The left-hander will try to record his third win in as many games during his home debut Thursday night against the Oakland Athletics.
Los Angeles made a splash during the offseason by signing Albert Pujols and Wilson. The Angels are also expected to hold a press conference Thursday to announce a contract extension for Gold Glove-winning shortstop Erick Aybar, reportedly for four years and $35 million.
Los Angeles (4-8), though, hasn't gotten much for its money so far, but Wilson has played a part in half of his new team's wins.
The left-hander allowed one run for the second straight game and scattered six singles over six innings during a 7-1 victory over the New York Yankees on Saturday.
"There's certain things about each (of the first two starts) that I'm not satisfied with," he told the team's website. "But ultimately I think I'm just feeling out what I have to do and where I can try to get a little bit more efficient and make less mistakes. That's really what it's all about as a pitcher."
Wilson (2-0, 1.38 ERA) will try to build on that outing by winning a fourth consecutive decision over the A's (6-7). He has a 2.33 ERA over those past four matchups and has allowed two runs or fewer in each of his last three.
Oakland has scored 11 runs in its past two games after totaling 13 over its previous seven, including a 6-0 defeat in Monday's series opener. The A's turned the tables on the Angels on Wednesday as rookie Yoenis Cespedes' three-run homer in the first inning was all the support Bartolo Colon needed in a 6-0 victory.
Cespedes is batting .238, but has a team-leading four homers and 12 RBIs in his first 12 games.
Pujols, on a career-worst 12-game homerless streak to start a season, had one of the Angels' season-low four hits in Wednesday's loss. Los Angeles has scored a combined three runs over its back-to-back defeats after totaling 18 over its previous three games.
"Our offense has been a little bit spotty, and we need to get simple at the plate," manager Mike Scioscia said. "Some guys are starting to get into their game - but as a unit, we're not finding that offensive chemistry."
Cespedes will try to lead his team to a season-high third straight win while the Angels will try to avoid matching their three-game skid from April 11-13.
Southern California native Tommy Milone (1-1, 2.57) will try to send Los Angeles to that defeat during his eighth career start. The left-hander is coming off his first major league loss, 4-0 in Seattle on Saturday.
Milone, 1-0 with a 3.81 ERA in five starts for Washington in 2011, gave up all of those runs over six innings after throwing eight scoreless against Kansas City in his debut for Oakland on April 9.
"As a pitcher, you want to go out there and throw up zeros, but I didn't do that today," Milone said.
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