Liberties Stones Ratio
The liberties/stones ratio (LSR) is the number obtained by dividing the liberties of a group by the number of stones belonging to that group.
The LSR can serve as a measurement of flexibility and connection. The higher the LSR, 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 at all. A lower bound for this ratio is not really relevant, but it is a nice mathematical exercise.
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.
Dieter: The best value for this ratio would probably lie between 3 and 3.5 .