Is it realistic to think that the Red Sox might have a chance?

Those around the club recognize the reality of their circumstance. Even with a 9-3 stretch that helped offset the brutal eight-game losing streak that bookended the trade deadline, the Red Sox still face a steep uphill slog in their pursuit of a wild-card berth. It is no small feat to make up a handful of games in the standings over a month.

It’s a long shot, but it’s enough to keep the Red Sox from raising a white flag at this point.

THE ODDS

The Red Sox are one of four teams jockeying for the final two American League wild-card spots. Through Thursday, Cleveland had fallen back to the pack a bit, but still sat in the top wild-card spot with a seven-game edge over the Sox and 2½ on the Rays (while holding a 1½-game advantage over the A’s for the right to host the wild-card game). The A’s were 5½ games in front of the Sox, while the Rays were 4½ games in front of Boston.

For the Red Sox, the problem is twofold. First, they have to sustain a scorching hot stretch — something they have been unable to do this year, and an undertaking made more difficult by the injury to Chris Sale and the lack of reliability in the rotation beyond Eduardo Rodriguez. Second, they have to hope for stumbles not just by one team but two.


Even if, say, the Rays endure a skid and get overtaken by Boston in the four-game late-season matchup between the teams, that won’t be enough to ensure the Red Sox a playoff berth. They’d also need the A’s or Indians to crash. That combination is a hard one to pull off, as reflected in the postseason odds being ascribed to the team:


Fangraphs gives the Red Sox a 7.6 percent chance of making the postseason.

FiveThirtyEight gives them a 5 percent chance.

STRENGTH OF SCHEDULE

Just under half of the Red Sox’ remaining games (13 of 28) are against teams with records of .500 or better. In other words, if they are to mount a postseason push, they’ll have to do something that they’ve done infrequently this year: beat winning clubs.

The Red Sox have a .383 winning percentage against teams with a record of .500 or better, worst among their postseason competitors.

That said, Cleveland has been almost as bad (.408 vs. .500 or better teams). Moreover, the Sons of Tito have the most remaining games against such teams, including interleague matchups against the Phillies and Nationals. Given the injuries faced by the Indians — most notably the loss of Jose Ramirez — is there a chance they endure a nosedive? It can’t be dismissed, though 14 games against the bottom-feeders of the AL Central represent a significant firewall.

AL wild-card contenders Through games of Aug. 29 Record vs .500+ To play vs. above 500 To play vs. below .500 Red Sox 23-37 (.383) 13 15 Rays 28-32 (.467) 12 16 A's 31-24 (.564) 7 23 Indians 20-29 (.408) 15 14 SOURCE : Fangraphs, MLB

Not only do the A’s have just seven games remaining against teams with winning records, but they have more than held their own against such teams (.564 winning percentage, tied for third-best in the majors). Once they get past a three-game series against the Yankees this weekend, they face a downhill September.

The Rays have 11 of 27 remaining games against teams with winning records. They’ve held their own against the stiffest competition in the league, with a .468 winning percentage. To make the four remaining contests against the Rays meaningful, the Sox must hope the Rays stumble in a series or three against sub-.500 clubs.


HISTORY

There have been some incredible September comebacks in baseball history — but most required teams to leapfrog just one team. The 2011 Rays ran down the Red Sox after entering September with a nine-game deficit, but Tampa Bay required the collapse of one team — not two — to complement its surge. The 2009 Twins overcame a seven-game September deficit against the Tigers — including a three-game hole with four to go — to win the AL Central, but again they were running down just one team.

The 2007 Rockies were the last team to make the playoffs by blowing past multiple teams that entered September with at least a four-game advantage over them. In the 24 postseasons since the introduction of the wild card, that Colorado team is the only one to delete September deficits of at least four games to multiple teams.

MORE RECENT HISTORY

But what of this Red Sox team? Do they have a shot at jumping past their chief competitors given the dwindling number of games?

The best 28-game stretch of the season for this 2019 edition came after the team reached its low point. On April 17, the Red Sox fell to 6-13 – the worst record in the American League – after getting swept by the Yankees in a two-game series in New York. But they rebounded with a 19-9 stretch over their next 28 contests.


During that sprint, the Red Sox gained five games on both Tampa Bay (13-13) and Cleveland (14-14) while outplaying Oakland (12-15) by 6½ games. Boston’s best stretch coincided with dips by all three of the teams now in front of them in the wild-card peloton.

If identical circumstances occur, then the Red Sox could find themselves playing beyond the last regular-season game. Of course, the simultaneous occurrence of one of the best Sox stretches of 2019 with extended downturns by at least two of the three teams within their reach represents an improbable development. The postseason hopes, though not extinguished, remain faint.

Alex Speier can be reached at alex.speier@globe.com. Follow him on twitter at @alexspeier.