Will Mike Trout replace Derek Jeter as the face of baseball?

The Derek Jeter Farewell Tour stops in Anaheim on Monday, 18 years after the celebrated shortstop played his first game there, so long ago that the home team had Jim Abbott on the mound, Rex Hudler in center field and California Angels as its name.

On September 6, 1995, eight months before Jeter played his first game at the Big A, Cal Ripken broke Lou Gehrig’s record for consecutive games played. The Angels lost that game, then showed their respect by gathering in their dugout to watch the postgame coronation. Ripken was the everyman shortstop that played every day, the guy who saved baseball after a calamitous strike.

He was the face of baseball.

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“For me, it went from Cal Ripken to Derek,” said Gary DiSarcina, the Angels’ shortstop in Ripken’s milestone game and Jeter’s Anaheim debut. “Whoever picks it up from Derek has big shoes to fill.”

In time, we might look back upon this week as the time when the torch was passed from Jeter to Mike Trout.

When Jason Giambi visited Angel Stadium with the Cleveland Indians last week, he did not even pause at the question of who might replace his old New York Yankees teammate as the face of baseball.

“The kid over there,” Giambi said, thrusting his thumb toward the Angels’ clubhouse. “That’s a good place to start.”

Trout grew up in New Jersey, with posters of Jeter on the walls of his room. He said his favorite memory of Jeter is the famous “flip play,” when the shortstop dashed across the infield, cut off a throw from right field and delivered the ball home with a backhand flip. The runner was Oakland’s Jeremy Giambi, Jason’s brother. He was out, and the Yankees stayed alive in the 2001 playoffs.

Trout was 10.

He is 22 now, old enough to sign a new contract for $144.5 million, young enough that his mother could go on ESPN last week and talk about how her son still makes a mess of his room when he comes home.

The notion that he might succeed Jeter as the face of baseball is laughable, bordering on offensive, to Albert Pujols. It is not that Pujols does not consider Trout worthy of the label. It is that Pujols wonders why there needs to be a rush to anoint Trout.

“That’s a lot of pressure you’re going to put on a guy with two years in [the major leagues],” Pujols said. “Right now, he doesn’t need to get caught up in you guys trying to compare him to different people.

“He’s a good player, with the ability to get to the Hall of Fame. I’ve encouraged Mike not to get caught up in what you guys think and write.”

Still, whether you bring up Jeter or Trout within a clubhouse, the responses tend to be similar: enthusiasm, humility, respect for the game, respect for teammates and rivals, raised in a great family.

“Every time I talk to him,” Jason Giambi said of Trout, “he’s the nicest kid on the planet.”

Jeter played two decades in the greatest media market on Earth, without a stain. When the late Yankees owner George Steinbrenner chastised Jeter for staying out too late and partying too much, Jeter and Steinbrenner turned what could have been a negative into the positive of a Visa commercial, one that ended with Steinbrenner chasing Jeter in a conga line.

Jeter was accommodating and respectful on the field, exceedingly private off the field, even in the TMZ era, in which scandal is but a cell phone camera away.

“He played in the toughest town in the world to play in, and he kept a little piece of himself for him,” Giambi said. “That’s hard to do in that town. It really is an incredible thing.”

Said DiSarcina, now an Angels coach: “He had to work hard at being unnoticed off the field. He never got caught up in steroids, or drunk driving, like the guys you see on the police blotter. He did it the right way.”

Trout said he marveled at Jeter’s ability to “not put himself in the wrong place at the wrong time.” That is one element of the Jeter mystique that Trout had no doubt he could emulate.

“I’m not a guy that goes out a lot,” Trout said. “I don’t drink a lot. I don’t do anything bad.”

For all of Jeter’s accolades — his hitting ability, his smoothness afield, his knack for delivering in the clutch, his class in representing the most storied franchise in American sports — he never has been considered the best player in the game. His highest finish in most-valuable-player voting: second, once, when he was 32.

Trout has established himself as the best player in the game. He has played two seasons and finished second in MVP voting both times, at 21 and 22.

The Angels did not make the playoffs in either season. Jeter had the Yankees brand behind him, but he also won a World Series championship at 22 ... and 24, and 25, and 26.

In Ripken and Jeter, baseball had faces that were identified with one team — Ripken with the Baltimore Orioles, just like Tony Gwynn with the San Diego Padres, just like Pujols used to be with the St. Louis Cardinals — and, today, to a lesser extent, like David Wright with the New York Mets, David Ortiz and Dustin Pedroia with the Boston Red Sox, Buster Posey with the San Francisco Giants and Clayton Kershaw with the Dodgers.

Trout could rise above all of his contemporaries if the Angels win. For now, all Trout can do is play well and take another page out of the Jeter playbook, by raising his national profile as a corporate spokesman, without taking any controversial stances on public issues.

That, Giambi said, is why Trout is well-positioned to replace Jeter as the face of baseball.

“Trout is really athletic. He’s a good-looking guy. He’s built,” Giambi said. “And you can see him walking down the street and say, ‘I’ve seen that guy in a Subway commercial.’ ”

bill.shaikin@latimes.com

Twitter: @BillShaikin