BOSTON — The pitching arm is extremely demanding. You can’t just ignore it and expect it to work when you need it. Thankfully, though, it isn’t picky. Just ask David Robertson.

Ten weeks before he returned to the majors with the Tampa Bay Rays to face the Boston Red Sox, Robertson needed somewhere to pitch. It was late June and he had already helped the United States Olympic team qualify for the Tokyo Games. But the international tournament was weeks away, and Robertson’s arm was begging for competition.

So Robertson suited up for an amateur men’s league team at Cardines Field in Newport, R.I., not far from his home in Barrington. He pitched two innings but does not remember the name of his team.

“I had to give my jersey back; I didn’t want to take it from ’em because I wasn’t coming back,” Robertson said on Sunday, before a somewhat higher-profile game at Fenway Park. “I know it was the Sunset League, though, and I was definitely the oldest guy.”

For the record, Robertson pitched for Westcott Properties against R&R Construction. Before long he was in Tokyo, earning two saves and returning with a silver medal, and from there it was onto the Durham Bulls, the Rays’ Class AAA affiliate.

And now, after a September call-up, he is back in the postseason for the seventh time. Robertson, a right-hander, worked a scoreless inning against Boston at Tropicana Field in each of the first two games of this American League division series, which was tied ahead of Game 3 on Sunday at Fenway.

“Robbie has been there and done it all,” said Rays Manager Kevin Cash, who caught Robertson for the Yankees’ World Series title team in 2009. “He’s pitched on the biggest stage, biggest moments. I think his veteran knowledge of how to navigate through challenging times and challenging venues has been a big benefit to our entire roster.”

Robertson, 36, is not the Rays’ oldest player — designated hitter Nelson Cruz is 41 — but he is the oldest pitcher. He reached the majors with the Yankees in 2008, and two years later began a streak of nine seasons with at least 60 appearances.

Then his arm betrayed him. In his first month of a two-year, $23 million contract with the Philadelphia Phillies, Robertson tore his flexor tendon and ulnar collateral ligament. His recovery went well, he said, until the pandemic sidetracked his routine, setting him back and costing him the abbreviated 2020 season. The Phillies declined his club option for 2021.

Robertson put off signing with a team until after the Olympics, where he closed out victories against South Korea and the Dominican Republic and also pitched against Japan, which won gold. Playing before no fans, he got a taste of the surreal major league experience he had missed in 2020.

“It was an interesting trip, put it that way — just a huge stadium with no one in there and you could hear everything,” Robertson said. “They were very rushed games, because of the time constraints they had between innings. But it was awesome.”

Robertson chose the Rays, he said, because of his familiarity with the Tampa area and the A.L. East. He also knew the Rays had some injuries in their bullpen and thought he could slide easily into a late-inning role.

Much of the Rays’ success, though, comes from embracing the unconventional. They had 14 different pitchers with a save this season, setting a major league record, and their relievers know to be ready at all times. (On Sunday they used Andrew Kittredge, their only All-Star reliever this season, to stifle a rally in the third inning.)

Robertson, as it turned out, was up for anything.

“In the initial interview, he’s like, ‘Whatever, I’m good, three innings, no problem,’” said Rays pitching coach Kyle Snyder, who also let Robertson start a game. “You could get some guys who come in here, at least halfway from a previous generation, that don’t necessarily buy into this.

“I know from an industry standpoint, what we do is looked at a little bit critically. But we’re just doing what we do. We can’t ride that same wave everybody else does; we can’t spend the money they can. We have to figure out ways to maximize our roster.”

In some ways, of course, the Rays are a troubled franchise. With chronically poor attendance, they have been pushing for a dubious dual-city plan in which they would play half their home games in Montreal. Their persistently low payroll — just $83 million for the 40-man roster this year, according to Baseball Prospectus — gives them the freedom to experiment with mostly low-cost players just happy to have the chance.

Their success presents an issue for the players as a whole. By proving they can win with a low budget (the Rays have had the best record in the A.L. in each of the last two seasons) are the Rays diminishing the earning value of players?

Robertson, as a former player representative to the Major League Baseball Players Association, said he was not concerned.

“It always irons itself where the union and the M.L.B.P.A. come to an agreement where guys will be able to get more of a share of their market value,” he said. “This is more of a spot where guys can come in, figure out what they’re doing and then they might leave here because they’re earning too much to stay on this roster.”

While they are together, though, the Rays seem to know they are part of an ever-evolving experiment in how to build a winner. It does not always work; a pitching staff encouraged to fill up the strike zone is sometimes hit hard, as the Rays have been since their shutout in the opener of this series.

But their postseason presence is a testament to their ingenuity. The Rays will look anywhere for a player who could help, even if he pitched against R&R Construction on his winding path to October.