Since the Yankees are alleged to love analytics so much, they have to be discouraged by a number that finally appeared on Fangraphs during this weekend’s sweep at the hands of the rival Red Sox, the very first sweep suffered at Yankee Stadium this year.

Yes, the Yankees’ World Series odds finally hit zero. Yes, specifically, 0.0 percent.

So Fangraphs mathematically validated what we think we’ve been watching for a while now.

The Yankees, officially (or as officially as it gets in baseball), have no chance to attain their well-known annual goal of winning the World Series.

Which puts them in the company of only the Tigers, White Sox, Royals, Angels, A’s, Nationals, Rockies and now the Mets, whose 1.5 percent odds to make the playoffs odds are actually three times better than those of the Yankees, thanks to the recent spirited play of the team from Queens.

The Yankees’ performance on Sunday was energized but ultimately demoralizing. The Red Sox — 6-5 winners of a game in which the Yankees came back three times to tie it — benefited from a surprise overturn of a safe call at home on a hustle play by Isiah Kiner-Faleda that seemed tough to tell (at least from the press box), a double by Greg Allen that was about three inches short of tying the score in the ninth and the continuing heroics of Mets castoff-turned-star Justin Turner.

Yankees manager Aaron Boone, whose press conferences have grown more specific (and obviously a lot less happy), stopped short of calling the Red Sox their “daddies.” However, Boone did memorably say this about the Boston team he’s famous for tormenting in 2004: “They’ve kicked our asses.”

Boston’s dominance is quite upsetting, not that the Yankees are especially great against most anyone else, either. The eight-game losing streak overall represents their longest such streak in 28 years, dating back to the season when Buck Showalter still managed to guide them into the playoffs.

Their chances of even reaching the postseason now are listed at 0.5 percent, which makes me think that they might still have a 0.1 percent chance to winning the World Series.

After all, if they make the postseason from here, they’d have to be presumed to be the hottest thing on this hot planet.

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“You always got a chance … we’re in a big hole,” Boone said, honestly, after perhaps the season’s tough defeat.

“We’ve got to be unbelievable the rest of the way, so it’s not about that,” Boone said in answer to a follow-up query about the big picture. “We’re so far removed from that. We’ve got to get a win.”

Yes indeed, reality has hit them at 161st and River. The aura seems less than confident now, the talk less than bold. This a very smart group, and even if they don’t regularly check Fangraphs, they know just where they stand.

The guys are obviously accomplished, but the trajectory trumps the talent at this point. The team is too reliant on the long ball (all five runs Sunday came via the home run), the rotation is iffy at the moment and the injuries overwhelming.

Anthony Rizzo is uncertain to play again this season. Aaron Judge and Giancarlo Stanton are back but neither looks close to 100 percent. On the other hand, Josh Donaldson looks perfectly fine, but he’s obligated to remain on the injured list until at least Sept. 14, thanks to a bookkeeping call (not that he was doing much when he was active).

Boone said before the game, in answer to a question about whether they may either be worn out or had given up, that they “definitely” had not given up. But if this is their best effort (and there’s no reason to doubt him), that may be even more damning.

The Yankees are now 11-22 since the All-Star break, and even more disheartening, 6-16 since Judge, the best player this side of Shohei Ohtani, returned from his severe right big toe injury. While barely hitting enough to challenge teams — their .230 batting average only beats the Oakland A’s, who shouldn’t even be in the league — this one may have been the most disheartening game of 2023.

No one expected the safe call on Kiner-Falefa to be overturned in the bottom of the eighth inning, but the Yankees understand they haven’t been good enough to emphasize or yell about one call (IKF only said he didn’t see a reason to overturn on the replay). At this point, it can’t be the umps or the league.

Ultimately, the Yankees still gave themselves a chance. After Turner doubled in the go-ahead run in the top of the ninth, the Yankees put runners on first and second with none out in the ninth, but Judge and Gleyber Torres struck out, leaving them with the .095-hitting Ben Rortvedt batting against Kenley Jansen, he of now 419 saves. Rortvedt gave it a ride. But alas, not quite far enough.

The ball settled into center fielder Adam Duvall’s glove in deep center to make it seven straight Red Sox victories over the Yankees. And solidify the Yankees’ chances at zero point zero.