In , Score came up to the major leagues (with Colavito) as a rookie with the Cleveland Indians at the age of 21. He quickly became one of the top power pitchers in the American League, no small feat on a team that still included Feller, Bob Lemon and other top pitchers, going 16–10 with a 2.85 earned run average in his first year. He appeared on the cover of "Sports Illustrated" magazine on May 30, 1955. Score struck out 245 batters in 1955, a major league rookie record that stood until , when it was topped by Dwight Gooden (Score, Gooden, Grover Cleveland Alexander, Don Sutton, Gary Nolan, Kerry Wood, Mark Langston, and Hideo Nomo were the only eight rookie pitchers to top 200 strikeouts in the 20th century). It was the first time in major league history that a regular starting pitcher averaged over one strikeout per inning.