The Wizards have their coach. Now they need to upgrade the roster.

The Washington Wizards completed their comprehensive search for a new coach and are set to formally announce the hiring of Wes Unseld Jr. on Monday. As is the case with every coach, it’s impossible to say if Unseld will ultimately prove successful.

The Wizards tried hiring “proven” coaches who couldn’t push the franchise into contender status. What made a coach effective with one team may not translate to another. With a few exceptions, past results as a head coach aren’t necessarily replicable in another context.

With Unseld, the Wizards are choosing one of the most respected assistant coaches in the NBA. His defensive schemes helped get the Denver Nuggets to above-average status desipte lacking quality individual defenders, and he’s known to be a superb communicator. Being the son of the franchise’s greatest and most important player is likely to bring him some goodwill and leeway from fans.

My guess, based on conversations I’ve had with friends around the league and with the Wizards over the years, is that Unseld is a good and effective coach. Whether that translates to wins in his first head coaching gig is going to be heavily reliant on the roster — something that’s true of every coach.

For Unseld to win, Tommy Sheppard and the front office must upgrade the player personnel. When I crunched the team’s regular season numbers by position, I found above average production at point guard and shooting guard, average production from center, below-average at power forward, and below replacement level from the wings.

More than 4500 minutes from last year’s rotation — Raul Neto, Alex Len, Robin Lopez, Ish Smith — are hitting the free agent market. That’s not necessarily a problem, because while each provided value, none performed at a level that makes them irreplaceable.

The challenge for the front office is that even if all four free agents depart, the team is left with meager player acquisition resources. To shop for free agents, they’ll have the midlevel exception ($9.5 million) and biannual exception ($3.7 million).

They also have a couple small trade exceptions — one worth $1 million from dumping Admiral Schofield, and the other about $2.2 million for dealing Mortiz Wagner. The trade exceptions can’t be added together, which means they’re likely to be used in another of Sheppard’s “marginal” trades.

The difficulty: they’ll start the offseason about $14.8 million under the luxury tax threshold, and using the full MLE, the full BAE and signing the 15th pick in the draft will cost about $16.6 million. So far, Ted Leonsis has shown little inclination to spend luxury tax dollars — an entirely reasonable place to draw the salary line, especially for a team that’s unlikely to reach contender status next season.

Of course, the Wizards could use their pick and younger players to make a trade that could fill a roster hole. Somehow, some way, the Wizards need to parlay their resources into:

• A starting SF.
• A backup PG.
• A backup SG with some size.
• Insurance at C in case Thomas Bryant loses something from his knee injury.

It’s conceivable that Unseld’s communications and player development wizardry will enable the franchise to grow from within. Perhaps they get more production at PF from Rui Hachimura making a leap in his third season and Davis Bertans reverting to career norms.

Perhaps Deni Avdija goes from replacement level to competent in year two.

Perhaps Russell Westbrook stays healthy and produces all season like he did the last six weeks.

Perhaps Bryant and Daniel Gafford make a formidable center rotation.

And, perhaps the Wizards win a handful of games they would have lost under Scott Brooks because Unseld is a different and better coach for this team.

This is the great thing about hiring a new coach: the possibilities seem limitless. While it’s improbable that the Wizards fortunes have significantly changed, Unseld brings new ideas and fresh perspective to a franchise in need. His reputation is that he’s a good coach and a good person who has a long history with the franchise and a personal connection to the last time it achieved significant success. Perhaps that’s just what the Wizards need over the next four years.