In the 10 games that followed the disaster that earned Daniel Bard a demotion, the Red Sox pitching staff recovered nicely. In two complete turns through the rotation, its starters averaged 6 2/3 innings per outing, allowed 12 fewer hits than innings pitched and posted a 3.68 earned run average. Overall, the team surrendered 3.5 runs per game — almost a full run better than the American League average this season.

But Boston went 3-7 in that stretch.

The reason for that record is simple; though what it says about the way the club has been built — or how it can be remedied — is not.

Those recent struggles are explained by the fact the Sox were held to two runs or less in five of those 10 games, though that futility is just another piece of evidence that Boston’s lineup isn’t what it once was. And that begs the question of whether, as baseball takes a decided turn toward a new era of pitching dominance, if the Sox can continue to build teams in the fashion and around the philosophies that served them so well for nearly a decade.

From 2003-09, no team reached base more than the Red Sox — and it served them well. Only the Yankees scored more runs, and Boston was baseball’s only two-time champion in that span. Assembled on the tenets of Moneyball, they took a lot of pitches, worked a lot of walks, practiced patience and got deep into bullpens.

Today, they’re still among the best teams in the game in terms of getting on base, and scoring, and seeing pitches. But the game has changed.

The .328 on-base percentage they brought into Saturday’s game at Chicago would’ve been baseball’s 24th-best when the Red Sox won their most recent World Series title, while in the meantime the major leagues’ average ERA has tumbled almost half a run to 3.99. Therefore, though Boston remains decent in relation to their contemporaries, in order for that offensive advantage to be relevant, Sox pitchers would need to improve at a commensurate level.

And that hasn’t happened. While the rest of the big leagues has improved by half a run in the past five years, Boston’s collective ERA was 4.42 from 2003-07 — and it was 4.36 this season, entering Saturday.

So as pitching has improved to the point no-hitters are beginning to almost seem routine, it’s become harder to execute an offense approach that seeks to feast on the weak because those hurlers are less prevalent. With a less-effective offense, their own pitchers have less margin for error. And without their own pitchers having made the same gains most staffs have over recent seasons, the Red Sox’ offense isn’t the difference-making unit it used to be.

As a result, they’ve become an incomplete team, with no playoff wins since 2008 and now under-.500 in mid-June. They lack the balance necessary to win consistently, which is why stretches like this latest run can happen, and why it’s not a coincidence that this team can’t seem to put it all together at the same time.

Good teams can do enough to make it somehow work most nights; the others can’t. And the fact the Red Sox are 26-4 when scoring at least five runs, compared to 5-29 when scoring four or less, suggests Boston belongs among the latter. On one hand, its offense is good enough to carry the club some nights; on the other, though, the Sox are more likely to score less than the AL average of 4.4 runs a game than they are to score more.

What worked for years isn’t working anymore. As the big numbers of the steroid era have given way to a age of arms proliferation that has leveled out offenses, it’s become more difficult to win by taking advantage of bad pitching when the pitching on almost every other team is better than your own. The game has changed.

And the Red Sox may need an overhaul — of personnel and principles — in order to change with it.

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To further illustrate how the Sox have struggled collectively to reach base, consider their individual numbers. Of the 11 players on the current 25-man roster who’ve spent at least three seasons in the big league, seven entered Saturday with an OBP below their career mark.

Among the four exceptions were backups Kelly Shoppach and Nick Punto (who had more walks than Jarrod Saltalamacchia, Kevin Youkilis, Mike Aviles or Ryan Sweeney), as well as Scott Podsednik, who’d played just 17 games. That left David Ortiz as the lone full-time regular reaching base at his expected level.

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With two more hits Friday, Podsednik moved to .387 with an .887 on-base plus slugging in his return to the majors after more than a year away — providing much more offensively than the Sox could’ve expected when acquiring him from the Phillies system for organizational depth.

It’s surprising, given that Podsednik was hitting just .197 at Triple-A when he was traded, and batted .254 in the minors last season. But since the start of 2009 he’s a .304 hitter at the major-league level, so there is some reason to believe that, if healthy, Podsednik can remain a reasonably productive option. Add in his six steals and steady defense, and he could be a useful piece of the Boston roster the rest of the way if the Sox stay in contention, or potentially an intriguing trade chip for someone seeking bench help in the outfield.

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STAT OF THE WEEK: Through Friday, Red Sox outfielders had totaled 15 home runs. In Oakland, ex-Sox Josh Reddick (15) and Brandon Moss (six in 32 plate appearances) had combined for 21.

Dave D’Onofrio covers the Red Sox for the New Hampshire Union Leader and Sunday News. His e-mail address is ddonof13@gmail.com.