Jered Weaver delivers for Angels in 7-4 win over Texas

The Angels will gather Tuesday for their organizational meetings, an annual two-day event in which front-office executives, coaches and scouts evaluate the team’s strengths and weaknesses and begin formulating ideas to improve the club this winter.

There will probably be much hand-wringing over the team’s underachieving offense, too-often unreliable bullpen, thin bench, sometimes shaky defense and fundamental lapses that cost the Angels a shot at their fourth consecutive division title.

But there should be plenty of hand-slapping over the Angels’ rotation, and especially ace Jered Weaver, among the few bright spots in a disappointing season.

Weaver delivered another quality start, giving up three runs and nine hits, eight of them singles, in 62/3 innings of Monday night’s 7-4 win over Texas in Angel Stadium.

The right-hander wasn’t dominant — he struck out only two — but he improved to 13-11 with a 2.99 earned-run average and lowered the rotation’s ERA to 4.10, fifth-best in the American League.

The win also assured that the Rangers will not clinch the AL West title on the Angels’ turf. Texas leads Oakland by eight games and the Angels by 91/2 games and has a magic number of six.

That the Angels are on the brink of elimination is no fault of Weaver, who ranks second in the AL in strikeouts (220) and fifth in ERA.

Weaver went through a 14-start stretch from June 25 to Sept. 4 in which the Angels scored all of 26 runs in the games.

“There’s no doubt if we supported him on the offensive side, he’d be in the race for the Cy Young Award,” Manager Mike Scioscia said of Weaver.

“Unfortunately, as a team, we haven’t put him in that position.”

But after backing Weaver with one run in four starts from Aug. 17 to Sept. 4, the Angels have scored 18 runs in his last three starts, including a three-run fourth inning and a two-run sixth Monday night.

Down and out

Scioscia said shortstop Erick Aybar will sit out the rest of the season because of a suspected sports hernia.

Aybar will travel to Dallas on Tuesday to meet with Dr. John Preskitt, who in November performed surgery on Hunter for a similar injury.

Aybar, who hasn’t played since Wednesday, hit .254 with a .306 on-base percentage, considerable drop-offs from 2009, when he hit .312 with a .353 on-base percentage.

20-20 vision

With his 19th and 20th home runs Sunday in Tampa Bay, Abreu, who has 22 stolen bases, has hit at least 20 homers and stolen 20 bases in nine seasons.

The only other players in major league history with more 20-20 seasons are the father-son combination of Bobby and Barry Bonds, who had 10 each.

“It tells me I’m still doing it, even though the average is pretty low,” said Abreu, 36, a career .299 hitter who is batting .256. “The power is good. Sometimes the average, you can get it back.”

Designated sitter

Hideki Matsui has four hits, including two homers, in 10 career at-bats against Texas starter Derek Holland, but Scioscia opted to start Juan Rivera at designated hitter against the Rangers left-hander Monday night.

The left-handed-hitting Matsui has hit .382 (34 for 89) since Aug. 14, “but we wanted to get as many right-handed bats in the lineup as we could,” Scioscia said. Matsui had a pinch-hit, run-scoring infield single in the seventh.

Short hops

Third baseman Alberto Callaspo suffered a bruised left foot when he was hit by a pitch in the seventh inning and left the game. Callaspo had X-rays and they were negative, but he won’t play Tuesday.

mike.digiovanna@latimes.com