Physics of anti-roll bars

[sosidge]

Can somebody with a bigger brain and more education than me clarify the physics behind our bent wire anti-roll bars.

I'm pretty certain that the straight centre section of the bar is stiffer if of greater diameter and/or shorter length.

But the bit that has me confused is the effect of the mounting position on the arm and the length of the "lever" part of the bar. Is it cancelled out by the mountings being identical on both sides of the car? Or is the effect cumulative on both sides?