Walls generally have studs that are 1.5" wide every 16", so more than 90% of points on a wall are not in front of a stud. You do need to punch a few inches away from the stud to account for the width of your hand and to get enough leverage to break the drywall, so maybe expand the width of the hand-break-zone from 1.5" to 8", and you've got around a 50% chance that punching a random spot on the wall avoids a stud.
> so more than 90% of points on a wall are not in front of a sud
That would depend on the wall length, no?
For example, a 1.5"-3" wall has 100% of points on a stud. Also many (most?) traditional residential constructed walls have end plates, at least one top plate, a bottom plate, fire blocking, support, kings, sisters, cripples, jacks, headers, etc.
Anyway, I think its probably safe to say more than 10% of the surface has wood or some other object behind it on many walls, and unlikely that you could "do the math on this" without surveying data.
The top and bottom plate are unlikely to get punched, as you're going to tend to punch towards the middle height wise. Fire blocking became required by code in maybe the 80s or definitely in the 90s; there's a lot of older housing that may not have it. Also, it seems like a lot of this punching or kicking of walls happens near doorways, you're going to tend not to punch the wall near the doorframe, and if you go in maybe one shoulderwidth, you're not likely to hit a stud.
Just felt like doing the math on that one.