Why Belichek's Science Adds Up
The change in absolute pressure is not from 12.5psi to 10.5psi, or 19%. It is from 12.5psi + the pressure of the atmosphere to 10.5 + atmosphere, or 8%. This difference is plausible given the weather conditions of the day. If the pressure was measured at 45 degrees F (280K) and 10.5psi, and inflated initially to 12.5psi, if no air was let out the initial temperature only has to be 280K*1.08=302K, or 84 degrees F. This is a plausible initial temp given that the ball had been rubbed vigorously in a 70F environment. Additionally, the act of measuring pressure itself is known to lose air; the more times the pressure was measured, the worse the estimates would have been.
Why Wouldn't the Colts' Balls, and the Pats' kicking ball, have been Underinflated?
There are several reasons this could be.
-Their initial pressure was closer to 13.5 than to 12.5
-They were not heated due to vigorous rubbing
-They were at a different temperature when they were measured
Results are consistent with this story:
http://www.thedailybeast.com/articles/2015/01/24/basic-physics-may-defeat-deflategate.html