Hayes was the second player (after Franklin Clarke) in the history of the Dallas Cowboys franchise to surpass 1,000 yards (ground or air) in a single season, and he did that in his rookie year by finishing with 1,003 yards. Also during his rookie year, he led the team with 46 receptions and set franchise records for total touchdowns (13) and total receiving touchdowns (12). He finished his 11-year career with 371 receptions for 7,414 yards and 71 touchdowns, giving him an impressive 20 yards per catch average (both career touchdowns and yards per catch average remain franchise records.) He also rushed for 68 yards, gained 581 yards on 23 kickoff returns, and returned 104 punts for 1,158 yards and three touchdowns.