NEW YORK — Until this week, the Tampa Bay Rays had played 731 straight regular season games without one of their starters throwing a complete game. When Ryan Yarbrough finished the ninth inning against the New York Yankees on Thursday afternoon, the Toronto Blue Jays suddenly had the longest complete-game drought in the major leagues.

The last time a Rays starter had thrown a complete game was May 2016, during a season in which the team finished 26 games under .500 and last in the American League East. Two months into this season, the reigning AL pennant winners — still using starters more sparingly than most, still trading the traditional for a data-driven sense of optimal — own one of the best records in baseball with one of the game’s lowest payrolls.

Tampa Bay continues to use openers as often as it does true starters, continues to shift bullpen roles and shuttle promising young pitchers from the majors to the minors and back as needed. Yarbrough had gone 24 starts without a win, a statistic that speaks far less to his success in recent years than to the ways in which the Rays pull pitchers when other teams would leave them in or use them as openers when other teams might slot them into traditional relief roles.

“We’ve talked a lot about Yarbs and whatever role he’s in, win, getting wins and not getting wins — look, he’s a winning pitcher,” Rays Manager Kevin Cash told reporters after the game. “ … Certainly thrilled that he got the win today. We can move off that subject maybe. And with the complete game maybe, we can move off that one and not spend the next five years talking about it.”

Unfortunately for Cash, Yarbrough’s complete game was the exception, not the rule — a reason to notice the Rays’ ways even more rather than end any conversation about the wisdom of their approach.

For most major league teams, a complete game is a pleasant surprise, not a stunner. But the Rays are not most major league teams, particularly when it comes to their approach to managing a pitching staff — their pioneering use of openers rather than starters, of following openers with hybrid relievers who can handle multiple innings, of using what true relievers they do have in matchup-based situations rather than traditional roles.

And most major league teams didn’t watch their approach to pitching fail them on the biggest stage as the Rays did in Game 6 of the 2020 World Series, when Cash pulled starter Blake Snell in the sixth inning of a game in which he was holding the Los Angeles Dodgers scoreless with strikeout-driven dominance. Snell is gone now, along with another starting stalwart from that team, Charlie Morton.

Few teams could lose two key starters from a World Series team that relied heavily on three, replace them with less-heralded veterans such as 41-year-old Rich Hill and somehow not slide down the standings. But Hill was named AL pitcher of the month after recording a 0.78 ERA in 34⅔ May innings. And the Rays entered June with the best record in baseball, atop the always bruising AL East — decidedly, in some ways inexplicably, at it again.

Entering Saturday, the Rays were 23-9 since the start of May, a stretch good enough to give them a one-game lead over the Boston Red Sox for first in the AL East after they split a four-game series at Yankee Stadium this week. During that stretch, Tampa Bay is 3-4 against the Yankees, 20-5 against everyone else.

The Rays continue to be baseball’s most mystifying and stupefying study in innovation: reliant on analytics, relentless in their infield shifts and unconcerned with traditional pitching norms. They keep winning despite a relative lack of player continuity, a comfort with turnover best summed up by the fact that they traded their starting shortstop and beloved clubhouse presence, Willy Adames, to the Milwaukee Brewers in May and have gone 10-4 since.

In some ways, the Rays are testing a hypothesis no one ever posed: that division of labor and reliance on interchangeable parts can change baseball the same way they changed production during the industrial revolution. Even the criticisms from traditionalists are similar — that the Rays are depersonalizing the game by preventing pitchers from seeing their work all the way through, removing human elements and organizational loyalty in favor of a kind of mechanical approach to winning that goes further in its commitment to the numbers than even Billy Beane’s vaunted “Moneyball” approach did 20 years ago.

“Baseball is just a never-ending circle of transactions for each and every team out there,” said longtime Rays outfielder Kevin Kiermaier, whose perspective may be skewed somewhat by the fact that he has spent the past decade with this team, for whom the transaction spin rate is much higher than most.

Kiermaier, drafted by Tampa Bay in the 31st round in 2010, is the longest-tenured player on the Rays, and he said he considers front-office executive Erik Neander “a genius.”

“We’re doing something right from top to bottom through our organization to have the success we’ve had in the major leagues and developing guys through our minor leagues. And I don’t think we’ll be changing that anytime soon,” Kiermaier said. “I think there are a lot of teams trying to replicate what we’re doing.”

Many teams began trying to replicate the Rays’ approach by taking some of their most high-profile minds. Dodgers team president Andrew Friedman is a former Rays GM. Red Sox Chief Baseball Officer Chaim Bloom used to be the vice president of baseball operations for Tampa Bay. But none of them have created the kind of machine that runs at Tropicana Field these days, none quite as willing to part with staple players or encourage data-driven in-game decisions as Neander and team president Matthew Silverman.

More recently, that duo have effectively built the model three-true-outcomes team of the three-true-outcomes era. The Rays’ offense leads the majors in strikeouts and is on pace to blow away the record for strikeouts in a season. It owns one of the lowest contact rates of any team in the majors.

But the Rays also have drawn the most walks in the AL and have one of the highest flyball rates. They rank in MLB’s upper third when it comes to home runs, but they have scored nearly 50 percent of their runs via the homer — all while scoring more runs than anyone but the Astros and Dodgers.

“It’s a roster that really complements one another. From a position player standpoint … they all kind of complement each other and make up whatever given nine they have that day,” Yankees Manager Aaron Boone told reporters recently. “And then obviously, from a pitching standpoint, they’ve become one of the really, really good teams at limiting runs.”

On Thursday, Cash said a weary bullpen meant the best way for the Rays to limit runs was to let Yarbrough carry them. Normally, they take a far different approach.

Yarbrough downplays the ways in which pitching for the nontraditional Rays affects the extent to which the baseball world views him compared with those pitching in more traditional roles. When the Rays began to experiment with openers more frequently a few years ago, Yarbrough was the guy who would follow those pitchers and eat innings behind them.

He has, therefore, been something of a test case for how the Rays’ use of openers and those who follow them can affect the players’ ability to monetize their success in arbitration. Because those hearings often rely on traditional statistics and comparisons to other players, Yarbrough’s experience often serves as the prime example of how the Rays’ approach to pitcher usage can limit pitchers’ ability to accumulate more traditional stats and, therefore, make those players more affordable. Yarbrough, 29, lost his hearing with the Rays this winter and will make $2.3 million in his fourth full big league season.

“Yarbs just continued to make pitch after pitch and be efficient. I’m sure he was probably sucking a little wind there in the eighth and ninth inning, but I hope it’s something that he wanted because we really appreciated him being able to complete it,” Cash said. Yarbrough confirmed later that he did, in fact, want it.

“It’s hard,” said Rays catcher Mike Zunino, acknowledging that the Rays’ approach to pitching roles can be a tough sell for pitchers used to more traditional, steady workloads. The Rays entered Saturday owning the fourth-highest called-strike-plus-whiff percentage in the majors, just behind the Yankees, Padres and Dodgers when it comes to an increasingly relied-upon statistic that combines the number of called strikes a pitcher gets with the number of swings and misses he induces — effectively quantifying his ability to throw strikes untouched as a measure of his dominance.

“I think the one thing that’s for certain, though, is when these guys are put into a game, they’re put into a spot where the matchup is very favorable for them,” Zunino said. “In the long run, when you put guys in those situations, the chances for positive outcomes are really high, and I think guys are buying into that.”