Bill Belichick is as well-prepared, demanding, and calculating as any coach in NFL history. Those traits have propelled him to greatness and helped him craft arguably the greatest coaching career ever. They also make him difficult to deal with occasionally.

Belichick was right to bench and then release Bernie Kosar from the Browns in the early 1990s, but it turned Belichick into a villain with the fans and the team’s owner. He was correct in his evaluation of Drew Bledsoe in the early 2000s, that the Patriots’ franchise quarterback was over the hill, but it was another decision that wasn’t always popular with his fans and the team’s owner.

Belichick is a football savant, breaking down film with his father at a young age and accumulating a vast universe of knowledge over the next five decades. He needed a quarterback who not only had the physical skills to succeed in the NFL, but the brains to outthink the defense, the drive to be the hardest worker on the team, and the abject fear of failure to make sure he remained at the top of his game.

Little did Belichick know, but his perfect quarterback walked into his life in 2000, when the Patriots drafted an unassuming player named Tom Brady with the 199th pick in the sixth round.

“Bill needed a guy that was going to be really, really sharp, and that could challenge him mentally,’’ said Charlie Weis, the Patriots’ offensive coordinator from 2000-04. “I think Bill likes people around him that are smart, and he likes players that are smart. Tom was a skinny little kid out of Michigan, but you could tell. He was on a mission.’’

The result, of course, was arguably the greatest dynasty in NFL history. The Patriots’ four Super Bowl titles in the span of 14 seasons can go toe-to-toe with the Cowboys of the 1960s and ’70s, or the 49ers of the ’80s and ’90s.

What’s not in question is that the Brady-Belichick pairing is the longest between quarterback and coach — now 17 years together as the 2016 season kicks off. Joe Montana and Bill Walsh lasted 10 years together. Terry Bradshaw and Chuck Noll went 14 years. Dan Marino and Don Shula 13 years. Roger Staubach and Tom Landry 11 years.

Brady and Belichick brought the Patriots their first Super Bowl title, then three more championships. They have reached six Super Bowls and 10 conference title games, and taken permanent residence atop the AFC East, winning 13 division titles in 16 years. Brady has won two MVP awards, Belichick three Coach of the Year awards.

“There’s a singular purpose in New England that is difficult to achieve,’’ said Boomer Esiason, the former NFL quarterback turned commentator. “And if you have what I consider the greatest quarterback of all time buying into what you’re selling to your team, and you are the greatest coach of all time in the NFL, then it’s easy to sustain success as long as they both believe in the process they’ve put forth, which they have.’’

Their careers are superlative on their own, but separating their accomplishments is nearly impossible. There is no mentioning Brady without Belichick, and no mentioning Belichick without Brady.

“I have a great respect for the way they play, the way they approach the game,’’ Peyton Manning said. “They’re both very similar that way. They are football junkies, if you will. I think that’s a compliment.’’

Their relationship is what you’d expect with two focused, driven, and competitive personalities — all business. They meet regularly every Tuesday in Belichick’s office to discuss the game plan, and again on Saturday to go over final preparations. They have played golf at Pebble Beach, and maybe have shared a beer together in a quiet moment in the offseason, but 99 percent of their relationship takes place within the walls of Gillette Stadium, talking about football.

“I love coaching Tom. Been fortunate to have him [his] whole career,’’ Belichick said. “We meet at least twice a week, sometimes more. Spend a considerable amount of time together. I think that’s important to have that relationship between the head coach and the quarterback so at least we’re on the same page [with] what we’re trying to do. He has great feedback. Nobody works harder or prepares better than Tom does. He’s about as good as it gets in that category. He’s got a lot of great ideas. Very smart, experienced player obviously and does a great job executing the team game plan.’’

Their relationship has thrived since 2000, when Brady worked so hard as a rookie that he forced Belichick to keep four quarterbacks on the roster.

Yet it was a death in the family that really served as the genesis behind their all-time greatness.

The Patriots suffered a sudden and shocking loss on Aug. 6, 2001, when quarterbacks coach Dick Rehbein died of heart failure at age 45. Rehbein was involved in drafting Brady, served as Brady’s position coach in his rookie year, and was one of his biggest supporters.

Weis remembers sitting in Belichick’s office in the days following Rehbein’s death and helping his boss decide how to replace their quarterbacks coach.

“We decided not to replace him, and [Bill] and I would handle it ourselves,’’ Weis said. “What we did was, any time I was going to speak to the whole offense, Bill would take the quarterbacks first. And while everyone saw Bill as a defensive guy, Bill really took that project.’’

That was the year that Brady famously took over in Week 2 after Drew Bledsoe was knocked out with an injury. Weis had the dual role of offensive coordinator and quarterbacks coach that year, but Belichick worked closely with Brady and helped him see the game through the eyes of the defense. The coaching worked so well that first year — ending with Brady’s first Super Bowl win, of course — that Weis and Belichick kept the same responsibilities in 2002.

“He was just unbelievable,’’ Weis said of Belichick. “He would teach them what the opposing defenses were doing, he would analyze each position player that they were going against in the secondary, their strengths and weaknesses. And I don’t think that there’s too many times in NFL history where a quarterback position would spend that much time with a head coach, especially one who was known to have a defensive background.’’

That dynamic didn’t change too much when the Patriots hired John Hufnagel as quarterbacks coach in 2003.

“Even when we brought in quarterbacks coaches, [Belichick] would always meet with [Brady] some on Tuesday, our players’ day off,’’ Weis said. “They would meet earlier in the day to go over personnel, then I’d meet him and go over plays later in the day. And I think that worked out great for us because those guys were always the best prepared, but they’re also as competitive in all they do as anyone I’ve ever met.’’

And Belichick had the perfect pupil in Brady, someone who couldn’t get enough film study or practice time on the field and couldn’t stop spouting ideas. Brady was mostly a yes-sir, no-sir pupil in his first couple of years, but his immediate success helped him develop a voice with his coaches.

“When he was young we’d usually tell him to shut the hell up, but where Tommy stood out was in the quarterback room,’’ Weis said. “You could see that he was right on top of things mentally. As he matured with both of us, it was more questions, more ideas, and by the time I left he was being more and more involved in the game plan.’’

“Sometimes he’d give me too many ideas — ‘Well, what about this?’ ‘What about that?’ I remember sitting there after Super Bowl XXXIX at about 3 o’clock in the morning, and I was leaving [for Notre Dame], and he goes, ‘What am I going to do now?’ I said, ‘You don’t need me, big boy. You’re way above me at this point.’ ’’

Brady has always been the perfect conduit for what Belichick and the coaches want to accomplish.

“Tommy never had wasted time,’’ Weis said. “Whether it was getting treatment, lifting weights, watching tape, meeting with other players, he always had a plan.’’

Belichick does not often play favorites with Brady, and in fact likes to make an example of him in front of the entire team.

“Tommy has said to me different times, ‘Belichick has a perfect soldier with me,’ ’’ Brady’s father, Tom Sr., said in the book “Brady vs. Manning,’’ released last year. “When Randy Moss comes in and sees Tommy getting chewed out and accepting it, the other 52 guys fall in line . . . Tommy is absolutely the perfect quarterback for Bill Belichick because he understands what Belichick is doing, and has enough pride to know that no matter what Belichick might say to diminish his efforts, it’s not going to impact who he is and what he knows he can do.’’

The relationship with Belichick is not always perfect. There are Brady’s famous fits of rage on the sideline, mostly directed at his receivers but occasionally at a coach (remember Bill O’Brien in 2011). Brady was not happy with the Logan Mankins trade or the direction of the team early in 2014, and wasn’t thrilled with the way the coaches split practice snaps between himself and Jimmy Garoppolo this training camp.

Rodney Harrison, the former Patriots safety and now a commentator for NBC, said that part of Josh McDaniels’s role now is to be a buffer between Brady and Belichick when they are clashing.

“First and foremost they’re both stubborn, to a point where they think their way is the best way,’’ Harrison said. “So I think at times, Tom wants to do certain things his way, and it’s part of him being a competitor. But the one common denominator is just mutual respect. I think Tom understands that it was Bill Belichick that gave him an opportunity when no one else saw the potential.’’

And even after 17 years, Brady and Belichick never really kick back and enjoy downtime together.

“I don’t think we ever have,’’ Brady said in the book. “Whenever we have time, nothing ever comes of it.’’

“To my knowledge, he and Tommy have never been to dinner, never been to lunch,’’ Brady Sr. said. “That’s perfectly fine with Tommy, because he’s got a whole bunch of great friends. He doesn’t need to be personal friends with the coach.’’

But the profound respect between Brady and Belichick is obvious.

“We don’t probably talk as much as people may think,’’ Brady said in the book. “He trusts me to do my job and lets me do my job. There’s times where I get to express certain things to him, and I think he has a lot of trust in the things that I say.’’

Belichick has never been one for self-promotion — and Brady is an extension of Belichick, of course — but Belichick’s heart has warmed a bit the last few years. After the big win against Cincinnati in 2014 — the “on to Cincinnati’’ game — Belichick presented Brady with a game ball for surpassing 50,000 career passing yards.

“We’re certainly not big on individual stats around here, but 50,000 yards . . . ’’ Belichick said before trailing off and hugging Brady.

And this past spring, speaking at the Salesforce World Tour in Boston, Belichick casually referred to Brady as “the greatest quarterback of all time.’’

“He’s been just a tremendous leader and a tremendous player for our organization,’’ Belichick said.

The million-dollar question, of course, is who deserves more of the credit for the Patriots run? Belichick was a sub-.500 coach in Cleveland before Brady, and Brady was an NFL afterthought until Belichick got his hands on him. Belichick has never won a title without Brady, and the reverse is true, too.

Coming to an answer scientifically is futile, and it simply comes down to opinion. All that matters is that for 17 years, Belichick has been a great coach, Brady has been a great quarterback, and the two have propelled each other, and the Patriots, to levels of excellence rarely achieved in the NFL.

“What difference does it make?’’ Weis said. “How many can claim to be the best? Not that either one of them would say it, but they’re both arguably the best there’s ever been at what they do.’’

Ben Volin can be reached at ben.volin@globe.com. Follow him on Twitter @BenVolin