
Tom Brady has the best chance of breaking Dan Marino's record. Photo from Flickr, tagged Attribution-ShareAlike 2.0 Generic (CC BY-SA 2.0).
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In 1984 Dan Marino, playing in just his second season, set the NFL single season passing record with 5,084 yards. Right now there are three NFL quarterbacks who are on pace to break that record. There is also a rookie quarterback that is not far off of the pace.
The Record Holder
Dan Marino, Miami Dolphins, 1984, 16 games, 5,084 yards, 317.75 yards/game (yds/gm) average.
The Challengers
Tom Brady, New England Patriots, 2011, 6 games played, 2,163 yards, 360.5 yds/gm, on pace for 5,768 yards.
Remaining Games: @Steelers, Giants, @Jets, Chiefs, @Eagles, Colts, @Redskins, @Broncos, Dolphins, Bills.
Drew Brees, New Orleans Saints, 2011, 7 games played, 2,477 yards, 353.9 yds/gm, on pace for 5,662 yards.
Remaining Games: @Rams, Bucs, @Falcons, Bye, Giants, Lions, @Titans, @Vikings, Falcons, Panthers.
Aaron Rodgers, Green Bay Packers, 2011, 7 games played, 2,372 yards, 338.9 yds/gm, on pace for 5,422 yards.
Remaining Games: Bye, @Chargers, Vikings, Bucs, @Lions, @Giants, Raiders, @Chiefs, Bears, Lions.
The Rookie - just off the pace
Cam Newton, Carolina Panthers, 2011, 7 games played, 2,103 yards, 300.4 yds/gm, on pace for 4,806 yards.
Remaining Games: Vikings, Bye, Titans, @Lions, @Colts, @Bucs, Falcons, @Texans, Bucs, @Saints.