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Maybe we look at the ratio of country perimeter to area? Counting the number of exclaves could also be a factor. And maybe a ratio of the distance to cover all the exclaves divided by their area?
So if a country were a perfect circle it's perimeter to area ratio would be 2/r, it has zero exclaves and then it's width would be the diameter.
If a country were two perfect circles of the same diameter, separated by a distance of the same diameter, it's area ratio would be 2/r, exclaves would be one, and it's width would be three times it's diameter.
So now you can imagine a country like Chile, modeled as a really skinny rectangle, has a pretty large perimeter to area ratio, no exclaves, and a width roughly the length of the rectangle.
I guess you'd have to decide if archipelago nations are measured as the geometry of the sea they own, or as discrete islands.
I would do perimeter^2/area, to avoid biasing toward small countries. Divide one circular country into two circles with the same total area and p^2/A goes from 4 pi to 8 pi. Divide a square country in two and p^2/A goes from 4 to 6.
I did this all in my head. I think you are right. Point being, small simple algebraic expressions stacked as a a polynomial can be used to create relative scores for this type of analysis.
Thanks for the proposal. That gets us somewhere already, although only for non-landlocked countries. Using the perimeter also opens us up to the coastline paradox.
I think that it might serve us better to consider them as distinct islands, to keep the measures comparable with landlocked countries.
Will you use the sea borders instead of the coastline to avoid the paradox?
You didn't really mention how this is all being tabulated. Just in theory? Do you have access to data sets or are you making them? The coastline paradox only really exists for smaller and smaller measuring devices. If for example your method is using satellite images of a given resolution, or another consistent measuring tool, the measurements should be comparable between country borders and therefore the error or the paradox should come out in the wash.
I would imagine using some sort of shapefile that I can run calculations in a scripted manner. So, in that case it will depend on the resolution of the shapefile.