The 5’8″ 155-lb Norman took a long time to stick, always having to prove a little more to make up for his stature. He pitched in 14 cities in his first 11 pro seasons, and it wasn’t until 1972-73 with San Diego that he started two consecutive seasons in the same city. The Padres didn’t have many good pitchers, and they stuck with him after acquiring him in June 1971 despite his 3-12 record; his 3.33 ERA for San Diego showed that he wasn’t pitching that poorly. He went 9-11, 3.44 in 1972, his first full season in the majors, and six of his wins were shutouts, third in the NL. When Norman started 1973 1-7, Cincinnati, always short of solid pitching, acquired him for almost nothing. He went 12-6 the rest of the way to help the Reds to a second consecutive division championship. He pitched one-run ball for five innings in Game Four of the NLCS as the Reds won in twelve innings.
Norman went on to have five straight winning seasons for the Reds, including a 12-4, 3.73 record in 1975 followed by 12-7, 3.10 in 1976. He got his sole postseason victory in the 1975 LCS, winning Game Two 6-1. In 1978, he set a since-broken ML record by making 31 starts without a complete game. After going 11-13 for the Reds in 1979, he closed out his career as a relief pitcher and spot starter for the Expos.