Yet the exception came in 2004, when their Game 1 loss led to a sweep by the Red Sox -- who themselves rallied back from two Division Series-opening losses, in 2003 against Oakland and in 1999 against the Indians.
So neither side considers this series decided on the eve of Friday night's Game 2 at Fenway Park at 8:37 p.m. ET.
"Every game this time of the year takes on its own personality and flavor," Boston manager Terry Francona said, by way of diminishing the carryover effect of any postseason situation.
Nonetheless, if the Angels are to get off the mat and get on the scoreboard, they need to shed the weights from their bats and the shackles from their legs.
The two go together, and neither got anywhere in Game 1.
Now, giving a football twist to Mike Scioscia's rally call, the Angels will have to establish their hitting game before going to the running game.
The Los Angeles manager calls it "batter's box offense."
"We can talk all we want about creating runs," Scioscia said, "but we need to start by creating some batter's box offense."
The Angels appear likely to have more weapons for that purpose. Unless he suffered an unexpected relapse to his sore triceps in Thursday afternoon's light workout, Vladimir Guerrero is expected to return to right field -- where he hasn't appeared in a month, since Sept. 4.
That would create a vacancy at DH, either to get Juan Rivera's or Kendry Morales' bat in the lineup, or keep Reggie Willits' speed in it.
"It would just give us more options for our batter's box offense," Scioscia said. "Unless we start making more things happen in the batter's box, we won't be able to play our game."
It will be up to Daisuke Matsuzaka to continue the "prevent defense" mounted by Beckett, whose near-flawless effort prevented any offensive response from Los Angeles.
"When pitchers make their pitches, it's hard to do anything," Chone Figgins said. "Especially our team. When we don't get guys on, we can't do anything."
Truth be told, the Angels have been doing very little for quite a long time. Even in their last five regular-season games, they totaled only 10 runs.
On Thursday, both teams alternated a light workday. They were "optional" workouts, but, judging by the attendance, obviously players considered it their only option.
A break in the Sox's momentum did not concern Francona, who said, "A day off can never be a bad thing. You don't forget how to play -- and I was pleased by every aspect of [Wednesday's] game."
"I'll be honest with you," said Scioscia, addressing the new Division Series scheduling with more byes that extends the five-game tourney to potentially eight days. "This is a weird setup. And the fact the Series stretches so long, we'll see if it affects any team.
"Our guys are disappointed at the offensive effort, and we want to get out there."
When they get out there on Friday night, Fenway Park will be back to its boisterous self. In other words, it will be a typical day at The Fens ... April, July or October.
"Every game here is treated like a playoff game. And I think that's the culture we want to have," said Francona, perhaps touching on a reason the Angels have dropped five consecutive postseason games here, reverting to Game 2 of the 1986 ALCS.
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"Every game means so much," Francona added, "so that when you get into games that do mean so much, it doesn't make you do something you don't want to do. You don't react in a negative way."
In this place, another football concept, "taking the crowd out of the game," can be huge.
"This is not an easy place to play. You feel like the fans are on the field with you," said reliever Brendan Donnelly, now an injured member of Boston's bullpen who recalls coming here with the Angels for the '04 Division Series.
An East-West adjustment could also be at play here. Until the season's last weekend (when the Angels took two out of three in Oakland), the AL West was baseball's only division in which every team had a winning record at home and a losing record on the road.
So while the Angels' streaky offense is regarded as always capable of sparking, it has been mostly flammable in Angel Stadium, and a flameout elsewhere.
The man at the ignition, Figgins, at least wielded a more potent swing on Wednesday night than he had in a week, while dealing with tender wrists.
Figgins' first-inning single -- the Angels' lone knock off Beckett until Guerrero's single in the seventh, snapped an 0-for-28 drought. Figgins also drilled a pair of liners -- although both turned into outs on Coco Crisp's sliding catch in the sixth and left fielder Jacoby Ellsbury's diving catch in the ninth.
But even those outs had to be heartening to the Angels, who know how torrid Figgins can be when he embarks on a streak. Figgins began his season 12-for-99 and ended it with that 0-for-28 slump, but in between he was a .437 hitter for nearly four months.