Born in Maracaibo, Venezuela, Alvarez represented his hometown in the 1982 Little League World Series, where they finished with a 2-1 record. Alvarez began his professional baseball career when he was signed by the Texas Rangers as an amateur free agent on September 23, 1986. He made his major league debut at the age of nineteen on July 24, 1989. Five days later, he was traded with Scott Fletcher and Sammy Sosa to the Chicago White Sox for Harold Baines and Fred Manrique. Alvarez provided one of the highlights of the 1991 Chicago White Sox season on August 11, pitching a no-hitter against the Baltimore Orioles at Memorial Stadium in only his second Major League start. It was quite a contrast to his only previous appearance, when he faced five batters for the Rangers and gave up two walks, a single and two home runs without retiring a batter, giving him a career ERA, prior to his no-hit gem, of infinity.\n', '

Alvarez had control problems in the minors, and it carried over to the big leagues. After shouldering a very heavy workload in 1991, he was kept under scrutiny for most of the 1992 season. Between the majors, minors and winter league action, Alvarez worked close to 300 innings in \'91; a significant number for anyone, but especially for a 21-year-old pitcher. It wasn\'t until 1993 that he managed to break into the rotation permanently. That season, Alvarez won 15 games and finished second in the league in earned run average, but his control problems continued; he led the league with 122 walks.\n', '

In 1994, Alvarez went 12–8 and made the American League All-Star team. After a disappointing 8–11 in 1995, he had 15 wins and 181 strikeouts in 1996.\n', '

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