Murphy's best season was in 1983, when he led the NFL with nine interceptions and returned them for 127 yards. He finished his eight season career with 27 interceptions and 282 return yards, along with six fumble recoveries for 22 returns yards, in 109 games. He also made the Pro Bowl in 1982 and 1983.
Murphy was the Redskins representative to the NFL Players Association. He served on the bargaining committee in the players' strike that caused the cancellation of seven games during the 1982 season. Many suspect that the Redskins' decision to release him after the 1983 season and the reluctance of any other team to sign him was retribution for his union activity.