Bill, the ratio you are seeking is (background
minus focusing distance) over background distance. The blur size is directly proportional to that,
all other things being equal.
For a camera perfectly focused on the background, blur is therefore zero (ignoring diffraction, aberrations, shaky hands, etc).
For a camera very close to a subject with a far background, the blur size starts to approach the aperture diameter and could even exceed it if we get into macro territory (m greater than 1).
As to Grahame's specific comparison,
I think that the only way to quantify the bokeh difference would be by ray-tracing through all the lens elements at their actual distances and thicknesses,
like here , and I certainly can't do that. My calc is only for a perfect thin lens.
HTH ...