Stanford could be headed to one of Pac-12’s lowest bowls

Stanford running back Christian McCaffrey (5) during the second half of an NCAA college football game against Arizona, Saturday, Oct. 29, 2016, in Tucson, Ariz. Stanford defeated Arizona 34-10. (AP Photo/Rick Scuteri) less Stanford running back Christian McCaffrey (5) during the second half of an NCAA college football game against Arizona, Saturday, Oct. 29, 2016, in Tucson, Ariz. Stanford defeated Arizona 34-10. (AP Photo/Rick ... more Photo: Rick Scuteri, Associated Press Photo: Rick Scuteri, Associated Press Image 1 of / 5 Caption Close Stanford could be headed to one of Pac-12’s lowest bowls 1 / 5 Back to Gallery

With a newly healthy Christian McCaffrey and Bryce Love and a defense that has held three teams in a row to exactly 10 points, Stanford certainly can win its remaining four games.

But even if the Cardinal beat Oregon State, the top two offensive teams in the conference in Oregon and Cal, and a Rice team that is 1-7, the Cardinal (5-3, 3-3 Pac-12) can climb only so high in the bowl picture.

And that’s not very high at all.

First, they have to hope Washington runs the table, too, and that won’t be easy. The Huskies face Cal, USC and Arizona State before playing the only other unbeaten team in conference play, Washington State, in the Apple Cup in Pullman. Then they would have to beat Colorado, Utah or USC in the Pac-12 title game.

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As the conference’s only 8-0 team, Washington is its sole contender for the four-team College Football Playoff. If it falls short, Stanford and all the other potential postseason teams would drop one bowl in the pecking order.

For the sake of this discussion, let’s say the Huskies make the CFP. In that case, the Rose Bowl wouldn’t necessarily have to take the Pac-12 runner-up. It could take a Washington State team with one conference loss or another South Division team.

In the bowl reckoning, it’s Pac-12 records that count, not overall records. The current order is Washington and Washington State at 5-0, Colorado (4-1), Utah (4-2), USC (4-2, but with a loss to Utah), then Stanford. Besides the Apple Cup, the key game in the bowl picture would appear to be Utah at Colorado on Nov. 26.

After the Rose Bowl selection, here’s the “draft” order for the bowls with Pac-12 agreements: 1. Alamo (Dec. 29 in San Antonio), 2. Holiday (Dec. 27 in San Diego), 3. Foster Farms (Dec. 28 in Santa Clara), 4. Sun (Dec. 30 in El Paso, Texas), 5. Las Vegas (Dec. 17), 6. Cactus (Dec. 27 in Phoenix).

There are a few things to remember: One, the Alamo, Holiday and Foster Farms bowls don’t have to pick the best record available; they could opt for a team that’s one game behind the one with the best record. The Sun, Vegas and Cactus bowls don’t have that privilege; they have to go strictly by the record.

Second, teams that “travel well” — that is, tend to bring the most fans with them — tend to get priority. That would help a team like Colorado, whose travel-happy fans haven’t been to a bowl since 2007. That wouldn’t help the Pac-12’s smallest school, Stanford, which doesn’t travel well.

Third, TV ratings matter to bowl people. USC tends to produce higher ratings than Stanford by virtue of its rich tradition and the size of its market.

Fourth, bowls try to book teams they haven’t had lately. The attractive Holiday Bowl probably would prefer not to have USC for a third straight year. That might help Stanford, which beat USC, except that, again, there are too many teams in line above the Cardinal.

The upshot is that, despite having a marquee player in McCaffrey, Stanford could end up in one of the lowest bowls, especially if Washington doesn’t make the playoff.

In typical head-coach fashion, Stanford’s David Shaw said Tuesday that the team’s only goal is to “win this week.” Bowl speculation is “for everybody outside our small world to think about,” he said.

Briefly: Guard Johnny Caspers, who missed the Arizona game Saturday night because of an injury, is questionable for this Saturday’s game against Oregon State, and fullback Daniel Marx, out the past five games, is doubtful, Shaw said. He hopes Marx plays the following Saturday at Oregon. … The Oregon game will kick off at 1 p.m.

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