Tom Brady and the New England Patriots' run of three Super Bowl titles in four seasons has only been matched by the Dallas Cowboys in the early '90s. But since 2004, New England's only claim to fame is being the champions of the regular season.

On Sunday in Miami, they will attempt to secure their eighth AFC East championship in nine years. The only year they missed the playoffs was in 2008, when Brady suffered a season-ending knee injury in the first game of the season. But New England has no Super Bowl rings to show for...