A member of the Cuban national team, Garbey fled to the U.S. in the 1980 “Freedom Flotilla.” While hitting .321 for Evansville (American Association) in 1983, he was suspended for a month during an investigation of charges that he had fixed games while in Cuba, but was exonerated. He was suspended a second time in 1983 after threatening a heckling fan with a bat.
He joined the Tigers in 1984 and batted .287 for the World Champions. He was an aggressive, line-drive hitter, but could not play any position well. His temperamental behavior led to his November 1985 trade to the A’s, with whom he never appeared. He played in Mexico before resurfacing with the Rangers in 1988.