STANFORD — There’s a lot on the line this Saturday in the 120th rendition of the Big Game, which dates back to 1892.

No. 20 Stanford (7-3, 6-2 Pac-12) needs a victory at home to keep its hopes alive for a rematch with No. 12 USC in the Pac-12 championship game at Levi’s Stadium on Dec. 1.

The Cardinal also needs No. 15 Washington State to lose next week in the Apple Cup against No. 16 Washington.

If everything breaks right, Stanford head coach David Shaw could claim the Pac-12 title for a fourth time in six years.

“The big thing for me is you can’t ever forget that I’m a Stanford alum, so I take kind of double pride in any success that we have,” said Shaw, a wide receiver on The Farm from 1991 to 1994. “All that being said, for us this week, and it sounds crazy, that’s kind of secondary. This is Big Game, this is about the Axe, this is about our biggest rival.” Get Pac-12 Conference news in your inbox. Sign up for the Pac-12 Hotline newsletter.

Postseason implications aren’t only limited to Stanford.

It turns out Cal (5-5, 2-5) needs one more win to become bowl eligible under first-year head coach Justin Wilcox, who was indoctrinated into the lore of the Big Game during a three-year stint as the linebackers coach for the Bears over a decade ago.

“I’ve been a part of it before, so I recognize it’s one of the greatest rivalry games in college football,” Wilcox said. “For the university, the alumni, the student body, it’s a huge deal.”

Not to mention the players.

“It’s huge,” Stanford safety Frank Buncom IV said. “It’s just an honor to be a part of just a storied tradition and I think everybody gets excited for it. You see it around campus, there’s a lot of excitement for the game.”

Stanford leads the series 62-46-11, a statistic boosted by seven consecutive wins against Cal, which is a fact Wilcox must certainly be aware of.

“I’m sure he’s been reminded how many times in a row they have not won the Axe,” Shaw said.

(• Of note, this is the 35th anniversary of the “The Play” — the unforgettable five-lateral, 57-yard kickoff return for a game-winning touchdown in 1982 after Stanford had taken a 20-19 lead with four seconds left.)

At his weekly Pac-12 teleconference, Shaw noted the Big Game is “probably not one of the nastier rivalries in America, but at the same time it’s still very heated, it’s still very personal.”

He added: “In the Bay Area many alums cross paths and work together and are friends and know each other pretty well, so it’s one of those times where you sometimes draw a line down the middle of the street or down the middle of the household sometimes for this week to have bragging rights for a year.”

Shaw squeaked out a 31-28 victory in 2011, his first year at the helm after Jim Harbaugh departed for the San Francisco 49ers.

None of the next five meetings were decided by fewer than 13 points, including a 63-13 drubbing at Stanford Stadium in 2013.

“We talk to our guys all the time about having tangible evidence, about having a trophy,” Shaw said. “It’s always great to play for pride, play for your family, play for your teammates, play for your school, but it’s great to have something to hold after the game.

“It’s a challenge for the seniors, of course, to keep the Axe — and I think our guys are fired up for the game.”

It’s different for the true freshmen, considering Stanford recruits across the nation.

The coaching staff tries to warn them about the atmosphere at the Big Game, but “they won’t get it,” Shaw added. At least not until the pregame warm-up.

“You’re going to feel it before the game ever starts,” Shaw said. “You’re going to feel that in the stadium. So we try to get them ready, we try to prepare them for that, but the older guys know. There’s going to be more emotion in this game, there’s going to be a lot of passion in this game.”

Stanford quarterback K.J. Costello, a redshirt freshman with three career starts, including the past couple of weeks, tried to downplay the significance of Saturday’s visit from Cal.

“The title of the Big Game it’s cool, but at the end of the day we pride ourselves in every week is a big game,” Costello said. “It is a crosstown rival, but once again it doesn’t change our preparation. But as a whole, it maybe adds a little bit excitement to the atmosphere outside.”

Let’s see if that holds true on the field for Costello, who tends to wear his emotions on his sleeve whenever he’s wearing a helmet and pads.

“K.J. exists in a plain of high energy at all times,” Shaw said. “So it’s not like he goes really high and you have to calm him back down. He’s just up there. He’s fired, he’s energetic, he’s passionate. … You can’t stop it, you might as well direct it in the right direction. He’s also been calm, he’s also been cool, he’s also been collected. Only had a few moments where he got antsy in the last game. But he’s settled in and we’ll give him a plan that he can orchestrate.”

A lot of that game plan will revolve around running back Bryce Love, who can pad his Heisman Trophy candidacy with a primetime game at 5 p.m. on Fox.

It’s just a matter of how his body holds up, considering the 5-foot-10, 196-pound junior hobbled off the field a few times in last week’s 30-22 victory over Washington. The Huskies were touted as the nation’s top defense but left gashed for 166 yards on 30 carries and three touchdowns by Love, whose pain threshold is not under question.

“We’ve learned not to ask him how he feels, because he’s always OK — ‘I’m fine, I’m OK,’ ” Shaw said. “We have to actually see functionally what he can do and what he can’t do, because he can play through ridiculous pain. … It’s amazing to watch. Don’t need to talk about any specific awards, but for what he’s doing, I don’t know that anybody else is doing it at any position — injured, still effective, still leading the nation in rushing … when everybody knows he’s going to get the ball. That’s just rare.”

An even better opportunity to improve his Heisman odds awaits next week, when Stanford hosts No. 9 Notre Dame under likely national scrutiny.

Is it all possible that the Big Game against the Bears turns into a trap game for the Cardinal?

“As cliché as it sounds, you never like looking ahead, but you’re never going to look past a rivalry game,” Buncom said. “So we’re all just focused on playing this game and coming out with a win and keeping the Axe for our seniors.”

“We haven’t earned the right to look past anybody, we’re still looking for our own consistency,” Shaw said. “This is a rivalry game, it’s a home game, we’re playing for the Axe, we’re playing for the seniors, so I think we have a lot to play for this week.”