[How beloved is Tom Brady in New England?]

Smith wasn’t the only unexpected hero of the 2002 Super Bowl. David Patten, a former Arena Football League player who spent four mostly mediocre seasons with two other N.F.L. teams before joining New England, scored the team’s only offensive touchdown in the game when he faked and slipped behind a defender for an 8-yard reception in the end zone that put the Patriots ahead by 11 points.

Patten made 165 catches for the Patriots over four seasons, and 15 more in the playoffs.

Fast forward to the next Patriots Super Bowl victory, in 2004. Wide receiver David Givens was not a reject from another N.F.L. team; he came to the Patriots as the 253rd overall pick of the 2002 draft, taken in the seventh round. He played very little in his first two seasons, catching just 43 passes. But in the 2004 Super Bowl against the Carolina Panthers, Givens emerged from the shadows to make a 5-yard touchdown reception that gave New England a 14-7 lead just before halftime.

Givens had five catches for 69 yards in the game, none more important than an 18-yard reception on third-and-9 that put his team 3 yards from the end zone. It set up the Patriots’ final touchdown, with less than three minutes left.

The litany of Patriots who were shrewdly lured from other teams and then became Super Bowl heroes includes Corey Dillon, who was one of the best running backs in the N.F.L. for six years, until his production for the Cincinnati Bengals dropped precipitously in 2003.

Dillon’s career seemed in jeopardy as he approached his 30th birthday, and then the Patriots traded for him before the 2004 season. Dillon had the best season of his career and led all rushers in the 2005 Super Bowl. He scored a touchdown and ran for 9 key yards in the Patriots’ final scoring drive in a 24-21 victory over the Philadelphia Eagles.

In 2015, the surprise performer was Malcolm Butler, an undrafted, reserve rookie cornerback whose goal-line interception averted certain defeat against the Seattle Seahawks.