– Jan. 3, 2000. A date that changed NFL history and set in motion a 15-year odyssey for Pete Carroll, Bill Belichick, the New England Patriots and the Seattle Seahawks.

On Sunday, the four will converge in Super Bowl XLIX and fight for enduring legacies that were unfathomable 5,504 days ago.

On that day, Jan. 3, 2000, Belichick had a sub-.500 record from five seasons in Cleveland and hadn’t been a head coach in a game in five years. Carroll was two games over .500 (33-31), including a one-year, 6-10 stint with the Jets in 1994, and was in the process of being fired by the Patriots that very morning.

“Pete Carroll,” the Associated Press wrote in its lead sentence that day, “was a nice guy who finished last.”

Four paragraphs later, it was noted that Patriots owner Robert Kraft had asked the Jets for permission to interview Belichick but was denied because he was elevated that morning from defensive coordinator to head coach, replacing Bill Parcells.

Belichick, of course, resigned a day later and ended up succeeding Carroll. But not until the league forced Kraft to compensate the Jets with a first-round draft pick.

That bit of history wasn’t lost on Carroll this week. With Belichick one victory from tying Chuck Noll for most Super Bowl titles by a head coach (four) and Carroll attempting to become the seventh coach to win back-to-back Super Bowls, Carroll playfully brought up their humbler days during Friday’s joint news conference.

“[They] got a first-rounder for you?” Carroll asked Belichick. “I was barely a free agent. Maybe that’s why Robert threw me out of there after three years. Huh, Robert?”

Not missing a beat, Belichick said, “I was a free agent after Cleveland.”

Three months after Jan. 3, 2000, the Patriots drafted quarterback Tom Brady in the sixth round and began a stretch of six Super Bowls in 14 seasons a year later. A victory on Sunday and Brady ties Joe Montana and Terry Bradshaw for most Super Bowl wins (four) by a quarterback.

Meanwhile, Carroll used Jan. 3, 2000, as the motivation that propelled him to two national titles at Southern California before returning to the NFL and leading the Seahawks to their first Super Bowl win. A win on Sunday and his defense will have felled Peyton Manning and Brady in back-to-back Super Bowls.

“The pain and struggle and hardship, and then the challenges of bouncing back, were all part of the rebirth of a philosophy and a mentality,” Carroll said. “[The Patriots] supported me in a tremendous way until they couldn’t anymore. Then they made one of the great moves in the history of the NFL by hiring Bill Belichick.”

Sunday, after two weeks of “Deflate-gate” controversy over the Patriots’ use of underinflated footballs against NFL rules in the AFC title game, the attention finally shifts back to the football field. An old dynasty meets possibly the next dynasty as two “retread” coaches, as Carroll put it, show off the many ways in which they turned their careers from pink slips to Lombardi Trophies.

Here are six examples — three for each coach — for how they’ve done it:

Chemistry lesson

Seahawks offensive coordinator Darrell Bevell expects to become an NFL head coach someday. He hopes he’ll have Carroll’s feel for team chemistry and his conviction to protect it. Even when doing so results in a counterintuitive move such as trading Percy Harvin, one of the league’s most gifted and versatile athletes, at the discounted price of a fourth-round draft pick.

“It’s fun to sit there and watch and see how he reacts and handles different situations,” Bevell said. “Not only that one. He’s made a lot of hard decisions. That’s one that ended up being a huge decision, but in the long run you could tell it was the best move for the Seahawks.”

Harvin’s volatile and high-maintenance personality was pulling Seattle away from its team-oriented identity. So Carroll pulled the unpopular trigger two days before a loss at St. Louis dropped Seattle to 3-3.

“It’s a difficult deal because you have a player who is so talented on the field and can do so many things,” Bevell said. “Your mind as an offensive coordinator is just going with all the positive things that he can do on the field.”

But since that St. Louis game, the Seahawks are 11-1.

“It was good to watch what that decision exactly came down to,” Bevell said. “Then, ultimately, it was good watching Pete being able to pull the trigger on a move that was needed.”

A beautiful X’s & O’s mind

Belichick took his penchant for morphing his team’s look on a weekly basis to another level when he unveiled a four-man offensive line with running back Shane Vereen reporting as an ineligible player in the divisional playoff win over the Ravens. Belichick was inspired when his former protégé, Alabama coach Nick Saban, tried it last fall.

Baltimore coach John Harbaugh complained, but no rules were broken because officials notified the Ravens of the ineligible player. Former Colts coach Tony Dungy said it was vintage Belichick “finding a loophole” that the league’s competition committee will have to examine this offseason.

Vereen, who could have received a backward pass even as an ineligible receiver, said the players weren’t surprised when Belichick introduced the look.

“We do so many things with our offense, I guess we figured it was only a matter of time before we start doing something like this,” Vereen said. “We have like 10 million different formations. But, yeah, part of me was surprised that nobody had tried this before.”

Carroll keeps it cool

Heath Farwell, the former Viking who became essentially a coaching intern while on Seattle’s injured reserve this season, bets you’ll never guess what the Seahawks did to open their first team meeting upon their arrival in Arizona.

“We brought our basketball hoops to the meeting rooms here,” Farwell said. “And we started that first team meeting here with a shoot-off. It got the competitive juices flowing. That’s what this organization is all about.”

Whether it’s “Competition Wednesdays,” “Turnover Thursdays” or some other creative motivational twist, players respond to Carroll’s spirit and positive attitude. As for on-field production, well, the Seahawks are tied with the Patriots with a league-leading plus-51 turnover ratio the past three seasons.

Success breeds conformity

Running back LeGarrette Blount is the latest in a long line of reclamation players who misbehaved elsewhere but then conformed to the “Patriot Way” because they’re in awe of Belichick’s success and his interest in them.

“Coach Belichick doesn’t trust everybody,” said Blount, who rejoined the Patriots this season after the Steelers released him for leaving the field early in a Week 11 loss at Tennessee. “I appreciate that he trusts me that much.”

The powerful running of the 6-foot, 250-pound Blount is a tough matchup for Seattle’s stellar defense. Yet when he became available this season, not a single team put in a claim. It didn’t help that he was facing a marijuana charge that has since been dropped.

“You’d have to ask Pittsburgh about Pittsburgh,” said Belichick, proving again he doesn’t judge a player by his past. But neither does he become attached to anyone beyond their usefulness to the team.

“Guys like him because he wins,” receiver Julian Edelman said. “But you also know when your play is slipping that he is going to replace you. I love Coach to death, but I know that’s there.”

Calling timely sparks

Less than 20 minutes remained when the Seahawks lined up for a field goal while trailing the Packers 16-0 in the NFC title game.

“We needed points,” Farwell said, “but we needed a spark that only a touchdown could provide.”

Conventional wisdom called for the field goal. But Carroll had a fake that was dependent on one very predictable Packer, Brad Jones. If Jones lined up, Carroll was convinced the fake would work because Jones always rushed a certain way, leaving open field behind him.

Jones lined up, so holder Jon Ryan executed the fake. His 19-yard touchdown pass was the beginning of the end for the Packers.

“It was so well-designed by Brian Schneider, our special teams coach,” Farwell said. “But for Pete to have the guts to call it when he did was impressive.”

Perfecting a system

Edelman is a perfect example of Belichick perfecting his system’s ability to replenish specific skill sets by unconventional means.

In 2008, Edelman was a Kent State quarterback who wasn’t invited to the NFL combine. Today, the former seventh-round draft pick is a clone of predecessor Wes Welker in terms of size, skills, toughness, quickness and unselfishness.

Of course, Belichick should have a lot of this stuff perfected. After all, he has been an NFL coach for 40 consecutive seasons.

“I’ve been fired a couple times myself,” Belichick said. “I’ve had a couple ups and downs there, but through it all there is always something to be gained and learned from those experiences. What doesn’t kill you makes you stronger.”