Angels are improving, but offense remains a concern

Pitcher Dan Haren said the Angels have no reason to “hang their heads” after Sunday’s 7-3 loss to Texas. The bigger picture, after all, looks bright for the Angels, who have won 10 of 12 games to cut the Rangers’ American League West lead from eight to 41/2 games.

“We’re playing a lot better baseball than we did the first six weeks of the season and won two of three from the best team in baseball,” right fielder Torii Hunter said. “You have to be happy with that.”

There is still much to be concerned about, though, particularly an offense that, despite receiving a huge boost from leadoff hitter Mike Trout and power contributions from Mark Trumbo and Albert Pujols, has not been much more productive while going 22-13 in the last 35 games than it was during a 6-14 start.

The Angels are averaging only 3.9 runs in their last 35 games, compared to 3.7 runs in their first 20 games.

Hunter has three hits in 45 at-bats since May 3, an .067 slump that has dropped him from .319 to .235, and the Angels aren’t getting much from regulars Howie Kendrick (.253), Erick Aybar (.222), Alberto Callaspo (.235), Maicer Izturis (.227) and Bobby Wilson (.171).

“One thing during this stretch that hasn’t blossomed is the offense,” Manager Mike Scioscia said. “We’ve been pitching well, playing good defense, and the bullpen has been lights out; that’s a great combination to have. But we still need more offensive production. There’s more in this club.”

Draft dodgers

The Angels will be watching from the bench Monday when the 2012 amateur draft begins with first-round selections and one compensation round. They won’t swing into action until Tuesday because they lost their first- and second-round picks as compensation for signing free agents Pujols and C.J. Wilson.

The Angels’ first pick will be the 114th overall, in the third round, which forced the Angels to shift their scouting strategy away from cream-of-the-crop prospects.

“When we pick, the 113 best players will be off the board, so we focused our efforts on scouting smart,” General Manager Jerry Dipoto said. “We watched some of those guys early in the season and late in case they slide in the draft.

“But we didn’t waste valuable time hammering away on guys we know will be off the board. In my estimation, we’ve done a good job of making sure, by the time we pick, that we know the players we’re picking better than anyone else.”

Short hops

Reliever LaTroy Hawins (broken right pinkie) gave up one earned run and two hits and struck out two in a rehabilitation appearance for Class-A Inland Empire on Sunday. … Trout was selected AL rookie rookie of the month after hitting .324 with six doubles, three triples and five home runs in May. … Catcher Chris Iannetta, out since May 9 because of a broken bone in his right wrist, has been cleared to long toss and could return in two weeks. … Scioscia will manage his 2,000th game Monday, becoming the 16th in major league history to manage 2,000 uninterrupted games with one team.

mike.digiovanna@latimes.com