- In 1997 led the National League in appearances by a pitcher (89).
- Made major league debut on 7 August 1993.
- Named to Baseball Digest magazine's 1995 Rookie All-Star Team.
- Pitcher with the Cleveland Indians (1993-1996), San Francisco Giants (1997-1999), Colorado Rockies (2000), Chicago Cubs (2001), Florida Marlins (2002), Pittsburgh Pirates (2003), and St. Louis Cardinals (2004).
- He began his Major League Baseball career with the Cleveland Indians. (1993)
- He's played for the Cleveland Indians, San Francisco Giants, Colorado Rockies, Chicago Cubs, Florida Marlins, Pittsburgh Pirates, St. Louis Cardinals, and is now a member of the Boston Red Sox. (2006)
- Signed to a minor league contract by the Washington Nationals. (March 2009)
- (19 June) Designated to AAA Nashville by the Milwaukee Brewers. Tavarez was 0-1 with an 8.59 ERA and 10 runs (7 earned) in 7 1/3 innings. (2008)
- (June 25) Rejected the Milwaukee Brewers' designation for assignment and elected to become a free agent. (2008)
- (May 24) Granted free agency by the Boston Red Sox after refusing to accept an assignment to Triple-A Pawtucket. (2008)
- (July 8) Signed with the Atlanta Braves through the remainder of the season. (2008)
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