As teams take turns to attack the others goal line they use their own set of balls, so by gently under-inflating theirs New England made it easier to both grip and throw especially in cold rain which was falling that day.
What makes it more astonishing is that New England were favourites, and would surely have won anyways. They did and went on to take the prestigious Superbowl a month later.
So why risk it all with underhand tactics?
Listen to it all (just under 5 minutes).