Stakes are high in the Red Sox’ trip to New York, but only for the Yankees

The Red Sox arrive at Yankee Stadium with an 11-1/2-game lead in the AL East.

Boston, MA: 4/11/18: The benches cleared and the Yankees Tyler Austin (26, left) was still looking to get at Red Sox pitcher Joe Kelly (not pictured), with Boston's Brock Holt (12) right behind Austin. The fight began after Austin charged the mound in the 7th inning.  The Boston Red Sox hosted the New York Yankees in a regular season MLB baseball game at Fenway Park.  (Jim D avis/Globe Staff)
The Boston Red Sox hosted the New York Yankees in a regular season game at Fenway Park on April 11, 2018. The benches cleared and the Yankees Tyler Austin was still looking to get at Red Sox pitcher Joe Kelly, with Boston's Brock Holt right behind Austin. The fight began after Austin charged the mound in the 7th inning. –Jim Davis/Globe Staff

NEW YORK — The last time the New York Yankees saw the Boston Red Sox, they were walking out of Fenway Park in the wee hours of the morning, dragging their luggage, equipment bags and metaphorical tails behind them.

It was early August, and the Yankees had been swept in a four-game series — the final one gifted by a throwing error from Miguel Andujar and a meltdown from closer Aroldis Chapman — turning what had promised to be a fight-to-the-finish race for the best record in baseball into a runaway in Boston’s favor.

“We can’t let this define what’s been a great season for us,” manager Aaron Boone said that night, sitting at his desk inside the cramped visitors’ office in Boston.

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Alas, six weeks later, that series has indeed defined the Yankees’ regular season, one that has turned from great to somewhere between solid and good. Though they are all but assured a playoff berth, the Yankees have not gotten any closer than six games away from the Red Sox, who arrive at Yankee Stadium with an 11-1/2-game lead in the American League East and a magic number of two to clinch the division.

Boston will have three chances to celebrate in the Bronx, beginning with a rare midweek day game Tuesday — the Yankees having chosen to start at 1 p.m. rather than conflict with Yom Kippur, the Jewish holiday, which begins at sundown.

It would be the second time in three seasons that the Red Sox celebrate a division title at Yankee Stadium, though this season’s would no doubt be less awkward than two years ago. In 2016 the Red Sox — needing a win or a loss by Toronto to clinch — trudged off the field after Mark Teixeira’s walk-off grand slam, then let loose with a raucous celebration in the clubhouse because the Blue Jays had lost moments earlier.

Other than procuring Champagne and beer, the Red Sox arrive this time with a modest to-do list for the final two weeks of the season: making sure ace Chris Sale’s left arm is primed for the playoffs, outfielder Mookie Betts is healthy, and everyone else (particularly the bullpen) gets the right amount of rest.

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The Yankees have a more pressing agenda, beginning with holding off the Oakland Athletics in the standings to ensure home-field advantage in the wild-card game. The Athletics trail the Yankees by 1 1/2 games, but have a less formidable schedule — six games against the Los Angeles Angels, three against the Seattle Mariners and three against the Minnesota Twins. The Yankees have six games with the Red Sox, four at the red-hot Tampa Bay Rays, and three with the Baltimore Orioles.

Beyond that, they have an offense to get healthy and get right. Aaron Judge, who fractured his wrist on July 26, was activated Friday but has not yet taken a swing in a game. (The team said he took 11 at-bats on an off day Monday against pitchers A.J. Cole, Chance Adams and Phillip Diehl; Chapman, also hoping to return soon, faced hitters, too.)

The Yankees can only hope Judge (and Chapman, for that matter) finds his form quicker than Gary Sanchez. His lengthy stay on the disabled list did not reverse what has been a disappointing season, as he is batting .191 with two home runs since returning on Sept. 1. And the Yankees’ other threatening slugger, Giancarlo Stanton, has been just as feeble lately, batting .145 with two home runs since Aug. 24.

If only they were as consistent as Boone, who has been adamant in his belief that the Yankees will right themselves. But the memories of April, May and early June, when the Yankees looked like a juggernaut, are becoming increasingly distant.

Since June 21, the Yankees have gone 41-36 — the 11th-best record in baseball in that period.

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This has come despite a soft second-half schedule. Since the All-Star break, the Yankees have played only 16 games against teams with a winning record — Boston, Tampa Bay, Seattle and Oakland — and won just five.

Still, the Yankees thought they would have their chance.

It was these two September series with the Red Sox that the Yankees have been eyeing since they last saw their rivals. They even tweaked the rotation so that their three best pitchers — J.A. Happ, Luis Severino and Masahiro Tanaka — would be lined up against the Red Sox.

When the Yankees swept a four-game series in Baltimore late last month, they had closed within six games of first place. And with Boston set to play tough series against Cleveland and Houston, an opening seemed to lay ahead.

“Our thought process is they’re going to win every series the rest of the year, too, and when we play them, that will be our chance to gain some ground,” utility player Neil Walker said on the day the Yankees swept the Orioles. “Those are obviously going to be important.”

And for one team, they will be.