Fitzsimmons had another 18-win season in 1934, and led the NL in putouts for the fourth time, tying Grover Cleveland Alexander's major league mark. However, his career then began to plateau. He had years of 4–8 and 10–7 in 1935 and 1936, with the Giants winning the NL pennant again the latter year; he led the NL in shutouts in 1935, blanking opponents in all 4 of his victories. His troubles returned in the 1936 World Series against the New York Yankees; he lost Game 3 by a 2–1 score, and was bombarded in the final Game 6 loss, leaving in the fourth inning while trailing 5–2. After a 6–10 start in 1937, he was traded to the Dodgers in June for reliever Tom Baker, who made only 15 appearances for the Giants. Brooklyn shortstop Leo Durocher praised his new teammate's competitiveness, saying, "I wish we had nine guys like Fitz. We'd never lose." Though his record in 1938–1939 totaled only 18–17, in 1938 he tied Grimes' mark of 74 career double plays, passing him the following year; Warren Spahn broke his record in 1964. He came back in 1940 with a 16–2 campaign, finishing fifth in the MVP voting. His .889 winning percentage broke the NL record of .842 (16–3) shared by Tom L. Hughes (1916 Boston Braves) and Emil Yde (1924 Pittsburgh Pirates), and stood until Roy Face posted an 18–1 mark (.947) with the 1959 Pirates.