For those of you who aren't keeping up with the up to the minute minutae of the New England Patriots (American football team) scandal (presumably because you have lives), head coach Bill Belichick gave a press conference a few hours ago where he provided a hypothesis of what might have happened: as many people know, quarterbacks like their game footballs prepared in specific (sometimes elaborate [0]) ways prior to use in games. Belichick says that the team went over the process they use for games a few days ago and they determine that the preparation process they use for their footballs (which he claims they do right up to the point they are given to officials for pre-game testing) increases the air pressure in the balls by about 1 psi [1]. Therefore, the balls appear legal when tested by officials, but after a few hours of sitting around, the pressure reduces to below the legal limit. He doesn't specify the process used by the team, but presumably it's some kind of rubbing that heats the ball up, and when it cools down the interior air pressure is reduced accordingly.

I'm sure someone will test this out and verify or discredit the claim.

[0] http://www.nytimes.com/2013/11/24/sports/football/eli-mannin...

[1] http://www.boston.com/sports/football/patriots/extra_points/...