Stanford’s David Shaw will wait on Keller Chryst’s status before naming QB

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To any Stanford fans who were expecting David Shaw to proclaim, “Eureka! We have found a quarterback and his name is K.J. Costello”: Sorry, Stanford’s head coach doesn’t work like that.

Costello took over a struggling offense late in the first quarter Saturday night and guided the Cardinal on nine scoring drives in a 58-34 win over UCLA. It would seem obvious to many observers that, regardless of Keller Chryst’s health, Costello should have the job until he plays his way out of it.

Shaw, though, can be as conservative on lineup decisions as he frequently is on play-calling. As is his custom, he won’t disclose the nature of Chryst’s injury, although he said the redshirt junior is “feeling better.”

Shaw said he didn’t know who would start Saturday afternoon against Arizona State at Stanford Stadium. He might use a combination of Costello and Ryan Burns if Chryst can’t play. If Chryst can, it’s possible all three will play, Shaw said.

“To a certain degree,” he said, he has a policy that a starter doesn’t lose his job because of an injury. He offered no time frame on when Chryst would be cleared or not. “We have to go through a process to see how it goes,” Shaw said.

Costello was the third quarterback Shaw used against UCLA. Burns was ineffective in two series after Chryst was hurt on a keeper on Stanford’s second possession.

Without comparing Costello with the other two quarterbacks, teammates lauded him for his vocal leadership. And so did Shaw.

He called his performance “impressive. He’ll be the first person to say it wasn’t perfect. The first few drives, he wasn’t completely on. We corrected him on a couple of things. But the bottom line is the kid’s got moxie. He’s got a little fire to him. He can throw the ball extremely well.”

Shaw also pointed out that Chryst was 6-0 as a starter coming into the season. He “led us to some pretty important victories at the end of last year.” Chryst is also a leader, he said. “That’s why he was voted as a captain by a lot of votes.”

Chryst played poorly in the loss at San Diego State after playing well against Rice in the opening blowout win and the loss to USC. “He played well all last year when he was inserted as a starter, and I’m not going to take that lightly,” Shaw said.

Costello was excellent in his first extended work, but, Shaw said, “I’m not going to overreact.”

On Trump vs. protesters: Asked how he felt about President Trump lambasting NFL players who kneel to protest social injustices, Shaw took a measured approach.

One of the most prominent black head coaches in college football, he said the president is entitled to his opinions and is as free to express them as any other citizen. “If he wants to put it on Twitter, I don’t have a problem with it,” Shaw said.

Some Stanford alums were among the more than 200 NFL players who protested Trump’s labeling Colin Kaepernick and any other previous protesters as “a son of a bitch” and his call for each of them to be fired.

If Shaw were an NFL player currently, “I wouldn’t kneel,” he said. “That’s just not me. But I love some of those who are. Some of those guys are like family to me. Their points are very, very valid. What they’re trying to accomplish is noble.”

He said, “I’m an American that loves his country. There’s an unhealthy discourse right now. … For some reason nowadays, we just want to yell at each other rather than finding common ground.” Athletes don’t give up their right to free speech when they turn professional, he said.

But asked specifically if Trump’s blasts were ill-advised, he backed off. “That doesn’t matter to me. I’m a football coach. I’ve been called every name under the sun. I’ve learned not to be swayed by other people’s opinions.”

Barton out for season: Inside linebacker Sean Barton is out for the rest of the season as a result of an injury in the San Diego State game, Shaw said. It appeared to be to his right knee.

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

Arizona State

vs. Stanford

When: 1 p.m. Saturday

Where: Stanford Stadium

TV/Radio: P12Net/1050