1901-1920 Red Sox: Cy Young
The name Cy Young is synonymous with greatness in pitching. Since 1956, the best pitchers in MLB are given an award named after him. Young is one of the greatest pitchers of all time and his stats back him up. He boasts a career 163.6 WAR, which is second most of any pitcher ever; only Walter Johnson tops him. He has 98 more wins than the next man on the leaderboard and that number (511) will never be surpassed.
Young played for the franchise before they were even called the Red Sox. They were the Boston Americans until 1908 when they changed to the Red Sox. In his time with Boston, Young was able to put up some elite numbers, especially considering he was 34 when he left St. Louis.
In that tenure, he held an even 2.00 ERA with 192 wins. Out of 297 games started, he had 275 complete games and 38 shutouts.
He led the Americans to their World Series in 1903 where they defeated the Pittsburgh Pirates five games to three; which was the first World Series between the American and National leagues. During that season, he went 28-9 with a 2.08 ERA and 176 strikeouts.