Combining emotion and durability with a competitive nature, Mays was a six-time AFL All-Star, and was selected to the All-Star team at two different positions. He played in 126 straight games for the AFL Texans and Chiefs, and used his speed, agility and strong "second effort" to once recover and return a Jets' fumble 58 yards for a touchdown. His contribution to the Chiefs' strong defense helped them defeat the Vikings, 23-7, in Super Bowl IV. He was a captain in Super Bowl I and Super Bowl IV.
Mays was named to the All-time All-AFL Team in 1970 and announced his retirement after that season. He then returned to Dallas to work for a construction company owned by his father, Avery. He died of malignant melanomacancer in 1994, two years after the death (from cancer) of his former teammate, Buck Buchanan. The other starting defensive end from the Super Bowl team, Aaron Brown, was killed in 1997 when struck by a car from behind, leaving Curley Culp as the lone survivor of the Chiefs' vaunted front four from the championship club.