David Shaw is amazed that Stanford, by this time, is not known as a football school.

Maybe we’re too amazed to admit it.

Shaw stepped into Jim Harbaugh’s chair in 2011. The Cardinal was 12-1 the year before. Since then it is 54-14 overall and 36-9 in the Pac-12, with three Rose Bowls and four major bowls in five seasons. Three times it has finished the season ranked in the Top 10, including No. 3 last year, after Christian McCaffrey kept running away from Iowa in the most fruitless game of “tag” in Pasadena history.

“When you mention football schools, our name doesn’t come up,” Shaw said. “I think Christian is the best player in the country but from what people say, he’s barely top three in the Heisman Trophy this year. We’ve won as many games as anybody, but we’re still establsihing, We haven’t arrived. Regardless of what anybody says, we take the underdog mentality.”

Few of life’s underdogs find their way into Stanford, of course, and that was always the question. Why was football so uniquely mediocre? Between Tyrone Willingham’s final year and Harbaugh’s first, Stanford was 16-40. Then Harbaugh went 9-15 his first two seasons.

Stanford went 28 seasons between Rose Bowls. In the 80s it went to one bowl and had two winning seasons. Many fans quit going to games, quit waiting for the next Jim Plunkett to parachute in. Aside from John Elway, Stanford was best-known for fallen tuba players.

Now Stanford is the preseason Pac-12 favorite. That has never happened before. In Shaw’s years, the NFL has drafted 28 Cardinal players. That compares to 29 for USC, 27 for Notre Dame, 21 for Oregon and 23 for UCLA.

Seven of those are offensive linemen and four are tight ends, which tells you how Stanford moved forward. It basically stood still.

While college teams swooned over spread offenses and frenetic pace, the Cardinal held onto their dial-up system and perfected it. Suddenly Stanford was the exotic team that huddled, ran with force, and mystified defensive coordinators who had shredded everythihg they previously knew.

“This is the football I grew up with,” said Shaw, whose dad Willie was a renowned NFL assistant coach. “We run the ball, we use the play-action pass. As the son of a defensive coordinator, I believe you stop the run and hit the quarterback. Football starts in those two places.

“But the best coaches are thieves. We’ve stolen ideas from everybody. We probably stole more from (Oregon’s) Chip Kelly than anybody else. You watch our games and see something that looks like Oregon. His stuff is phenomenal.”

“They know who they are,” said UCLA coach Jim Mora, who has lost six games to Stanford in five seasons. “They’re physical, they run downhill and they find athletes who want to do that. When you play a lot of spread offenses and then you have to deal with the way they play, it can be difficult.”

Stanford has a bottomless array of motions and formations, and a thousand cutting-edge ways to free up McCaffrey, who carried 337 times last year and caught 45 passes.

“The last thing you want to do is pump the brakes on him,” Shaw said. “Are you kidding? I’m going to give him more responsibilities. I remember when Rich Gannon was the MVP of the NFL, quarterbacking in Oakland. Jon Gruden was coaching and he said the natural tendency was to not worry about your best player. He said you should actually do the opposite. When you have a great player, you challenge him. More on his shoulders. He can handle it.”

But Stanford is not winning on scheme. Shaw, and Harbaugh before him, realized that the Cardinal’s entrance demands were a hidden plus. There are only so many top-flight high school players who also excel in AP courses and hit Stanford’s demands on entrance exams. Shaw and his staff can put an electron microscope on that group. Since few parents will let their kids say no to Stanford, it works.

“Our pool this year might be 22 players,” Shaw said. “When the process starts it might be 75-100 players. At the end, the players are recruiting us.”

So Stanford isn’t jarred by the loss of 13 starters, not with receiver Michael Rector deciding to come back and with a depth chart Shaw calls “scary.” The question at quarterback, where Kevin Hogan used to win, is who, not how. Either Ryan Chryst or Keller Burns will have everything he needs.

Stanford knows who it is. And in case anyone else wants to know, two Stanford guys invented Google.