Improve every year. Win over the locker room. Connect with your franchise superstar. Make the playoffs in the brutally competitive Western Conference.

Monty Williams checked all the boxes for the New Orleans Pelicans.

So of course, they fired him on Tuesday.

Despite meeting an ownership mandate to make the playoffs -- and doing so with a 45-win season that would've made New Orleans the No. 6 seed in the East -- Williams was let go Tuesday with one year left on his contract.

And speculation among rival teams and coaching industry sources immediately turned to a head coach who is still employed: the Bulls' Tom Thibodeau, who was a candidate for the New Orleans job when the team hired Williams.

Long-simmering tension between Thibodeau and the Bulls' front office is now common knowledge throughout the league, and rival teams expect the Bulls and their gravelly voiced, defensive genius to part ways once Chicago's playoff run is over. How long that playoff run goes, of course, complicates matters; how do you fire a coach who leads you to the conference finals or beyond? And if the parting is mutual, what, if any, compensation would the Bulls demand for Thibodeau to jump teams?

If Thibodeau and the Bulls, indeed, parted ways, it would set off shockwaves in the coaching business. Iowa State coach Fred Hoiberg is widely believed to be the Bulls' preferred replacement, but who would replace him in Ames, Iowa? There's a growing belief that Iowa State would try to lure another Cyclones great from the NBA: Suns coach Jeff Hornacek, currently making less than Hoiberg's average salary with less security than college jobs offer.

From there, where does Scott Brooks land? Which team will be able to lure offensive guru Alvin Gentry away from the 67-win Warriors? The coaching carousel will be spinning in high gear.

The announcement of Williams' firing was made via press release in which executive vice president Mickey Loomis and GM Dell Demps expressed nothing but praise for Williams, who'd become not only popular in the locker room but also influential in the league as a member of the competition committee and, like Thibodeau, an assistant with Team USA.

But league sources pointed out Tuesday that the people whose names were on the press release may not be the ones making the decision. Former Pistons executive Joe Dumars, a Louisiana native, has been providing input with the team and has a close relationship with Loomis and owner Tom Benson.

What's clear is that, with the presence of Davis alone, the New Orleans job jumps to the top of the list of available head coaching vacancies so far this summer -- ahead of Orlando and Denver. With the pre-draft camp under way in Chicago and the conference finals around the corner, here’s the rest of the news moving the needle in the NBA:

Gasol game-time decision. The Bulls are uncertain whether Pau Gasol (hamstring) will be able to suit up for Game 5 against Cleveland Tuesday night. As we saw in Game 4, the Bulls are a lot easier to defend without Gasol. LeBron James skipped shootaround to continue treatment on his sprained left ankle but declared himself "ready to go."

Hawks, Warriors back in control? Could one night be the difference between a disappointing playoff exit and the kind of experience and resilience that all championship teams need to develop during their postseason journey? We'll know Wednesday night, when the top-seeded Hawks and Warriors return home after tying their second-round series 2-2 with Game 4 victories on the road.

It turned out that the Warriors didn't need to play faster; they needed to be more patient. It was like watching a different offensive team in Game 4 than the one that was so disorganized and rushing shots in the previous two games.

What did we learn about the Hawks? They can mimic the Spurs all they want -- from their front-office approach, to their head coach’s style to their strategic approach on both ends of the floor – but there is no substitute for going through a postseason experience together as a team. Will the Hawks be Spurs-like and take command in Game 5, or will they falter again and give life to an opponent that doesn't need much external motivation to believe it has what it takes to pull off an upset, even without All-Star John Wall?

Would Tim Thibodeau leave Chicago for New Orleans? (USATSI)
Would Tom Thibodeau leave Chicago for New Orleans? (USATSI)