Column: Super Bowl forecast: Will Saints face Patrick Mahomes, the QB they wanted to draft?

Locals only.

That’s basically the story of the NFL’s conference championship games in recent years. History is squarely on the side of the home teams.

Visitors — as the Rams and New England Patriots will be Sunday — are 0-10 in these title games the past five years, and 4-16 in the past decade. The last time road teams won they did so together, in 2012, when both Baltimore and San Francisco won to advance to the Super Bowl.

So the New Orleans Saints, who play host to the Rams, and the Kansas City Chiefs, who welcome the Patriots, can find a sliver of solace in those statistics.

But no one is breathing easy, not with the red-hot Rams coming to the Superdome — they are 14-3 away from home under coach Sean McVay, counting a London game — and Tom Brady playing at Arrowhead Stadium, or anywhere for that matter.

The Super Bowl LIII picture is coming into focus, with the Rams, Chiefs, and Saints all angling for their second Lombardi Trophy, and the Patriots shooting for their sixth.

A look at the four possible Super Bowl permutations:

Rams-Patriots: This is a rematch of Super Bowl XXXVI in New Orleans, when the Patriots pulled off a stunning upset at the Superdome, 20-17, to win their first ring. The game launched Brady into superstardom, and denied the “Greatest Show on Turf� Rams their second title in three years. There are still some people who believe the Patriots filmed the Rams’ walk-through a day before beating them, although the newspaper that originally reported that story, the Boston Herald, later apologized and acknowledged it was false.

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Receiver Brandin Cooks and cornerback Aqib Talib, key players for the Rams this season, are both former Patriots. And once again, the “BEAT L.A.� chants will echo through the stadium, as they did with the Red Sox-Dodgers World Series, and last week with the Chargers playing a divisional game in Foxborough, Mass. (Of course, it was those Lakers-Celtics battles, with a little help from the Philadelphia 76ers, that spawned that chant decades ago.) Rams-Patriots would pit Goff versus GOAT, third-year Rams quarterback Jared Goff and Brady, whose nickname is an acronym for “greatest of all time.�

The matchup also would pit a great young offensive mind in McVay and a defensive legend in New England’s Bill Belichick. McVay, 32, is the youngest coach to win a playoff game; Belichick, who won the first of two rings as defensive coordinator of the New York Giants when McVay was a year old, is the only head coach to win five Super Bowls.

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The New Orleans Saints feature a future Hall of Fame quarterback, the NFL’s best wide receiver and an unrelenting running game. Stopping the explosive Saints is objective No. 1 for the Rams in Sunday’s NFC championship game.

Saints-Patriots: Both teams have first-ballot Hall of Fame quarterbacks in Brady and Drew Brees. And both have coaches who are disciples of Bill Parcells, in Belichick and Sean Payton. The Patriots won their first of five rings at the Superdome.

Tight end Benjamin Watson, who was drafted by New England in 2004, will retire with the Saints after this season. He won a Super Bowl ring as a rookie, even though he was on injured reserve for the game. On more than one occasion, he’s been a finalist for the Walter Payton Man of the Year Award.

In 2009, the season the Saints won their Super Bowl, they beat the Patriots at the Superdome 38-17. That might have been the best game of Brees’ career, as he completed 18 of 23 passes for 371 yards and five touchdowns, earning him a “perfect� passer rating of 158.3.

With this year’s Super Bowl in Atlanta, the NFC team will work out and practice at the Falcons’ facility. Having the Saints use that as their home base surely would be fingernails on the chalkboard for their bitter NFC South rivals. What’s more, this matchup would have New England in town, and the Patriots were the authors of an excruciating Super Bowl comeback against the Falcons a couple years ago.

Saints-Chiefs: It was 49 years ago in New Orleans, at Tulane Stadium, that the Chiefs won their only Super Bowl. Hank Stram was coach of that Kansas City team, famously urging his players to “matriculate the ball down the field.�

Stram coached the Chiefs from their inception as the Dallas Texans in 1960 to 1974, and ended his NFL career as coach of the Saints. He was fired after a season-ending defeat to the Tampa Bay Buccaneers, who snapped a 26-game losing streak that stretched over two seasons.

These franchises have had a few notable players in common, among them Hall of Fame offensive lineman Willie Roaf, but a big story if this matchup happens will concern the quarterbacks. The Saints were in position to draft Patrick Mahomes in 2017 at the No. 11 spot, and had him atop their board along with cornerback Marshon Lattimore. They were looking for a quarterback who could be an heir apparent to Brees.

Brees was actually in the draft room as selection time approached, and Payton had to pull him into the hallway and explain how the Saints might have to select Mahomes. By the time the two came back into the room, though, Kansas City had traded up with Buffalo to take the Texas Tech quarterback with the No. 10 pick. For the record, the Saints are plenty happy with Lattimore.

Rams-Chiefs: Who needs Super Bowl fireworks when you have the pyrotechnics of these two offenses? These teams faced off in the best game of the season, with the Rams prevailing 54-51 at the Coliseum. It was the only game in NFL history in which both teams scored at least 50 points.

Rams-Chiefs would feature two spectacular young quarterbacks, Goff and Mahomes, the likely NFL most valuable player. Combined age of the starting quarterbacks: 47.

Former Rams receiver Sammy Watkins now plays for the Chiefs, and up-and-down Rams cornerback Marcus Peters spent his first three seasons in Kansas City before Los Angeles acquired him in a trade last spring.

This game would guarantee a winning coach from L.A., as it would either be McVay or Chiefs coach Andy Reid, who grew up in the Los Feliz area.

The regular-season meeting between these teams was supposed to be played in Mexico City, but because of poor field conditions was moved at the eleventh hour to the Coliseum.

Organizers in Mexico City already were feeling terrible about that fumble. Imagine if that turned out to be an actual Super Bowl dress rehearsal.

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Follow Sam Farmer on Twitter @LATimesfarmer