From the Empire State building?
Would it survive the fall, or would it pop?
Is there a formula to figure it out?
MtM
Basketball!!! Not Besketball!!! DAMN!!!
MtM
My basketball would not bounce very high at all.
But then, it’s flat.
If you can find the coefficient of restitution of a properly inflated basketball on pavement, square that and multiply it by the height of the initial drop, you should have the height it will bounce up on the first bounce.
aktep’s suggestion assumes that there’s no air resistance as the ball falls. I’d imagine it’s quite likely that the ball will reach terminal velocity falling from that height.
So what we need to do is find the terminal velocity of a basket ball, and it’s coefficient of restitution.
Then calculate from what height the basketball would need to fall in a vacuum to reach the above velocity, and multiply that by the coefficient of restitution squared.
This assumes that air resistance on the way back up has minimal effect.
As far as survival, I assume that we can probably work out from experimentation the maximum force of impact that a basketball can survive without compromising its overall structure… (can’t really see any way of doing this without killing some.)
We can get terminal velocity, as per Fromage’s post, and the weight of the basketball. Assuming (was a WAG) that the stopping distance is somewhere in the vicinity of a sixth of the diameter of the ball, that would give us the force of impact. If that is greater than the force that the ball can survive, then the ball ‘pops’.
When I was a kid, our family belonged to an Athletic Club that had a building downtown. The building had stairs with a large opening in the middle. From 20 floors up, easily enough to reach terminal velocity, the ball would generally bounce up only three floors or so. They wouldn’t pop, but from how loud it was I can guarantee that there was at least some major compression.
They hated us there.
Some modeling issues
[BB physical & compression specs here](The Evolution of Basketballs)
…And I just thought you were Jewish. 
For a minute there, I thought you were Jackie Mason.
Oh, right – real-world physics. Not that everything-in-a-vacuum physics I learned in 10th grade.