Angels take a flier on UCLA’s Kyle Molnar, who has pitched one inning since 2016

One of the most peculiar moves the Angels made in the amateur player draft that concluded Wednesday after 40 rounds was choosing a right-handed pitcher who has thrown only one competitive inning since 2016.

Kyle Molnar, a 6-3, 210-pounder from Aliso Viejo, was plucked out of UCLA, a team for which he did not play this year, in the 26th round.

Molnar led UCLA in wins and ERA (3.32) as a freshman, delivering on the hype that followed him through his career at Aliso Niguel High, where he nurtured a fastball that regularly touched the mid-90s and became Baseball America’s 53rd-best prospect of the 2015 draft.

But a torn ligament in his elbow derailed his career. After missing the 2017 season recovering from Tommy John surgery and suffering a setback late in his rehabilitation, Molnar finally made it back to the mound in April 2018 — only to be shut down for the rest of the season after one scoreless inning of relief. Molnar underwent a second elbow ligament reconstruction in May 2018.

“Obviously, he was a very high-end recruit out of high school,” Angels scouting director Matt Swanson said. “Actually, I was with the [St. Louis] Cardinals when they drafted him. We thought very highly of him. He battled some stuff over his four years at UCLA. He’s been through a lot. I think the opportunity to stay local in a system that’s in his own backyard is pretty special for him.”

Molnar, 22, was one of 13 players selected out of UCLA in this draft, and the only one the Angels picked.

Despite not playing, Molnar was active this spring. He used UCLA’s facilities throughout his rehabilitation and is now almost recovered from surgery. He has been throwing bullpen sessions for the last two months.

“It’s been a long journey through UCLA but I made my way through,” Molnar said when reached by text message. “It was exciting [to be drafted] because all the hard work paid off.

“I’m really excited for the next step in my baseball career.”

The Angels, a team plagued by arm issues at the major league level for several years, are well positioned to nurture Molnar’s progress. They took a patient approach with last year’s picks, , keeping 12 of the 21 pitchers selected off the mound through the summer. They are willing to follow the same tactics so long as their draftees don’t miss out on critical development time.

“They can take eight, nine months and get their base beneath them,” Swanson said. “Some of them had really big workloads in college. So I think it’s just understanding their history and where they’re at physically.”

The Angels did not shy from selecting players with injury histories. Left-hander Jack Dashwood of UC Santa Barbara, picked in the 12th round, spent his freshman year recovering from Tommy John surgery. He finished his two seasons pitching for the Gauchos with a 3.53 ERA and 7.86 strikeouts-per-nine-innings. Right-hander George Veliz missed half of his 2018 season at Miami because of arm trouble. Moved to the bullpen this year, Veliz struck out 69 in 42 1/3 innings and held batters to a .194 average.

For the second year in a row, the Angels went arm-heavy in the draft. They used 26 of their 40 picks on pitchers. The majority of the position players they chose played up-the-middle spots.

They also chose three two-way players in the draft, including high-profile Vanderbilt commit Spencer Jones. The 6-foot-7 left-handed pitcher and first baseman from La Costa Canyon High fell to the 31st round because he was deemed unlikely to sign, but the Angels took a last-gasp chance on someone Swanson said “is about as legit of a two-way guy as there is.”

The Angels have a little more than a month to come to terms with players on signing bonuses. MLB’s deadline for signing 2019 draftees is July 15.

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Short hops

Outfielder Justin Upton, out all season recovering from a sprained left big toe, faced live pitchers for the first time since spring training. He hit two home runs, manager Brad Ausmus said, and “looked good.” He could begin a rehab assignment soon. … Matt Harvey, on the injured list because of upper back strain, will begin a rehab assignment Saturday for triple-A Salt Lake. Harvey, who has a 7.50 ERA in 10 starts, will not face restrictions in what will be his first outing since May 23. … Fellow starter J.C. Ramirez was on a 75-pitch count in Salt Lake on Wednesday in his second rehab start since undergoing Tommy John surgery in April 2018. He allowed thee hits, three runs and three walks over 4 1/3 innings. Ramirez might need another outing before being activated. … Shortstop Andrelton Simmons recently took swings for the first time since sustaining a grade 3 sprain of his left ankle May 20. There is still no clear timeline for when Simmons will return.

maria.torres@latimes.com

@maria_torres3