The first thing that came to my mind when i read that phrase was that whatever this "script" is, it must be a pretty awesome piece of work.
It is called an analysis because you are “analyzing” the meaning of “Ring Around the Rosy.”
If im on the right track then a way to right it with dashes would be: Sacrificing her was a mistake-a mistake that could have been avoided. but i may not have understood the question??