Liberties Stones Ratio
The ratio (liberties of a group)/(stones belonging to that group).
The higher the ratio, the more flexible the stones are, and also the more probable it is that they work efficiently. The lower the ratio, the surer their connection.
This ratio obviously has an upper bound at 4. At this value the stones aren't connected anymore.
A lower bound for this ratio is not really relevant, but it is a nice mathematical exercise.
The best value for this ratio would probably lie between 3 and 3.5 .
hotcoffee: is there any measurement to describe the number of liberties a shape has the potential to make (in one move)? Would it be useful to compare shapes this way, with a "potential liberties"/stones ratio?
A major drawback with this plan is that the liberties/stones ratio is simple, understandable and elegant, and a measurement involving looking ahead would not be.