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Following a waiver claim from the Angels on May 13, the 32-year-old Mattheus posted a 4.09 ERA and 1.527 WHIP in 57 appearances. Over his 55 innings, he retired 39 of his 57 first batters faced and stranded 13 of his 19 inherited runners.
Villarreal, 28, split the 2015 season between Cincinnati and Triple-A Louisville. In 29 big league games, often as a long or middle reliever, he had a 3.42 ERA while stranding 13 of 18 inherited runners.
The bullpen was a weakness for the Reds last season, and they have several openings for roles heading into spring. Mattheus didn't post superlative numbers, but proved durable and versatile for use in multiple middle-inning spots. Villarreal showed an ability for decent long relief and worked two innings or more five times over his final 10 appearances.
Mark Sheldon is a reporter for MLB.com. Read his blog, Mark My Word, follow him on Twitter @m_sheldon and Facebook and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.