Buck Showalter’s Baltimore Orioles have ignored the critics and remain a legitimate contender for the playoffs as the season enters its final month. (Jonathan Newton/The Washington Post)

Buck Showalter points out quickly and profanely that he prefers his old cellphone. The Baltimore Orioles manager wrestled with a stubborn iPhone one recent afternoon, struggling to scroll through the address book.

“My thumbs are too fat,” Showalter groused, before finally finding the name of Mike Griffin, the pitching coach for the Orioles’ Class AAA affiliate.

“Hey, Griff, you got a second? . . . Griff, who’s starting for you guys tonight, Berken or Zagone? . . . And Arrieta tomorrow? . . . How about Thursday, you got Clark or Berken? . . . Okay. Where does Clark go? . . . Where does Eveland go? And that’s a loaded question — I got a place he can go.”

Translation: More roster moves were on the horizon. Business as usual for the Orioles, perhaps baseball’s most surprising and inexplicable team this season, having forced their way into September’s playoff hunt on a wave of one-run wins, an ever-changing roster and a bullpen that overshadows its starting rotation.

In the middle of it all has been Showalter, who was fired by three previous teams despite winning baseball games, an old-school character who doesn’t seem impressed with much, not with any worse-than-advertised phenom and certainly not with any summer-month standings.

On a roster void of superstars, Showalter is winning games with timely roster moves, shrewd matchups and artful bullpen management. In Baltimore, big wins have come down to small decisions.

The Orioles have won 24 of their 31 games decided by one run. If they maintain this pace through the season’s final month, they’ll post the best winning percentage in one-run games in baseball history. The further back you stand, the less sense their success makes. The Orioles are in the bottom half in most major offensive and pitching categories. Only four teams have fewer quality starts. Only four have a worse on-base percentage. The Orioles have won 15 more games than they’ve lost, even though they’ve given up 35 more runs than they’ve scored. How is this team only two games behind the New York Yankees, a team with a roster that costs more than twice that of the Orioles?

“Nobody knows,” Showalter says by way of explanation. “We don’t overanalyze.”

Which couldn’t be further from the truth, spoken by a man who dissects and studies everything.

Proof is in the results

No one has ever complained about the results. Showalter twice has been named manager of the year. In his second full season in Arizona, the Diamondbacks posted a 35-game improvement. His second full year in New York, the Yankees improved by 12 wins. And in his second full season in Texas, the Rangers posted an 18-game improvement. The Diamondbacks and Yankees both won the World Series the year after Showalter was shown the door.

The manager came to Baltimore with a reputation: He tinkered too much, wasn’t always well-regarded by players, was wound too tight. When J.J. Hardy was traded to Baltimore prior to the 2011 season, that’s all anyone would tell him.

“But when I came here, I didn’t see that at all,” Hardy said.

What changed? Did time away soften Showalter? The seasoned manager isn’t soft enough to admit any such thing.

“Every situation calls for something different,” he said. “I know in New York, it was one way, then Arizona was another way, Texas another way, here’s another way. Who’s wrong? Who’s right? Does it mean that I’ve changed according to the needs? Or does it mean the critiquers don’t get it? I don’t know. I don’t spend a lot of time analyzing it. At 56, there are many things I don’t really give a [care] about.”

Whatever is it, Showalter’s way is working in Baltimore. The Orioles currently carry only nine players who were on the 40-man roster when Showalter came to town. The results? A franchise that hasn’t posted a winning record since 1997 matched last year’s win total (69) just 126 games into the season. And they’ve done it without consistent stars and dependable heroes, using a formula that probably won’t inspire a best-selling book. The victories are all in the details; for Showalter, they always have been.

“Buck was fantastic to work with,” said Judson Burch, the producer of ESPN’s “Baseball Tonight” during Showalter’s tenure as an analyst there, “because he always got us thinking about baseball as being much more complicated than it looked on TV. . . . He was always asking questions, always challenging the idea that baseball was simple.”

Moving parts

One day last week, pitcher Zach Britton allowed only one run in eight innings, striking out 10 in a big way. After the game he was demoted. Showalter figured: It’s not like Britton would start again the next day, so why waste a roster spot? In all, the Orioles have made 157 roster moves since setting their opening day roster. Norfolk, the team’s Class AAA affiliate, has totaled 226 transactions, using 75 different players.

“You’d think we’re having a bad season or something with all the moves,” said Steve Johnson, Baltimore’s 25-year-old rookie pitcher. “But that’s not the case.”

Johnson is especially familiar with the route from Baltimore to Norfolk. He’s been optioned four times this season. Three of his stays with the big-league team lasted barely 24 hours.

“We’ve had a lot of moving parts all year, but guys know if you perform, they’re going to find a spot for you,” Johnson said.

While the heavy-handed approach might have rubbed some clubhouses the wrong way, in Baltimore the players can’t complain when it translates to wins. “We’re grown men,” Adam Jones said. “He don’t need to sugarcoat nothing.”

Showalter makes no apologies. He’s treated the organization’s so-called phenoms the same way he’s treated the guys found on the scrap heap. “There’s this new thing called ‘pitch better,’ ” he said without a laugh. “Just like me and you, right? We don’t deliver the goods, what are we doing next week?”

One day last week, he called Jake Arrieta into his office. Arrieta had started Baltimore’s home opener the past two seasons, but for the second time this year, Showalter sent him packing to Norfolk. Arrieta had been one of the organization’s top prospects, but a 3-9 record and 6.13 ERA couldn’t save his spot in the clubhouse.

“Jake, you can’t hold back talent,” Showalter says he told the young pitcher. “It will happen.”

Similarly, Brian Matusz, the Orioles’ first-round pick in 2009, was sent down in July. But like so many, he earned his way back to Baltimore last month and is fighting every day to stay with the team.

Ready for anything

Showalter and Dan Duquette, the Orioles’ first-year general manager, say their 25-man roster is really a 50-man roster, as they continually shuffle the pieces. And if they don’t like the options in the organizations, they go elsewhere.

Outfielder Lew Ford hadn’t played in the majors since 2007, bouncing from Japan to Mexico to an independent team league. The Orioles signed him in May, called him up in July and saw him homer in three consecutive games in August. In the bullpen, Pedro Strop and Darren O’Day were both claimed off waivers. Last week Baltimore signed 36-year-old Randy Wolf, who was released by the Milwaukee Brewers on Aug. 22 and on Sunday became the 50th player to wear an Orioles’ uniform this year

A team that spent years trying to buy big-name stars is winning with carefully-plotted patchwork. Peter Angelos, the owner who once swung for the fences with his checkbook, is apparently on board with the revamped philosophy.

“What people miss about Peter is how many times he says yes,” Showalter said. “He’s willing, trust me. He and his family, they’ve been great. I don’t know whatever perception before I got here, since I’ve been here I couldn’t ask for a better owner.”

Showalter spent 3½ seasons far away from the dugout before the Orioles called midway the 2010 season. Working as an ESPN analyst then, he said he wasn’t fretting about whether he’d ever manage again. Two years after taking the job, the Orioles could be headed to the postseason. Whether Showalter believes this or not, he says he’ll be okay either way.

“I thought long and hard before I came here,” said Showalter, the fifth man in a six-season stretch to sit behind the manager’s desk in the Baltimore clubhouse. “I was sitting in the backyard one day and I noticed, ‘Damn, look how red that cardinal is. Ooh, listen to the wind pass through the leaves.’ I’m not consumed by this. While I’m here, I’m very serious about it. But it doesn’t define me.

“When Peter comes in and says, ‘I’ve had enough of your [stuff], I’ll say, ‘Thanks for the opportunity, it was an honor.’ And then I’ll be out the . . . door.”