Angels might find some relief right in their midst

The Angels have one-third of their opening-day lineup — left fielder Josh Hamilton, right fielder Kole Calhoun and third baseman David Freese, who suffered a small fracture of his right middle finger Friday night — on the disabled list, yet offense is the least of their concerns.

Their most glaring weakness, one they must fix if they are to end a four-year playoff drought, is a bullpen that entered Saturday night’s game against the Texas Rangers with a 4-5 record, 4.20 earned-run average, four saves in eight opportunities and had allowed 20 of 45 inherited runners to score.

Ernesto Frieri was demoted from the closer role April 25 after a 9.35 ERA and five home runs in 82/3 innings of 10 games. Middle relievers such as Kevin Jepsen, Fernando Salas and Nick Maronde have struggled to keep games close.

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The relievers ranked 11th in the American League with a .729 OPS (on-base-plus-slugging percentage) allowed and gave up 11 home runs, third-most in the league. They are the primary reason the Angels are 2-7 in one-run games.

But the Angels could find relief in the most unlikely of places — their farm system, which Baseball America rated as the worst in the game going into 2013 and 2014.

“It’s funny, but right now, our primary weakness at the major league level is our primary strength at the minor league level,” General Manager Jerry Dipoto said. “We have some really nice bullpen arms in the system, and that’s fortunate.”

One of them is already with the Angels. Mike Morin, 23, was called up from triple A last Sunday, and the right-hander showed Friday night why he could gravitate toward the back of the bullpen, mixing a 94-mph fastball and pull-the-string, 71-mph changeup to strike out the side — Alex Rios, Donnie Murphy and Leonys Martin — in the eighth inning.

“He looked very good,” Manager Mike Scioscia said. “If he gets acclimated, there’s no doubt his potential is to be more of a back-end guy. We’ll ease him in and see where his performance takes him.”

The Angels have two bigger arms at double-A Arkansas in 22-year-old right-handers R.J. Alvarez and Cam Bedrosian, who both mix explosive fastballs that sit in the 96-97-mph range with power sliders.

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Alvarez, a third-round pick out of Florida Atlantic University in 2012, did not give up an earned run in 131/3 innings of his first nine games, in which he struck out 19, walked four and gave up seven hits.

“He’s cut his walk rate, which is big improvement for him,” Dipoto said. “He’s always had dominant, swing-and-miss stuff. Now he’s combining that with better strike throwing.”

Bedrosian, the son of 14-year big league closer and 1987 National League Cy Young Award winner Steve Bedrosian, dominated for five games at Class-A Inland Empire, giving up one hit, striking out 15 and walking two in 52/3 innings.

In his first six games at Arkansas, Bedrosian, a first-round pick out of East Coweta (Ga.) High in 2010, has given up two runs and four hits in six innings, striking out 12 and walking one.

Can Alvarez and Bedrosian help the Angels this season?

“Oh sure,” Dipoto said. “Once you get to double A and you’re doing what they’re doing, you’re a phone call away. They’re doing it against high-level professional hitters. I feel like both can help sooner rather than later.”

There are more reasons for optimism. Right-hander Dane De La Rosa, the team’s primary setup man in 2013, will begin a rehabilitation stint with Salt Lake on Sunday and should return from forearm and shoulder injuries by mid-May. Frieri has pitched well in three low-leverage situations and is close to regaining a back-end role.

“It’s not raining on our bullpen,” Dipoto said. “Things are looking up a bit. We had our struggles in the first month, and we’re making progress.”

mike.digiovanna@latimes.com

Twitter: @MikeDiGiovanna