I understand that, but couldn't you also say that it makes it harder to throw the ball long range?
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Also, what I don't understand: are these balls not checked before the game?
Checked 2 hours prior to the game. It would be very easy for someone to deflate balls on the sideline, seeing as teams wrap them in towels much of the time to stop them from being too slippery and cold when the offense gets back on the field. The argument is, that after the refs returned the balls to the Pats, somehow 11/12 balls were found to be 2 PSI (16%) lower than NFL rules at halftime. As opposed to the Colts balls which were still fully inflated. Assuming the reports coming out are correct.
Most teams don't throw the long ball much in those conditions. And the Pats offense specifically is mostly short passing, and crossing routes. A slightly deflated ball is perfect for that, as it is easier to catch a ball coming in at high speed if it is slightly deflated, and it's easier to grip and throw with accuracy for those short passes.
The biggest question is, why on earth would they knowingly break the rules, and alter the inflation of the ball if it wasn't desired by Tom Brady? Clearly they wouldn't, and clearly they thought it would provide an advantage. Did it, in this specific game? Not enough to matter. They crushed the Colts. But what if they did it against the Ravens the previous week? A 4 point game. That could have been the difference between receivers dropping a couple more passes, or Brady missing a couple more throws.