Following his graduation from Cuyahoga Falls High School in 1968, Sams was taken in the third round of the amateur draft by the Pittsburgh Pirates, who offered him a $3,000 bonus and a new Corvette. Sams turned it down and went to Miami (Ohio) University instead, earning a letter in 1970 as a pitcher. When Sams worked out for the Pirates, his catcher was noted major leaguer Manny Sanguillen, who said Sams was the hardest thrower he had ever caught.
In 1971, his fastball having been clocked at 95 miles-per-hour, Sams was drafted again, this time by the Cleveland Indians, who took him in the second round of the secondary phase of the draft. Sams reported to the rookie league Gulf Coast Indians in 1971 and used his high-powered fastball to compile a 4-1 record with five saves and a 3.29 ERA, striking out 47 in 41 innings. The next year, Sams pitched for Class A Reno in the California League and struggled because of a serious arm injury, compiling a 7.96 ERA in only 26 innings.
As a high school flame thrower, Sams was selected All-Ohio in 1967 and 1968 and was a major contributor to Cuyahoga Falls’ 36-2 record his senior season.