Liberties Stones Ratio

Definition

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.

Examples

Simple connections  

One stone has a LSR of 4. A chain of two stones has LSR 3. A chain of three stones has LSR 2.66

The empty triangle  

The empty triangle has LSR 2.33

Other basic shapes  

The one space jump has LSR 3.5 . The keima has LSR 4. The diagonal has LSR 3.

Comments

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 .