Both will be on the mound during the intrasquad game Friday afternoon on Nolan Ryan Field.
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"Both the guys are here because of their stuff, and they have a track record," assistant general manager Josh Boyd said. "The encouraging thing about those guys is they have definite pluses. We just need to see the best way of maximizing it."
The Rangers are eager to see Wagner, 26, pitch after claiming him off waivers Nov. 18 from the D-backs. He avoided the waiver merry-go-round other players went through this offseason because the Rangers see him as a darkhorse candidate for their rotation.
"He is a sinker/slider pitcher with a track record of athleticism," Boyd said. "His competitiveness has been a big draw. Put all those pieces together, and the track record of success is very attractive."
Wagner, the Brewers' fourth-round Draft pick in 2012, was a closer at the University of Utah before Milwaukee switched him to the rotation. He moved up quickly and, after going 11-5 with a 2.25 ERA at Double-A Biloxi, he made his debut with the Brewers in September 2015.
Wagner made three starts before being traded to the D-backs in the offseason. But his season was cut short last year after eight outings because of a strained right latissimus dorsi muscle. He didn't pitch past May 13 and was designated for assignment after the season.
"I know my ability," Wagner said. "I know I can pitch. The DFA came because I was hurt and I wasn't able to prove to the D-backs I was able to pitch. It's part of the game. I'm excited about the opportunity here."
Webster, originally drafted by the Dodgers, has been a part of two big trades in his career. He was one of five players -- including James Loney -- who were traded by the Dodgers on Aug. 25, 2012, for Josh Beckett, Carl Crawford, Adrian Gonzalez and Nick Punto. In 2014, the Red Sox included him in a three-player package with the D-backs for Wade Miley.
Webster, 27, was a significant part of each trade, a young right-hander with a fastball averaging 94 mph and an outstanding changeup. The breaking stuff has been a work in progress, but he still had the talent to excite scouts.
"Live arm, plus changeup, huge velocity," Boyd said. "We brought him here to see if our guys can find a way to get the complete package."
The ability hasn't translated to success in the Majors. He has made 23 starts and five relief appearances at the big league level and is 7-6 with a 6.13 ERA. He spent last season in Korea, but his season was cut short after 12 games because of a calf injury. The Rangers signed him to a Minor League contract this winter.
"Everything I've done I have learned from," Webster said. "Even going overseas, I've learned a lot that will make me a better pitcher. I'm looking forward to this, and I'm going to do my best to get on the team. That's my goal."