Frank Vogel leaves the Paceers as the winningest coach in franchise history among those who have spent three or more seasons with the team. (Michael Conroy/Associated Press, File)

For a franchise desperately searching for an identity since Dwight Howard’s melodramatic departure in 2012, the Orlando Magic made a surprisingly cerebral decision last week by plucking Frank Vogel to be its new head coach.

The move was made after Scott Skiles, who reportedly didn’t want to be there, stepped down following his first season.

Vogel, 42, spent the last decade with the Indiana Pacers, amassing a 250-181 overall record in his six seasons as the team’s head coach (he previously served as an assistant). He is the winningest coach in franchise history among those who have spent three-plus seasons with the team, and took the Pacers to back-to-back conference finals appearances in 2013 and 2014. Orlando, on the other hand, has been atrocious over that stretch, winning a combined 140 games the past five seasons while failing to qualify for the playoffs once. That 140-win total is tied with the Sacramento Kings for the second fewest over that stretch; only the Philadelphia 76ers, a team reputed for its wholesale tanking stratagem, amassed fewer.

However, with Vogel in the fold, the Magic should see improvement on both sides of the ball.

Indiana twice led the NBA in defensive rating under Vogel and ranked in the top 10 every full season he was head coach. The bruising David West-Roy Hibbert tandem turned away shots at the rim like a four-armed flyswatter set to the beat of a metronome, suffocating offensive rebounding opportunities for opponents. Second-chance scoring happened sparsely, and the Pacers allowed the fewest points in the paint in the league in three of Vogel’s five full seasons at the helm.

Hibbert wasn’t a defensive player of the year nominee before studying under the tutelage of Vogel — and certainly hasn’t been since he left that system. This could be good news for Nikola Vucevic, a 7-footer with a strong offensive acumen and repertoire, who allowed opponents to shoot 54 percent at the rim against him this season.

Vucevic, at least in recent seasons, has played like the antithesis of a Vogel defensive system: subpar on that end of the floor and providing little back-line assistance. The Vucevic-Aaron Gordon tandem has been mostly a failure thus far, allowing 107.9 points per 100 possessions this past season. But both are dynamic big men who might just need the right defensive guidance to make this pairing opportunistic.

Offensively, the Magic is very much an identity-less team, as it has been for years. There’s talent in the low block and along the perimeter, but no surplus of either. The team did show signs of scoring improvement in the second half of the season, putting up 7.2 more points per contest after the all-star break than before it.

Subscribing primarily to a bruising, back-to-the-basket offensive methodology while West and Hibbert were in the fold, Vogel found success along the perimeter with his small-ball lineups this past season. Indiana saw an 8.6 percent uptick in three-point attempts in 2015-2016 and connected on virtually the same percentage as the season prior, which could be something to look for when he heads to Orlando, which ranked 20th in three-pointers taken per 100 possessions.

Evan Fournier was far and away the team’s best three-point shooter this season, finishing in the top 10 in the league in three-point percentage among players who hoisted more than 300 shots from the perimeter. But he is an unrestricted free agent this summer. Victor Oladipo improved his three-point stroke this season, as did Elfrid Payton, and both will likely see more perimeter looks under Vogel. Indiana and Orlando both were above-average teams this past season in total passes made per contest, but Vogel’s schemes found more open shooting opportunities; Indiana took 1.5 percent more open three-point shots — as defined by having four to six feet of space between the shooter and defender — than Orlando.

We can also expect Orlando, like Indiana, to find success generating turnovers. Oladipo, Payton and Fournier each averaged more than one steal per contest, and the Magic (8.7) ranked just below the Pacers (8.8) in steals per 100 possessions post-all-star break. Vogel should get the Oladipo-Payton combo forcing turnovers and hawking opposing guards along the perimeter in no time.

Making less-than-sparkling units shine is Vogel’s calling card and he’s certainly not entering an environment laden with all star-level talent. However, the team will have nearly $50 million in salary cap space to work with, per The Post’s Tim Bontemps, and last week Orlando landed the No. 11 overall pick in next month’s NBA draft to go alongside the No. 41 and No. 47 overall picks. Armed with a mostly solidified backcourt — both Oladipo and Payton are under contract at least through next season, unless the Magic decide to deal one or both of them — drafting a versatile wing is a necessity, so look for a player like Furkan Korkmaz, Taurean Prince or Timothe Luwawu to be selected in the upcoming draft. As for free agency, expect Orlando to aggressively work to re-sign Fournier and chase someone like Charlotte’s Marvin Williams or Portland’s Allen Crabbe.

With a latent group of up-and-comers like Gordon, Payton and Oladipo, Vogel will bring a hard-nosed outfit to the court next season. Orlando has spent four years without a playoff appearance. The city might not have to wait much longer.