% of overlap between region and circle model of same region

There is quite a difference in the simple model. I'm sure it's not as bad as with BBs, but in the regions I have selected there can be as low as 23% overlap. You can see why when looking at Abercanaid/Troedyrhiw shown here. The smaller the region the worse this effect is (settlements are "odder" shapes than counties?).
The flattening of the circle is due to some sort of datum/projection problem, there have been lots of conversions to get this graphic (this prob due to the cration of the tif, and the space it takes not being square, while the tif is square). It has no effect on the ratio of overlap area to polygon/circle area.

GIS

Note to self: when thinking about "just quickly doing x, using GIS" think a bit harder. The conversion routines such as gdal and ogr can seem simple and then turn out to be quite hard to deal with. EG gdal_rasterize does not actually create a tif file, you have to do it yourself first, and it has to be for the right area of the earth, the right size (granularity) with the right bands etc etc. What might initially seem easy can often not be and involve you in projections, and datums.

struggling with obtuse GIS conversion programs

Norm factor

this is what it is normalised by. the orange spike is just due to only having 7 items I guess.

normed on new regions

Normed by the underlying distribution. Smoothed by 21 point MA. The strange spike has gone as all the small places are now randomly selected,rather than just using all SNIS.

Calculating the area of the intersection of a polygon and a circle of the same area

How hard could that be? Quite hard it seems!

region selection

I am reselecting the regions to use for these tests. I now randomly select from the population within each band up to a maximum. Some bands have only a few members, in which case I end up selecting them all in that band.