Getting scientific on Deflategate!

The Patriots have been accused of intentionally under-inflating footballs in the AFC Championship game. Turns out there's a whole process of each team providing 12 game balls, 2 hours and 15 minutes before game time, which have to be between 12.5 and 13.5psi, and 14 and 15oz. Bla bla bla.

In the course of the game, an interception lead to the Colts sideline becoming suspicious of a ball and reporting that it didn't feel right. The ball was apparently measured at 2psi under the legal limit. Upon further investigation, 11 of the 12 Patriots' balls measured under the limit. The Patriots cheat! ... or do they?

While it's entirely possible that this was deliberate, there are many pieces of data missing that could completely alter the landscape. As background, the balls are inflated pre-game at room temperature. Tom Brady prefers the lower end of the legal limit so the Patriots' balls start 12.5psi. The game was played around freezing conditions. Pressure drops in enclosed volumes as temperature drops. So:

1. Does anyone ever audit ball pressure after a game?
Referees handle the balls every play, yet none of them found the balls suspicious. Maybe a drop of 1-2psi feels normal enough to them. Maybe this happens all the time, but no one has ever bothered calling for a verification.

2. Did anyone check the Colts' balls, and what was the change in their pressures?
Without this data point, we can't establish what the expected change is over the course of the game, for example due to "typical air loss" that may occur or as a result of the particular temperature changes that day. I have no idea how hard it is to make a football leak, but it can't be impossible. There are some pretty impressive collisions out there, and the ball gets in the middle of some of them.

3. Did any air escape as a result of measuring pressure?
Not sure what devices they're using, but every time I measure the pressure of something I cause some air to escape. In other words, measuring the pressure affects measurement. Downwards.

4. Were the reported measurements taken under the original inflation conditions?
If not, the pressure should be different. We'll get into some math later, but dropping from room temp to freezing is just about enough to cause a 2psi drop. If the measurements were taken right after game while the balls were still cold, they'd be invalid for comparison.

5. If the pressures were measured in freezing conditions, what should they be?
This is also interesting because it asks if the ball would be in an underinflated state and therefore someone might reasonably notice it. To answer this we'll turn to some gas laws and assumptions.
1. PV=nRT (we'll assume ideal gas and that footballs don't lose appreciable volume)
2. Initial pressure = 12.5psi
3. Atmospheric pressure = 14.7psi
4. Temperature at inflation ~= 20C...

To say that a ball is at 12.5psi means that it's at 12.5psi above atmospheric pressure (when completely "flat" or "0 psi", there's the same density/pressure of air inside as outside - we're measuring the net pressure). Thus, the actual pressure inside is about 27.2psi. Once outside for many hours in approximately 0C temperatures, we'd expect that the temperature of the ball and its contained gas has also fallen to 0C. Per ideal gas law [1] and the assumption that the volume of the football doesn't really change, the resulting pressure should be about 27.2psi * 273K / 293K = 25.3psi, which is a drop of about 1.9psi. Since the atmospheric pressure wouldn't change nearly as much, the measured loss of pressure of the football would be "approximately 2psi", which is exactly what sources are reporting.

While the last point is starting make its rounds on the internet, it's just one data point that needs to be collected. I've heard almost no mention of the other 4 points thus far (outside of the occasional forum comment); I'm curious what the details of the investigation will show. Of course if science is involved, everyone will ignore it and scream conspiracy or whatever.

Does the NFL need a science advisor?