Fifty years ago this weekend, the Steelers hired Chuck Noll. Nineteen years ago this weekend, the Patriots hired Bill Belichick.

Both are great coaches. Both were the grateful recipients of good fortune. The previous two sentences are not contradictory.

Before Belichick and Tom Brady became legends, they were a once-fired head coach with a losing record and a long-shot backup quarterback.

On the morning of Jan. 22, 2002, Belichick’s record as an NFL head coach was 52-60. Brady was a sixth-round draft pick forced into the starting lineup by an injury. Neither had won a playoff game. The Patriots were 11-5 and facing a home playoff game against Jon Gruden’s Raiders, featuring former Vikings quarterback Rich Gannon.

Had the Patriots lost that game, they would not have advanced to the Super Bowl, and Belichick and Brady would not have written the first page of their Hall of Fame résumés.

At that Super Bowl, Belichick’s defense throttled the Greatest Show On Turf and Brady led his first big-game, late-game winning drive.

The Patriots beat the Rams in the Super Bowl — and required a little luck to even get there. Don’t be surprised if luck sways the second Pats-Rams Super Bowl, because luck spends more time on Super Bowl victory podiums than on the bench.

Take this year’s Rams. If not for a call so egregiously missed that it will probably cause rules to be rewritten, the Rams would not be in the Super Bowl.

Take this year’s Patriots. If not for a barely justifiable roughing the passer call that gave the Patriots a key first down, they might not be at the Super Bowl.

The point here is not that these teams won only because of lucky breaks, but that winning NFL teams often require a combination of luck and ability.

Back to Jan. 22, 2002. The Raiders led 13-10 late in regulation. Raiders cornerback Charles Woodson sacked Brady. The ball popped loose and future Viking Greg Biekert recovered. Game over.

Or not. Officials reviewed the play and determined that Brady was “tucking” the ball as his arm moved forward, ruling the play an incomplete pass instead of a fumble. Adam Vinatieri kicked the tying field goal and the Patriots won in overtime.

Dynasties are built on such moments. Franco Harris’ “Immaculate Reception” now feels like part of a decades-long highlight reel of important Steelers victories, but at the time the Steelers had never won a playoff game.

There is no clear proof that Harris caught the deflected pass before it hit the turf, or that the ball didn’t bounce off of a teammate, which would have then made it an incomplete. The play stood, giving Chuck Noll his only playoff victory in his first five seasons as a head coach.

Viking fans know the flip side of luck. Drew Pearson’s game-winning touchdown catch at Met Stadium in the 1975 NFL playoffs is called, in Minnesota, The Push Off. Pearson caught the pass as Vikings cornerback Nate Wright fell, and one of the best Vikings teams in history failed to advance. The Steelers would beat the Cowboys 21-17 in the Super Bowl.

The Patriots required luck to advance to the first Super Bowl they would win. They required luck in their last Super Bowl victory, over Atlanta two seasons ago.

With about 2:30 left in regulation and trailing the Falcons 28-20, Brady threw a pass intended for Julian Edelman into a crowd. The ball was deflected, fell and bounced off a Falcon’s leg before Edelman gathered it in, an inch from the turf.

Great catch? Yes, one made possible by a lucky bounce. The Patriots would send the game to overtime and win.

There is no control group for these kinds of reminisces. We’ll never know whether that Vikings team would have won its only Super Bowl had Pearson been called for interference, or how differently the Patriots’ dynasty would be viewed if not for an altered call and a lucky bounce.

What we know for sure is that the winner of this year’s Super Bowl will have required luck to win it all.