The pieces have been coming together for the Red Sox, despite the insane rush of injuries. The offense leads the majors in runs (423) and runs per game (5.5). The rotation has found its rhythm, even without Josh Beckett, as Sox starters owned a 15-5 record and 3.14 ERA from May 29 through the start of Tuesday’s contest against the Rays.

Remarkably, even with the injuries to Victor Martinez, Dustin Pedroia and Clay Buchholz over the weekend in San Francisco, one could make the case that the biggest concern facing the Sox is represented by the bullpen. Sox relievers entered Tuesday with a 10-12 record and 4.50 ERA, the latter mark ranking 11th among American League squads and far worse than the league average of 4.00. The Boston bullpen has given up 33 homers and 1.4 homers per nine innings, with both marks representing the worst totals in the American League. So, too, is the team’s 13 blown saves the most in the AL.

That struggle represents inconsistency in virtually every member of the bullpen save, perhaps, for setup man Daniel Bard. Yet even with most members of the bullpen enduring their shares of ups and downs, GM Theo Epstein suggested that he is in no particular hurry to trade for a relief upgrade.

Naturally, the GM would like to see an improvement in the performance of his relief staff. That said, the lessons of mid-year acquisitions such as Eric Gagne and Scott Williamson have not been lost, namely that it can be nearly impossible to predict the performance of a reliever who is picked up mid-year, even one who has had an excellent season to that point. That being the case, the Sox are particularly cautious about dealing away prospects for a reliever. While the Sox picked up Billy Wagner for the stretch run a year ago, he did not require the Sox to part with anything beyond organizational surplus.

“I think every contending team could always use another useful reliever. It’s something we’re always looking to add to, and we’re no different. It’s no condemnation of our current bullpen, but to be realistic about it, you add a really good reliever it always makes our team better,” said Epstein. “That said, you trade for two or three months of a reliever, doesn’t matter if it’s a good one or a great one, you still don’t know what you’re going to get. So you don’t necessarily always want to give up good prospects to get that type of guy, because you’re not sure what you’re going to get in a small sample size from a reliever.”

As such, the Sox would like nothing more than for their current bullpen cast to achieve a form of self-correction. While Bard (2.06 ERA, major league leading 18 holds) has been tremendous, and the Sox believe that the track record of Jonathan Papelbon allows them to proceed without concern, the team would like to see the performances of its middle relievers stabilize.

Certainly, Manny Delcarmen, Hideki Okajima and Ramon Ramirez have all shown the ability to deliver value in middle relief. If that group — plus Scott Atchison, who has delivered meaningful multi-inning relief appearances over the last few weeks — can start to create consistent, safe passage through the middle innings, the Sox would consider that the ideal upgrade.

“It’s an important part of the team, we have to make sure we have a good ‘pen. We’ve had our ups and downs there. I think the number one way you can make your bullpen better is to try to develop as much consistency as you can out of the guys you have. In our case, we have plenty of talent out there,” said Epstein. “We haven’t had one of those years where it’s been seamless and consistent from day one in the bullpen. I think we’re fighting the ups and downs to get to a point where we have a really reliable ‘pen.”