Ryan, a Hall-of-Fame pitcher, joined the Rangers as president in 2008 and became CEO in 2011.
During Ryan's six seasons as a Rangers executive, the club went to the World Series twice (2010 and '11) and had the fifth-highest winning percentage (.551) in the major leagues.
"This is the right time for me to step down from my role of overseeing the Rangers organization," Ryan said in a statement. "I am extremely proud of what this organization has accomplished.
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Los Angeles Dodgers manager Don Mattingly said Thursday that injured shortstop Hanley Ramirez and center fielder Andre Ethier plan to be in the lineup for Game 6 of the National League Championship Series against the St. Louis Cardinals on Friday.
Ramirez, who has a fractured rib, was removed from the last two games in the seventh inning due to pain. He missed Game 2 of the series after sustaining the injury in the series opener. Ethier, who has a fractured left ankle, also missed Game 2 but played in the last three games.
The Cardinals lead the series 3-2.
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The Cleveland Indians re-signed right-handed reliever Matt Capps to a minor league contract on Thursday with a non-roster invitation to spring training camp.
Capps, 30, pitched in six games this season at triple-A Columbus before undergoing season-ending right shoulder surgery on June 5.