In the ScrumMaster training, I include a diagram that has a simple idea: to map the areas of complexity in a problem based on two dimensions: Agreement and Certainty. This diagram is an adaptation of the diagram by Ralph Stacey found in this article called Aides for Complexity by Brenda Zimmerman. This diagram or model can be used to help us understand where and how agile methods can be applied.
In the simplest way possible, if we have both Agreement and Certainty on a problem, then an agile approach is probably applicable, but not necessary. As we move away from that bottom left quadrant of the model, the usefulness of an agile approach increases since agile methods promote learning, careful search, feedback mechanisms, multi-disciplinary work, etc. The top right quadrant, “Chaos” is, like the bottom left, a case of possibly useful, but not a guarantee of any success. So agile methods seem most suited for a broad sweep of the diagram starting from the upper left and going down to the bottom right. Like so: