On a wall in the back of Andrew Luck Auditorium, the Stanford football team’s main meeting area, are photos taken after past Big Games of each year’s seniors.

All the Cardinal players hope to eventually get their faces on that wall. There’s one little Big Game stipulation to make that happen, however.

“If we win, we get the picture,” punter/kickoff man Jake Bailey said. “So we’ve got to make sure we get that picture up.”

This year’s senior group, including some fifth-year players, would be the sixth in a row on the Farm to go unbeaten for their careers against Cal. The Cardinal have won eight straight against the Bears and are slight favorites to win again in Saturday’s 121st Big Game in Berkeley.

Stanford (7-4, 5-3 Pac-12) came up short in its bid for the conference title, but can move up the league’s bowl pecking order by winning Saturday.

Head coach David Shaw, who has yet to lose the rivalry game since taking over the program in 2011, leaves no doubt about how much this game means to him.

121st Big Game Who: Stanford (7-4, 5-3 Pac-12) at Cal (7-4, 4-4) When: Noon Saturday Where: Memorial Stadium TV/Radio: P12Net/1050, 810

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“There’s something about holding that Axe after the game,” he said. “Even if we had beaten somebody who’s No. 1 in the nation, that still wouldn’t take the luster off winning the Big Game.”

The Axe is attached to a wooden plaque, and the trophy is a bit of a load, Shaw pointed out. “It is heavy, it’s dense. I think that was purposeful. When you go back in the history of it — being stolen back and forth a couple of times — they wanted to make it big and heavy and hard to hide.”

Frank Buncom, a senior academically but a redshirt junior in football, said that more than any other game this season this one probably will be remembered most by Stanford students, past and present.

“When you talk to alumni and all the people who care about this university, when they’re trying to weigh whether you had a good season or not, the first thing they ask is: ‘Did you beat Cal?’” he said. “It would be an honor to do this for the seniors — and the young guys so they know to set the standard for the next season.”

Going unbeaten against Cal “would be amazing,” said linebacker Bobby Okereke, the team’s leading tackler. The Santa Ana native didn’t know how big the rivalry was until he got here. “Being here for five years and being part of these games is a big deal.”

“Anytime you get a win is amazing,” fifth-year cornerback Alameen Murphy said, “but to say you never lost to Cal would be a notch on your belt. We’ve been waiting on this for a long time.”

It will be Bryce Love’s last crack at the Bears. In his three previous Big Games, he has rushed for a combined 200 yards and two scores, including a 48-yard run his freshman year. He ran for 101 yards and had a 57-yard scoring run in last year's 17-14 triumph.

Shaw raved about Love’s Cal counterpart, Patrick Laird. “He breaks tackles, he’s quick, he’s explosive, he’s got great vision and balance. ... This guy runs like his life depends on it every single play. You can’t help but appreciate it.”

Shaw singled out another important Cal player, 5-foot-11, 290-pound fullback Malik McMorris. “There are very few human beings that are that big, that are that athletic. The guy is so versatile for as big and physical as he is. He’s got great feet. He comes around as a puller. He blocks down the field. He had a run after catch (for a career-long 20 yards in the 2016 Big Game), and I didn’t think anyone was going to be able to tackle him. (He was) like a boulder rolling downhill.”

A loss to Cal (7-4, 4-4) would mean back-to-back seasons of at least five losses for the first time since Stanford’s recent bowl era began in 2009 under Jim Harbaugh.

The four losses have come against current No. 3 Notre Dame (12-0), No. 10 Washington (9-3), No. 12 Washington State (10-2) and No. 17 Utah (9-3). Washington and Utah will play for the Pac-12 title at Levi’s Stadium on Friday.

Despite what only can be considered a down year by Stanford’s standards, the players are in an upbeat and confident mood, Shaw said.

“Our older guys know how important this game is,” he said. “They’ve echoed my sentiments of how much energy and emotion there’s going to be in that stadium waiting for us. So we’ve got to bring our best game.”

Tom FitzGerald is a San Francisco Chronicle staff writer. Email: tfitzgerald@sfchronicle.com Twitter: @tomgfitzgerald