Fencer
Not left-handed either
Yup, most of the math and science seems on point here except 40 degrees F = 282 Kelvin. That changes the final answer of the first part from 11.5 psi to near 11.9 psi. Making a change in pressure of 13-11.9 = 1.1 psi. Since in this case it changed almost twice that, even with rain, it is improbable that temperature was the cause unless they were aired up in a much hotter room than 70 degrees F, which I suppose is still possible.
Also, keep in mind they measured the Colts balls as well and none of them were under regulation pressure. By the same math, even if they were inflated to the maximum 13.5 psi, you would get 12.3 psi which is also under regulation. Thus, something must be a bit off here. It could be a few things, one the assumption that the balls are aired up at 70 degrees F is incorrect or Amontons' Law (described as Guy-Lussac's Law here-name has changed) is not applicable as the assumption that a football is a rigid is incorrect. My guess is it is a little of both but the main issue is likely that a football only becomes rigid and of fixed in volume, under pressure which is not what this law was designed for.
Still great work by the scientist that put this together. They showed their work very well and it was very easy to follow. It was also a great idea on how to evaluate this situation and its author should be commended for all that.
I think given what I posted here and the significance of the pressure difference, it is pretty obvious someone deflated the balls. That said, its going to be tough to prove who did it, especially if the balls were in anyone elses procession. The only ways I think you can say no one purposely deflated the balls is if during one of the measuring periods, a bad gauge was used on only the Pats balls or if initially they were simply passed and not measured.
In the future, this whole thing could be avoided by simply putting the refs in charge of the balls and both teams play with the same balls. If the idea is to create a level playing field, whats more level than both teams using the same ball?
If the volume doesn't change it doesn't change, so I don't see what your point is about the footballs not being all that rigid, and indeed changing volume under pressure changes that weren't present in this case.
I get the point about the Colts' starting pressure supposedly being no more than 1 PSI above the Patriots, yet the ending pressure after equal treatment supposedly had a 2 PSI difference. However, those figures have not been reliably reported. Even if they had, the difference could be explained by the Colts' and Patriots' balls having different internal temperatures at the time of initial measurement.
You're entitled to wonder how such a difference is possible unless the Patriots fairly carefully planned for it, and in that respect I'm indeed on the side of the Patriot-doubters. But the evidence that the Patriots did anything wrong EXCEPT scheme carefully about the temperature at which they inflated their footballs is quite thin indeed.