Shaw's career took a significant turn when he was traded to the Chicago White Sox in 1958. It was with the White Sox that he truly began to shine. In 1959, Shaw played a crucial role in helping the team clinch the American League pennant. That season, he posted an impressive 18-6 record with a 2.69 ERA, establishing himself as a reliable starter in the rotation. His performance earned him a spot in the 1959 World Series against the Los Angeles Dodgers. Shaw's standout moment came in Game 5, where he pitched a complete game, allowing just one run and securing a victory for the White Sox.
Following his success with the White Sox, Shaw continued to be a valuable asset on the mound. In 1960, he was selected to the All-Star Game, further cementing his reputation as a talented pitcher. However, his time with the White Sox came to an end in 1961 when he was traded to the Kansas City Athletics. Shaw's stint with the Athletics was short-lived, as he was traded again in 1962, this time to the Milwaukee Braves.
With the Braves, Shaw continued to deliver solid performances. He remained with the team until 1964, when he was traded to the San Francisco Giants. During his time with the Giants, Shaw transitioned into a relief pitcher, adapting to the needs of the team. His versatility on the mound proved beneficial, and he contributed to the Giants' pitching staff until 1966.
In the latter part of his career, Shaw played for the New York Mets and the Chicago Cubs. Although his performance declined in his final seasons, Shaw's experience and knowledge of the game were valuable to the teams he played for. He retired from professional baseball after the 1967 season, concluding a decade-long career in the major leagues.
Throughout his career, Shaw was known for his competitive spirit and ability to perform under pressure. His contributions to the teams he played for, particularly the Chicago White Sox, left a lasting impression on the baseball community. After retiring from playing, Shaw remained involved in the sport, sharing his expertise as a coach and mentor to younger players.
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