him form relationships that his predecessor, Frank Vogel, never could.

"If you look around the league now, the coaches who are having successes ... [not only have] excellent knowledge but an ability to connect and hold [players] accountable," a league executive told Yahoo Sports' Vincent Goodwill. "He has a personable blend of that. A strong individual. He can garner respect from his players."

Vogel and Westbrook never got on the same page. That fact reportedly contributed to Vogel's ouster, per The Athletic's Sam Amick.

If Ham connects with Westbrook, maybe that's the key to turning things around. There's a universe in which Westbrook gets repurposed as a screen-setter and slasher who spends most of his time off the ball. That role could maximize his efficiency by giving him point-blank chances and opportunities to create offense for his teammates out of short rolls.

Then again, if the idea of putting a player in the right spot means having a 33-year-old, former MVP play a brand new style, that might suggest fit issues that no coach can solve.

Westbrook does his best work with the ball in his hands. So does James. If Davis ever stays healthy, he'll need plenty of chances, too, since L.A.'s hopes are almost entirely in the hands of its stars.

James is the only serviceable shooter of the three. Spacing will be at a premium regardless how the front office constructs the rest of this roster. Defense could be tricky, too, since Westbrook has never played it at a high level, and James' mileage sometimes forces him to conserve energy at that end, particularly if he continues being tasked with a heavy workload.

Ham, of course, knows all of this going into the gig, and the fact he still sought out the gig is a good sign. Surely, he has a vision of how this can work with Westbrook. It sounds like Ham might command the kind of locker room pull to sell that vision to his team.

Still, this only works under the assumption that any coach could navigate their team around the logistical issues that Westbrook's arrival created in L.A. Based on how this past season played out, it's fair to remain skeptical that this puzzle can ever be solved.