How do you flip a division on its head? How do you turn baseball inside out?

Be the 2018 Oakland Athletics.

On Saturday afternoon, the A’s completed their ascendance from almost worst to tied for first. On June 18, the A’s were 12 games behind Houston and languishing in fourth place in the American League West, exactly where most of us expected them to be.

On Aug. 18, they pulled into a tie for first place with the reigning World Series champions. With the 7-1 drubbing of the Astros on Saturday, the A’s won their 74th game of the season.

The last time the A’s were in first place, not counting April? Aug. 25, 2014.

It’s heady stuff for a team that carried zero expectations out of spring training. So is there any chance that summiting this peak changes anything about this embraceable A’s team? That they somehow tighten up and feel the pressure?

“I don’t really think we’re chasing anything, we’re just playing,” said manager Bob Melvin. “We know where we are in the standings. We’re one game better than we were yesterday. I don’t think there’s any pause at a certain time, when this team says, ‘Oh look where we are.’

“It’s hungry every day and confident every day based on the run that we’ve had. They know there are a lot of games left.”

Almost a quarter of the season — 39 games to be exact — remains. The Astros, who have felt the A’s hot breath on their necks for the past few weeks, will play the A’s just three more times after Sunday. That series will take place next week in Houston, where the A’s won three out of four in July.

“We’ve got to create our own mojo,” said Astros manager A.J. Hinch. “And we will.”

Maybe. But the Astros can’t be comfortable with how things have unfolded.

“(Opponents) have to be aware we can play these type of games,” said the A’s Matt Olson, who won Friday night’s game with his first walk-off home run and doubled twice Saturday in the A’s double-palooza (they tied a single-game record with eight).

The 24-year-old first baseman’s phone blew up all Friday night and Saturday morning after his delirious run around the bases. He’d never done that before but wasn’t stunned when it happened.

“It’s almost a feeling like, ‘At what point are we going to win the game?’” Olson said of the A’s mind-set. “It’s a situation where we don’t get down if we strand guys or fall behind.”

That didn’t happen Saturday. The A’s never fell behind, following up Friday’s shock with afternoon awe. Trevor Cahill was masterful — Melvin said it was as good as he’s ever seen him — pitching seven innings and giving up just one hit. The A’s scored early and added on late. The Astros didn’t make a peep, save for a solo shot in the ninth.

AL West race Through June 18 Team W L GB Houston 49 25 — Seattle 46 26 2 Los Angeles 38 35 10½ A’s 36 36 12 Through Aug. 18 Team W L GB A’s 74 49 — Houston 74 49 — Seattle (n) 70 53 4 Los Angeles 62 62 12½ n — Night game not included

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There’s a feeling of momentum, looseness and flat-out fun that is pretty familiar to anyone who’s been hanging around the Oakland Coliseum for a while.

On Saturday, just by pure happenstance, the team celebrated the 20-game winning streak team of 2002. Some of the greats, like Tim Hudson and Scott Hatteberg, were on hand, reminding us of another A’s team that wasn’t supposed to do much due to the loss of MVP Jason Giambi and its relatively small payroll.

“I think there might be more comparisons to the 2012 team, with the youth,” said Melvin, who won the AL Manager of the Year award in the 2012 season and may win it again this season.

That year the A’s, fresh off yet another roster blowup, won the division on the final day of the season and took the Detroit Tigers to five games, before falling to Justin Verlander (who pitches for Houston on Sunday).

Melvin is right, of course. Despite the slanted lore of “Moneyball” — both book and film — the 2002 A’s team was loaded, with the best rotation in the league and a league MVP in Miguel Tejada. The 2012 team had none of that. Nor does this team.

But, as always in Oakland, it’s just another variation fighting the odds.

“I think that’s happened in Oakland over the years a number of times,” Melvin said. “The analytics were starting back then and teams being put together a little differently. There are similarities among all these clubs.”

This A’s team is young and homegrown, with many players from nearby high schools and college programs. The veterans are not just looking for their next paycheck but seem committed and are enjoying themselves. The rotation isn’t what was expected but is performing better than ever could have been predicted, and the bullpen has been phenomenal.

“It’s fun to be a part of,” said designated hitter Khris Davis (who the A’s should sign to a new contract immediately). “I’m grateful that I’m here. I appreciate it.”

Appreciate it.

Once again, it’s all clicking in Oakland. And, once again, the A’s are flipping baseball inside out.

Ann Killion is a San Francisco Chronicle columnist. Email: akillion@sfchronicle.com Twitter: @annkillion