On Friday night in Baltimore, Red Sox shortstop Xander Bogaerts was ejected by umpire Todd Tichenor for arguing a called third strike. Bogaerts said after the game, “I let my team down coming out of the game but with all I’m going through, it felt good afterwards.” AP Photo/Gail Burton

The morning of Aug. 11 dawned with the Boston Red Sox in trouble. They had lost four straight, had just one win in their previous seven games, and were five games out of the American League wild-card race.

The season was threatening to spiral out of control.

Buoyed by the return of outfielder Kiké Hernández and pitcher Michael Wacha, the Sox have played much better baseball since then. They’ve won six of their last 10. Tampa Bay is the only AL playoff contender with a better record in that stretch.

For those efforts, Boston has fallen a game farther back in the wild-card standings.

That’s the stark reality for the Red Sox with 40 games remaining in the season. While they are playing better baseball, they find themselves on the back end of too large of a pack. It’s not enough to win games; the Sox need other teams — several other teams — to lose.

The math is pretty simple. The Sox probably need to win at least 85 games to make it to the postseason. That means they need to go 25-15 or better to get there.

That’s a .625 winning percentage. Meaning they need to win practically every series over these final six weeks of the season.

Yet even that wouldn’t be enough. The Sox would need the Mariners to go 19-21 in that stretch. Or they’d need to Blue Jays or Rays to go 19-23 in their remaining 42 games. In addition to that they’d need the Twins, Orioles and White Sox to win no more than 23 games.

It’s frustrating to realize the hole you dug might just be too deep. That frustration boiled over Friday night in Baltimore. Xander Bogaerts was ejected for just the second time in his career. Bogaerts was tossed for arguing with Todd Tichenor after Tichenor called strike three on a dubious pitch.

Bogaerts was unhappy with the call. But the anger he showed was built up from weeks of struggling at the plate, and a season full of disappointing baseball from the Sox.

“I wasn’t expecting to do this tonight,” Bogaerts told reporters after the game, “but I actually feel better. I’m sorry it was on the umpire, I’m sorry it was to him. I let my team down coming out of the game, but with all I’m going through, it felt good afterwards.”

All I’m going through. Was Bogaerts referring to the .209 batting average (.583 OPS) he’s posted in August? His pending opt-out decision? The fact that his team traded away a fellow veteran leader in Christian Vázquez at the trade deadline?

Likely, he meant all of it. Bogaerts has seen a lot over his 10-year career, but he’s never seen a confluence of disappointment like this.

Sunday was a reprieve for Bogaerts and the Red Sox as they celebrated their baseball roots in the wonderful setting of the Little League World Series in Williamsport, Pennsylvania. Bogaerts had been one win away from the Little League World Series twice as a youngster, losing to Curaçao both times. He clearly enjoyed his visit on Sunday, talking to young players and soaking up the atmosphere.

But even that day ended in disappointment. The Boston bullpen collapsed in the eighth inning, haunted by two walks and a hit batter. Bogaerts tried to lift his team with a ninth-inning home run but the Sox could muster nothing more.

That home run was too little, too late to save the day. And it’s looking like this recent run of better play won’t bee enough to save the season.

Tom Caron is a studio host for the Red Sox broadcast on NESN.