Sandy Koufax, pitcher of the Los Angeles Dodgers, holds up four baseballs in Los Angeles, Calif. on Sept. 10, 1965. On the night of Koufax’s perfect game in 1965 against the Chicago Cubs, the Dodgers were in a tight pennant race against Mays’ Giants. What makes a perfect game the rarest of no-hitters, is that it involves more than just giving up a hit. Scully called Koufax’s perfect game against the Cubs in 1965. “You start out every game to pitch a perfect game,” Koufax said, reflecting on the moment.