Baker was one of the most highly sought-after high school athletes to come out of West Virginia his senior year. He attended Greenbier East where he averaged 25.3 points in 75 games and racked up a total of 1,902 points in his school boy career. That made him the third leading career scorer in West Virginia state history for three-year high schools. In the rebounding department he pulled down 1,4125 rebounds for an 18.8 average. He guided Greenbier East to a 25-1 record and the West Virginia state tourney. Warren scored 91 points and grabbed 47 rebounds in three games. With very impressive credentials, he was presented with the Bill Evans Award as the outstanding high school basketball player in the state. Baker was voted to the Big All-State team his junior and senior years and also made the Class AAA All-State team both years. Bakers's strong points were his defensive play and his rebounding ability.

However, going into his freshman year, Coach Moran did not plan to push him but stated that he wanted Baker to make the adjustment to college basketball but he was going to see action on the varsity team. In fact, Baker went on to make a smooth transition from high school to college ball and he was one of a limited number of freshmen in the country who had a starting varsity role. He started all but two games and led the team in scoring, rebounding, and minutes played and tied with Larry Carr for best shooting percentage. Baker played both forward and center, although he never played anywhere but "in the hole" in high school. As a freshman, Baker was voted ECAC rookie of the week in January for his play against Cornell and Penn State. He was also voted to the all tournament team in WVU's Mountaineer Classic.

Returning for his sophomore year, Coach Moran believed that his year of experience playing cornerman had helped Baker in his ball handling and defensive play. That resulted in him leading the team in scoring on 10 occasions and hauling down the most rebounds 21 times. "Wonderful" entered his junior year looking forward to a total team effort and a winning approach. Baker scored 442 points in 27 games for a 16.4 average. He connected on 50.1 percent of his field goals—up five percent from the previous year—and shot 59.2 percent of his free throws, an eight percent improvement. For the third consecutive year Baker led the Mountaineers in rebounding with 280 (10.4 per game) and minutes played with 976. He added 40 assists while fouling out of only one game-the first since he was in junior high school. Returning his senior year it looked like his best performances were yet to come.