Parrish still holds the record for the best winning percentage by a head coach at Wabash, winning 42 of his 46 games at the helm of the Little Giant football program.
Parrish joined the Wabash staff as an assistant in 1977, helping the Wabash football team to reach the Amos Alonzo Stagg Bowl to play for the Division III National Championship.
He took over the Wabash program as the head coach the next season, leading the Little Giants from 1978-1982 and earning him a place in the Wabash Athletic Hall of Fame. His 1980 and 1982 Little Giant teams were unbeaten.
Parrish left Wabash in 1983 to return to Purdue University as a quarterbacks coach. His college coaching career started at Purdue in 1975 as a graduate assistant. He left the Boilermakers in 1984 to take over the reins at Marshall.
Parrish went on to serve as the head coach at Kansas State and as an assistant at Rutgers before moving the the University of Michigan. He served under Lloyd Carr at Michigan as the quarterbacks coach, working with current NFL quarterbacks Brian Griese and Tom Brady. Parrish was named the offensive coordinator in 2000, then stepped down from the program shortly before receiving a call from new Tampa Bay Buccaneers head coach Jon Gruden to join his staff in Tampa Bay as the Buccaneers' quarterback coach.
Parrish is not the first Wabash player to experience the Super Bowl firsthand. Wabash Hall of Famer Pete Metzelaars ’82 caught a touchdown pass in Super Bowl XXVI while playing for the Buffalo Bills. Metzelaars was part of the Bills' squads that played in four consecutive Super Bowls. He started in three of those four games for Buffalo, catching a total of four passes for 32 yards and one TD.