PEORIA, Ariz. — For a player hoping to start fresh, there may be no better place than Seattle. The closest major league neighbors are some 800 miles away in San Francisco and Oakland. The mountain vistas are breathtaking, the summer air crisp and clean, the ballpark gorgeous.

“There’s no bad place to play; it’s the major leagues and you’re making a lot of money living your childhood dream,” said Jack Zduriencik, the Seattle Mariners’ general manager. “But it’s a unique place. We are the only club in that part of the world, if you will. It could be a cult following.”

It could be, and it has been, but now it is not. The 2012 Mariners scored the fewest runs in the American League for the fourth year in a row. They finished last in the AL West for the seventh time in nine seasons. Most troubling, perhaps, the Mariners averaged only 21,258 fans per game, their lowest figure since 1992 in the Kingdome.

That is a steep tumble for a team that enthralled a generation in the Northwest with sluggers like Ken Griffey Jr. and Jay Buhner, who now coach in spring training. But it also sets up an unspoken dynamic where incremental progress — more than contention — would make this season successful.

Low pressure in a faraway setting seems ideal for Jason Bay, the former New York Met who spent three discouraging seasons in New York.

His former Mets teammate Oliver Perez has already shown the benefits of escaping to Seattle.

Perez was 3-9 with a 6.81 earned-run average in his final two seasons pitching with the Mets, walking more hitters than he struck out. After spending 2011 at Class AA in the Washington Nationals organization, Perez reinvented himself as a reliever last season, with a 2.12 ERA in 33 games for the Mariners.

“They gave me an opportunity when nobody wanted me,” Perez said. “I feel real good there, and right now we can surprise people.”

Perez, whose spot with the Mariners is secure, is playing for Mexico in the World Baseball Classic in Phoenix. Bay declined a spot on Canada’s team as he tries to earn a job with Seattle. That, he said, is just how he wants it.

After signing a four-year contract with the Mets before the 2010 season, Bay hit just .234 with 24 home runs in three seasons. Near the end, especially, he knew he was playing solely because of his salary. The Mets allowed him to become a free agent in November when he agreed to defer the $21 million remaining on the contract.

“I went about my business, stood in front of my locker every day and answered the questions; I think people respected that,” Bay said. “Ultimately it’s about production. When you’re not producing, it’s time to go. It didn’t work out. Nobody feels worse about that than I do.”

Bay, a British Columbia native, lives with his family in Kirkland, Wash., about 15 minutes from Safeco Field. His wife is from Seattle, and he said he planned to live there for the rest of his life. The Mariners had shown interest the last time he was a free agent — after he hit 36 homers for Boston in 2009 — but the Mets won with a $66 million bid.

This free agency was different. Zduriencik said the Mariners hoped to add offense and leadership in the offseason without sacrificing young talent. They accomplished that, he said, by acquiring Kendrys Morales, Michael Morse, and the former New York Yankee Raul Ibanez, who is also a former Mariner.

But the first move was a modest deal for Bay, who is guaranteed $500,000, an amount that doubles if he makes the opening-day roster. Bay, Zduriencik and their wives had dinner before he signed.

“It made a lot of sense for him to try to make a go of it where he’s living,” Zduriencik said. “He can drive his kids to school in the morning and then play baseball. I walked away thinking, ‘What a good guy, what a genuine person.’ ”

That was the impression Bay left in New York. His struggles were impossible to ignore, but his refusal to deflect blame or hide from scrutiny — and his difficulties with concussions — made him more a figure of sympathy than a target of scorn. He tried so many changes that he lost who he was as a hitter.

“The biggest thing was when I got there, I was hitting all right, but I had like three home runs through the first two months,” Bay said. “Whatever I’d done my whole career, I was doing it, I was still driving in runs, I was hitting about .300, but I wasn’t hitting the ball out of the ballpark, which is what I was there for.

“And then at that point, instead of being OK with that and saying, ‘Oh, it’ll come,’ I started to tinker a little bit. And then I tinkered more. I got hurt, I tried to do something new, and two years in, I had done 15 different things and I didn’t really know what it was I was doing.”

Bay bottomed out last season, missing time with a fractured rib and a concussion and ending with a .165 average and eight home runs in 70 games. When the Mets released him, he said, he called the team’s chief operating officer, Jeff Wilpon, and they spoke for 25 minutes. Bay said Wilpon told him he appreciated his effort and held no hard feelings.

Like Bay, Perez also left the Mets before the final year of his contract. He said he never worried that his career was over, focusing instead on the Nationals’ suggestion, after 15 Class AA starts in 2011, that he try relief pitching in winter ball in Mexico.

Perez impressed a Mariners scout there, and last season his fastball averaged 93.7 mph, according to Fangraphs; in 2010, with the Mets, it was 88 mph. Perez varied arm angles regularly, reborn in a new role.

“I said, ‘Whoa, this is a different Oliver than I’ve seen before,’ ” said Jaime Navarro, the bullpen coach. “Focused more, concentrating, locating his pitches, different angles, throwing it by somebody. He had a different mentality.”

Perez quickly agreed to a $1.5 million contract last winter to stay in Seattle, and Zduriencik added other long-shot pitchers, like Jeremy Bonderman and Jon Garland. His offensive imports have produced so far, with a major-league-best 30 home runs entering the weekend, including two by Bay.

Of course, the games in Arizona are only exhibitions, and such production is impossible to sustain. But the Mariners will take it. They are as eager to revive their franchise as Bay is to revive his career.

“It’s been a lot of fun, I can tell you,” Zduriencik said. “It’s refreshing, very much so, for our fans in Seattle to watch this.”