At the Winter Meetings after the ’65 season, Pappas was traded to the Cincinnati Reds with two others for Frank Robinson. With nine big league seasons under his belt, Pappas was still only 27 years old, and the Reds coveted his durable right arm. The Reds were willing to get rid of Robinson, one of the best players in the game, because at the age of 29 they felt the right fielder’s best seasons were behind him. They were wrong, as Robinson went on to win the MVP Award and lead the O’s to their first World Series championship in ’66. Meanwhile though, Pappas was exactly as advertised – he continued to take the ball and give his team a chance to win every 4-5 days. He won 12 and 16 games in his two full seasons with Cincinnati before being traded to Atlanta and then to the Chicago Cubs. His best success in the National League was with the Cubbies, where he won 17 games twice.
Pappas came tantalizingly close to hurling a rare perfect game with the Cubs on September 2, 1972. The 33-year old righty retired the first 26 batters and was facing #27 (Larry Stahl) when he ran the count to 2-2. His next two pitches were very close, but umpire Bruce Froemming called them both balls and issued a walk. Pappas and catcher Randy Hundley argued to no avail. Pappas retired the next batter for his no-hitter but he never forgave Froemming.
Pappas became the first pitcher to win 200 games without ever winning 20. He narrowly missed winning 100 in both leagues: he garnered 110 in the AL and 99 in the NL.