At Cleveland 's John F Kennedy High School, Sims averaged 15 points and 17 rebounds a game as a senior. As a junior he scored 17 points and grabbed 12 rebounds a game. Bob was named to the All-Scholastic Team in the grater Cleveland area which is composed of the top ten players in a 125-school area. Sims was also named to the All-Ohio team. His team played in the tough East Senate league in Cleveland and reached the regional finals in the state tournament before losing. JFK complied a 20-3 record during 1972-1973 and Sims led the squad in both scoring and rebounding while finishing fourth in scoring in one of Ohio's strongest basketball league. The team ranked in the top ten in Ohio all that season.

Going into his freshman year the coaching staff anticipated using Bob with the junior varsity team but there was a possibility he could have given bench strength to the varsity later on that season. Although he played center on his high school team he had excellent shooting range and was going to play either center or forward for WVU. That year Robert played in nine junior varsity games. He led the JVs in field goals made (89-48), field goal percentage (60.1), most free throws made and attempted (26-43, 60.5 average), most rebounds (141) and most points scored and highest overall average (204) and a solid 22.7 average. He also appeared in seven varsity games but only saw limited action