During his 28 seasons as the head coach of the Ohio State Buckeyes football program, Hayes's teams won five national championships (1954, 1957, 1961, 1968, 1970), captured 13 Big Ten Conference titles, and amassed a record of 205–61–10. Over the last decade of his coaching tenure at Ohio State, Hayes's Buckeye squads faced off in a fierce rivalry against the Michigan Wolverines coached by Bo Schembechler, a former player under and assistant coach to Hayes. During that stretch in the Michigan–Ohio State football rivalry, dubbed the "Ten-Year War," Hayes and Schembechler's teams won or shared the Big Ten Conference crown every season and usually each placed in the national rankings.