You can pick any number of words to describe Bill Belichick.

He is gruff, cantankerous, moody, sarcastic, and stubborn.

On the other end of it, the now-former Patriots coach is brilliant, creative, strong, adaptable, and innovative.

Those all fit. In his years with the Patriots, Belichick earned a spot in the pantheon of football coaches. He led the Patriots to six Super Bowl wins, and what could best be known as two separate dynasties. Or maybe it was one big one.

Whatever the case, he was part coach, part icon, part cartoonish villain for those who did not like him.

But by Thursday, he was out of a job. Owner Robert Kraft and Belichick said it was a mutual parting, but it’s hard to see that transaction in any other way than a firing.

Maybe that detail didn’t matter. Most things don’t end well, and are a little messy. After all, quarterback Tom Brady’s last pass as a Patriot was a pick-six to his former teammate, Logan Ryan, when the Tennessee Titans eliminated New England from the playoffs.

Yet, ugly as this last year has been, it serves real purpose to remember just how good Belichick was in his heyday. His first Super Bowl win, for the 2001 season over the St. Louis Rams, was an all-time upset. Belichick’s game plan, to beat the Rams up all over the field, is as good as any that has been used in a game of that magnitude.

The 2003 and 2004 Patriots cemented the team as no longer a plucky underdog, but the organization that everyone else was chasing. The ’04 Pats were as good as any in the modern era.

Even when Belichick’s teams fell just short, they still left an indelible mark. The ’07 team was a play or two away from an unbeaten season and inescapable immortality.

His failings as a personnel man later in his career are part of the reason he is no longer the coach. But his ability to see what many did not in players like Julian Edelman and Rob Gronkowski are another reason why he was able to win his last three Super Bowl titles.

Then, there was the personality. Oh, that personality. He was downright rude to reporters. Maybe he thought they deserved it. But anyone on the receiving end of his barbs has to admit there was an artistry to Belichick’s answers.

He was sometimes curt, others downright nasty. But, over time, fans — and some reporters — kind of wanted that from him. Any first-time media member who drew Belichick’s ire eventually saw it as a rite of passage.

Maybe fans don’t see it now, but many of them have taken it for granted that in every game since he became coach, Belichick was the smartest guy in the stadium. That is an unbelievable advantage that most people cannot even comprehend at this point.

Patriot fans would look forward with glee any time Belichick faced off against a rookie quarterback. It was like a tenured professor giving a test to a second-grader. There was no shot of the rookie quarterback processing what Belichick was sending his way. And those days are gone now.

But it was not just rookie quarterbacks who struggled with Belichick’s defensive acumen. Ask Peyton Manning how many Super Bowls he would have won if not for Belichick. Manning won two in his career, and maybe he has five, maybe more, without Belichick.

Yet, here we are, and Belichick never truly replaced Brady, and some think that’s a true stain on Belichick’s resume.

Perhaps. But as this chapter of Belichick’s career comes to a close, remember, too, to call him the greatest coach in the history of football. He is as much that as anything else.