I’ve dusted off today a long-lost engineering degree from what seems like five lifetimes ago to explain how air pressure drops when the temperature does.
The concept is known as the ideal gas law. PV equals nRT. The “P” is pressure. The “T” is temperature. If the “V” (volume) the “n” (amount of gas, in “moles”) and the “R” (the “ideal gas constant,” which is sort of like pi) remain the same, a drop in temperature necessarily results in a drop in pressure.
The folks at SportsScience addressed this issue in 2010. A ball exposed to 10-degree temperatures for an hour, the pressure drops from 13.5 PSI to 11 PSI.
Of course, that doesn’t fully account for a drop from 12.5 PSI to 10.5 PSI in 51-degree weather for 90 minutes or so. But it proves that, when it’s cold, the pressure inside a football drops.
In this specific situation, it could be that some pressure was removed from the balls, and that the 51-degree temperature did the rest. Regardless, when the mercury drops, footballs naturally deflate, at least a little.