Six months after Custer and his troops were outflanked and killed in the original battle between the Seventh Cavalry and the Indians, Felix Vinatieri was discharged from the Army. With an eye on pursuing his musical career, he and his wife settled in Yankton, S.D., where they raised eight children. Felix composed music, conducted an orchestra and traveled with various shows, including the Ringling Brothers and Barnum & Bailey circus, Karolevitz said. He died at age 57 in 1891 and was buried in Yankton, in the southeast corner of the state along the Missouri River.

Four generations and about 80 years later, Adam Vinatieri was born in Yankton. When he was 5, Adam's parents moved their four children to Rapid City, in western South Dakota, where Judy and Paul Vinatieri still live.

Sports, not music, was the focus of the family. ''We had the kids in everything -- soccer, basketball, football, wrestling, tennis, baseball,'' said Paul Vinatieri, who works for an insurance company. ''Keep them busy enough, and they can't get into any trouble. They're too tired.''

Adam Vinatieri was a letter winner in football, wrestling, soccer and track and field at Rapid City Central High School. Kim Nelson was his football coach. ''By the time he got to high school he was a very confident athlete,'' Nelson recalled. ''He was our kicker and punter and quarterback. He really wanted that leadership position and thrived under pressure.''

Nelson, a high school football coach for 23 years, admitted being surprised by Vinatieri's success in the National Football League, where he has been the Patriots' kicker for six years.

''Like a lot of kids, Adam told me, 'I want to play in the N.F.L. someday,' '' Nelson said. '' 'Well,' I said, 'You certainly have the ability if you stick with it.' I tell that to everybody.''

On Letterman's show, Vinatieri gave this humble version of his beginnings as a kicker: ''I started playing soccer when I was about 5 years old. And Pop Warner started in about fifth grade. And they said, 'Does anybody know how to kick?' And I said, 'Well, I play soccer so I'll try.' And we had a minitryout that day and I just happened to be the best kicker that day, and they said, 'You're our guy.' ''