William (Bill) Arnsparger (December 16, 1926 – July 17, 2015) was an American college and professional football coach.
When Shula left to become head coach with the Miami Dolphins after the end of the 1969 NFL season, he brought along Arnsparger, who was promoted to defensive coordinator. In just two seasons, the formerly moribund team had reached the Super Bowl, with Arnsparger fashioning what became known as the "No-Name Defense." World championships in each of the next two seasons, including an undefeated season during 1972, made Arnsparger a prime candidate for a head coaching position.
Following the Dolphins' 24–7 victory over the Minnesota Vikings in Super Bowl VIII, Arnsparger was named head coach of the New York Giants. With the Giants he managed just seven wins in his thirty-five games. Arnsparger was fired in the middle of the season on October 25, 1976, with the team having lost all seven of its games on the year.
Just two days after his dismissal from the Giants, Arnsparger was rehired by Shula and was restored to his previous position as Miami's defensive coordinator while adding the title of assistant head coach. In the team's first game under his leadership, the Dolphins won a 10–3 defensive battle with the New England Patriots, who had averaged thirty points per game entering the contest.
Miami finished the 1976 NFL season with a 6–8 mark, then narrowly missed a playoff berth the following season. During the next two seasons, the Dolphins reached the postseason, but dropped their first playoff game. During the strike-shortened 1982 NFL season, Miami reached Super Bowl XVII, but dropped a 27–17 decision to the Washington Redskins. Bill Arnsparger again had created an elite defensive unit, known as the Killer B's (so named because of the number of surnames beginning with "B" on the Dolphins defense).