How would filling with nitrogen do anything? The pressure is independent of the gas used for filling.
A regulation NFL football will fly farther when filled with helium as opposed to compressed air at regulation pressure (13 psi).
BUSTED
Under the same amount of impulse force under the same atmospheric conditions, balls filled with helium showed no significant difference from balls filled with compressed air. It was also shown that, under the same impulse, both types of balls had the same initial velocity; since the helium-filled balls have less mass than the air-filled ones, the helium-filled balls have less inertia in flight: in fact, they may perform worse than air-filled balls over larger distances.
Nitrogen has been proven to be less affected by temperature changes than just regular old compressed air. Racing teams have been using it for years. Now auto dealers are filling customer tires with it, too.
As an aside, when I helped a buddy in the pits with his open-wheeled sprint car (ran on asphalt, not dirt), we'd adjust the tire pressures right before the race. We'd also take pressure and surface temp readings as soon as he came back into the pits. There were always psi variances. We knew that the tires like a certain amount of pressure for optimum grip, so we started out with them a bit lower (been to long to recall actual numbers) than ideal, and as the car went round and round, they warmed up and went into that ideal range.
We could also tell if there were variations between races by checking end pressures/temps.
We eventually went to pressure-relieving valves that could be set at the maximum pressure you wanted to run, and would bleed air off over that pressure. We always had to add a bit of air prior to the next outing, simply because we knew they bled off during the race, and as they cooled between races, the pressure naturally dropped.
I guess there’s no reason to fill auto tires with nitrogen then.../s
To answer the question: “Stability of pressure in varying climates”. Just my take on it. They could even use their own ratio with other noble gases to detect tampering...if we’re now nitpicking on ball pressure in a multi-billion dollar so-called ‘sport’...