You know what they say, In Theory, there is no difference between theory and reality. But in Reality, there is.
For the Ideal gas law to apply, wouldn't the football have to be inflated entirely with 1 type of gas? I wasn't aware they did that. I bet the pats use Helium.
The Ideal Gas Law I remember used Degrees Kelvin, and Bars. Not Fahrenheit and PSI.
I don't know where that 460 came from, maybe it was an attempt to convert to Kelvin, but the conversion is not that simple.
I'm not sure 14.7 PSI is an accurate atmospheric pressure. It's probably close, but why not look up the weather reports and use the real number instead of just 1 atmosphere?
And finally, I'm not sure it's a valid assumption to say the volume is remaining constant. Footballs are kinda pliable.