This calculator uses the ideal gas law to compute the change in internal pressure of a football as it is taken from an initial temperature (e.g. inside a referee's locker room) to a final temperature (e.g. on a football field). The defaults are my best guess for what might be realistic values.
The formula used in the calculator is Pf=Pi*Tf/Ti where T and P are absolute temperature and absolute pressure. It is a very common error to forget to add atmospheric pressure to gauge pressure to obtain absolute pressure. The calculator does this for you automatically.
(a) Volume change: This assumes that the volume of the football did not change significantly due to the change in pressure. The leather case of the football probably stretches slightly when it get wet, this would increase the volume and result in a further reduction of the pressure. This effect is very difficult to estimate as it depends on the detailed properties of the leather used.
(b) Temperature equilibration with environment: It also assumes that that the temperature of the air in the football has time to equilibrate with the temperature of the environment. A reader of this page told me that he experimentally found this to take about 30 minutes (by sticking the ball in a fridge and monitoring the pressure change in the ball). Immediately after inflation the temperature inside the football can be higher or lower than room temperature, depending on how it was inflated. Wet balls are slightly cooler than dry balls due to evaporative cooling. This is a negligible effect if the air of the environment is very humid (as it was).
(c) Barometric pressure - the weather: It also ignores the effects of the barometric pressure change that night in Foxboro. This only has a very small effect which would have increased the measured ball pressure at half time. I have calculated this additional change to be about +0.05 PSI (see plot created with local barometric pressure data provided by Bob Hayes).
(d) Humidity: The calculator also assumes that the air in the football is dry. Humid air could lead to a further reduction in the pressure as the ball cools down because condensation of water inside the ball would remove gas from the football. This effect can be bounded by 0.3 PSI (this is what I get if I assume that the air was 100% humid at 75F and all of the water condenses out), but it is negligible if highy compressed and dry air was used for inflating the balls (as opposed to a hand pump which does inflate with moist air).