Tavárez entered the majors in 1994 with the Florida Marlins, playing for them three years before joining the Boston Red Sox (1997) and Baltimore Orioles (1998). His most productive season came in 1995 with the Marlins, when he posted career-numbers in batting average (.289), home runs (2), runs (31), RBI (13) and stolen bases (7). The next season, he appeared in a career-high 98 games, while hitting just .219.
In a five-season career, Tavárez was a .239 hitter (101-for-228) with three home runs and 33 RBI in 228 games, including 12 doubles, three triples and 13 stolen bases. He also played in the Seattle, Florida, Boston, Baltimore and San Francisco minor league systems from 1990–99, hitting .274 with 22 home runs and 259 RBI in 741 games.

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