Schrader was born in Fenton, Missouri. In 1971, he was the sportsmens champ at Lake Hill Speedway in Valley Park. That same year, he moved up to sprint cars, racing in various locations across the Midwest. In 1980, he started racing in USAC's Stock Car Division, and was the series' rookie of the year. He returned to USAC's Stock Car Division one year later, finishing third in points. Early in the decade, he moved to the USAC series, competing in its various sprint car competitions. Schrader attempted to qualify for the 1983 Indianapolis 500 but wrecked his car during practice. In the USAC series, he won four USAC sprint car races, six Silver Crown races, 21 in USAC midgets, and 24 midget races in other divisions.