Angels remain on the lookout for pitching

The Angels are not one of the clubs approaching the July 31 trade deadline with urgency. They already have accomplished their primary goal, fortifying their bullpen by trading for closer Huston Street and setup men Jason Grilli and Joe Thatcher.

The “have-to-get” part of the shopping list: relief pitchers. The “like-to-get” part: a starting pitcher.

So, with equal amounts of curiosity and diligence, the Angels dispatched a scout to watch Cliff Lee pitch for the Philadelphia Phillies on Monday. They also sent Matt Shoemaker out to face the Baltimore Orioles.

The night was not particularly successful for either pitcher.

In Anaheim, Shoemaker gave up a pair of two-run home runs to Adam Jones, accounting for all the Orioles’ runs in a 4-2 victory over the Angels. In Philadelphia, pitching for the first time since an elbow injury sidelined him for two months, Lee gave up six runs and 12 hits in 52/3 innings of a loss to the San Francisco Giants.

The Angels appear to be an unlikely landing spot for Lee. They cleared out much of their already thin minor league system in the trades for Street and Thatcher, and adding Lee’s $25-million salary next year would strain the Angels’ chance to keep the payroll low enough that owner Arte Moreno could avoid the luxury tax.

Although calculations of playoff odds put the Angels’ chances of making the postseason at well above 90%, the team would much rather win the American League West and get a five-game October guarantee rather than draw a wild card into a sudden-death elimination game.

The Angels, with the second-best record in the major leagues, are two games behind the Oakland Athletics in the AL West.

The Angels are thrilled with Garrett Richards (11-2, 2.47 earned-run average) and Jered Weaver (10-6, 4.33) atop the starting rotation. Beyond that, for now: Tyler Skaggs (5-5, 4.65), in his first full season in a major league rotation; swingman Hector Santiago (2-7, 4.32); and rookie Shoemaker (7-3, 4.54).

Veteran C.J. Wilson (8-6, 4.33), on the disabled list since July 10, is expected to return late this month or early next month.

“He could be the best trade-deadline acquisition we could make,” said Angels General Manager Jerry Dipoto.

Shoemaker, who could lose his rotation spot to Wilson or to a starter acquired in a trade, tied his career high with 10 strikeouts — albeit on a night both sides were flustered by the strike zone of plate umpire Eric Cooper.

In the first inning, Shoemaker gave up a leadoff single to Nick Markakis and a one-out home run to Jones.

Shoemaker then retired 15 consecutive batters into the sixth inning, when he gave up a one-out double to Markakis and a two-out home run to Jones.

The Angels scored a run in the first inning, on a one-out single by Josh Hamilton, and another run in the fourth, on a one-out single by Hank Conger.

In the fourth inning, with the bases loaded, Mike Trout struck out looking and disputed the call. The Angels did not get another runner into scoring position.

“You guys saw the replay,” Trout said. “I didn’t think it was a strike. It was a big part of the game. Leave it at that.”

Trout also disputed a called third strike in the seventh inning, prompting Manager Mike Scioscia to hustle onto the field to ensure his rarely agitated star did not get ejected. Trout said his issue there was about all the calls in that at-bat, not just the last one.

“He called one up on me, and one down,” Trout said. “It’s hard enough to hit, you know what I mean? That’s the way it goes. You can’t do anything about it.”

bill.shaikin@latimes.com

Twitter: @BillShaikin