Jason Isringhausen expected to have significant role with Angels

Reporting from Tempe, Ariz. — Jason Isringhausen signed a minor league contract with the Angels, but he could have a major impact on the bullpen. Manager Mike Scioscia indicated Thursday that the veteran right-hander is a near-lock to make the club.

“Jason is going to slot in with LaTroy Hawkins and Scott Downs [in a setup role],” Scioscia said. “We talk about that pyramid of guys getting to the closer [Jordan Walden]. It’s a little broader right now.”

A rhombus of relief, perhaps? Or a trapezoid?

“We’re looking at it as a pyramid,” Scioscia said. “If it forms itself into a trapezoid, so be it.”

Isringhausen, 39, will make between $700,000 and $1 million if he makes the club, and his deal includes incentives based on appearances. Last season, after missing most of 2009 and all of 2010 because of an elbow injury, Isringhausen went 3-3 with a 4.05 earned-run average in 53 games for the New York Mets.

The former Oakland and St. Louis closer, who has 300 career saves, was tough against right-handed hitters, holding them to a .178 average.

“I didn’t know what to expect last year, and it went better than I thought it would, so I wanted to play again,” said Isringhausen, who is expected to begin workouts Friday. “This team is built to win. That’s why I came here.”

Isringhausen lost 25 pounds since the end of last season, from 250 to 225, and feels no ill effects from the sciatic-nerve condition that sidelined him for the last month of 2011.

“I wasn’t in the best shape of my life last year … but I wasn’t planning on playing,” Isringhausen said. “I was home playing softball. My arm felt good, so I went and played with the Mets.”

mike.digiovanna@latimes.com