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.
That makes sense scientifically. The difference in weight for a helium filled ball vs an air filled one (assuming 13 psi) is roughly 2 grams per liter of volume. Assuming an NFL ball is roughly one liter in volume (just a rough estimate, but probably not too far off) that means that the weight of a helium filled ball it 2 grams lower than that of an air filled ball. The only other factor is buoyancy, which is dependent on the denisty of the ball. Increased buoyancy would tend to lead to longer distances travelled (the buoyant force would oppose gravity). The density of the helium filled ball would be slightly lower, but it’s negligible so the increase in buoyancy would also be negligible, which is right in line with what Mythbusters found.