Matt Patricia cuts a distinctive appearance on the sideline. Baseball cap worn backward, bushy black beard and his trusty No. 2 pencil always tucked behind his right ear. Basically, a grown-up version of your freshman year roommate.

If Paul Bunyan had a son, he would look like Patricia.

The New England Patriots defensive coordinator — for the time being — arrived at Super Bowl LII Opening Night in full character, pencil included, except he accessorized with a leather jacket.

Why the pencil for an interview session?

“My brain kind of spins all the time,” he said. “I write ideas down.”

His mind probably is spinning like a tornado this week. Game-planning to face the Philadelphia Eagles offense, first and foremost, but Patricia also reportedly will be the next Detroit Lions head coach, though nothing can become official until after the Super Bowl. Patricia can’t talk publicly about it, and the Lions can’t announce it, but the gig is his sometime after Sunday.

Patricia dodged repeated questions about the Lions with some variation of “I’m just worried about Philadelphia,” but his hiring immediately moves him to the top of the Smartest Head Coach in the NFL list.

Patricia owns a degree in aeronautical engineering from prestigious Rensselaer Polytechnic Institute (RPI). He spent two years working in that field before deciding that coaching football fit him better than rocket science.

That raises a pertinent question: Which is more challenging, rocket science or coaching the Detroit Lions?

The NFC North should be fascinating next season with two new head coaches, the return of Aaron Rodgers and a team that fell one step short of the Super Bowl.

The Chicago Bears replaced John Fox with Kansas City Chiefs offensive coordinator Matt Nagy, another Andy Reid disciple. The Lions followed the Vikings’ lead and hired a head coach with a defensive background.

Patricia never has been a head coach at any level but he’s worked alongside Bill Belichick for 14 seasons, the past six as his defensive coordinator.

Being exposed to Belichick’s genius for that many years provides a solid foundation but doesn’t guarantee that Patricia will transform the Lions into a playoff regular. Any number of variables dictate whether a head coach succeed or fails, beyond his résumé.

The manner in which Patricia handles being CEO of an entire football operation will determine if he wins big at a place where so many coaches before him have failed.

One thing is for certain though: Patricia knows how to construct a top-shelf defense, and that coupled with quarterback Matthew Stafford directing the offense makes the Lions more legitimate on paper.

The Lions ranked 21st in scoring defense this season; the Patriots finished No. 5. New England’s defense has ranked in the top 10 in fewest points allowed in all six seasons with Patricia as coordinator, including No. 1 in 2016.

“He will get the best out of you,” Patriots safety Patrick Chung said. “He’s a good dude. Sometimes he’ll get under your skin, but he’s doing it for a reason, to get the best out of you. He’s given me a lot of good years in my career.”

Chung described Patricia’s coaching style by noting his creativity with scheme and personnel.

“You never know what’s going to happen,” he said.

Patricia’s back story makes him a unique character in a profession littered with similar career paths. He scored “in the 30s” on his ACT and his favorite college courses involved theories and fundamentals of flight. He declined to name his least favorite class but noted that “thermodynamics was probably one of my more difficult ones.”

Belichick hired him as an entry-level quality control coach in 2004. Patricia slept so many nights at the office doing grunt work that his wife bought him a mattress to keep at the stadium.

“I actually have a nice little Tempur-Pedic rollout mattress,” he said.

He consider four hours of sleep at night a “luxury.” His fixation on No. 2 pencils began as a young coach when he worked into the wee hours diagraming plays by hand with the “old-school method.”

He used mechanical pencils as an aeronautical engineering student. He went authentic as a football coach.

“In the end, a good ol’ No. 2 finely sharpened was the best weapon,” he said.

A finely sharpened defense gets the job done, too. And Patricia has overseen a lot of those as Belichick’s trusted coordinator. Now he’ll try to bring that magic touch to Detroit, which makes the NFC North more interesting and potentially more competitive.