Stanford’s bowl fate tied to outcome of Pac-12 title game

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Arizona, a team that was not on Stanford’s football schedule, will help determine the Cardinal’s bowl game.

If the Wildcats (10-2, 7-2 Pac-12), ranked seventh in the College Football Playoff Rankings, upset second-ranked Oregon (11-1, 8-1) in the Pac-12 championship game Friday night at Levi’s Stadium, Arizona is sure to join the Ducks in the so-called “New Year’s Six.” Those six are the two national semifinals (Rose and Sugar) and the four other major bowls in the playoff rotation (Cotton, Fiesta, Peach and Orange).

In that case, the Foster Farms Bowl at Levi’s Stadium on Dec. 30 would probably take Stanford (7-5, 5-4) to play a Big Ten team.

The Cardinal have not played in the Bay Area bowl in its 12-year history. It was previously known as the Fight Hunger Bowl, Kraft Fight Hunger Bowl, Emerald Bowl and San Francisco Bowl.

Gary Cavalli, the bowl’s executive director and a former Stanford athletic department official, says he’d love to invite the Cardinal, especially after they finished the regular season by belting Cal and taking UCLA out of the title game in convincing fashion.

Even if Arizona — a 14 ½-point underdog — simply makes a reasonably good showing against Oregon, the College Football Playoff selection committee might put the Wildcats in one of the major bowls.

Arizona quarterback Anu Solomon (center) celebrates after clinching a spot in the Pac-12 title game. Arizona quarterback Anu Solomon (center) celebrates after clinching a spot in the Pac-12 title game. Photo: Rick Scuteri / Associated Press Photo: Rick Scuteri / Associated Press Image 1 of / 1 Caption Close Stanford’s bowl fate tied to outcome of Pac-12 title game 1 / 1 Back to Gallery

If so, the Alamo and Holiday bowls — which have the next picks among Pac-12 teams — would probably take UCLA and USC (each 6-3 in the conference). Then the Foster Farms bowl could pick Stanford, leap-frogging the Cardinal over Arizona State (9-3, 6-3).

After beating Arizona State, Arizona was moved up from 11th by the selection committee, a sign of strength for the Pac-12. The conference has six teams in the Top 25, including five from the South Division.

Arizona has already beaten Oregon once, 31-24 on Oct. 2, the Ducks’ first home defeat since 2012 — a 17-14 Stanford win.

On the other hand, if Arizona doesn’t wind up in the New Year’s Six, it could be passed over by the Alamo and Holiday bowls in favor of the Los Angeles schools. Conference rules would require the Foster Farms Bowl to pick Arizona because its conference record was two games better than Stanford’s.

In that scenario, the Cardinal would fall all the way to the Cactus Bowl because the Sun would be required to take Arizona State at 6-3, and the Las Vegas is likely to take Utah over Stanford. The last three bowls in the conference rotation are required to take the next team up in the standings. So Washington would be odd man out at 4-5.

The four national semifinalists will be announced Sunday at 9:45 a.m., followed by the other major bowl matchups and the final Top 25 at 11:45 a.m. The remaining bowl matchups will be determined over the next couple of hours.

Tom FitzGerald is a San Francisco Chronicle staff writer. E-mail: tfitzgerald@ sfchronicle.com