Abstract: Take your favorite classification problem in mathematics -- isomorphism of graphs, homeomorphism of topological spaces, or conjugacy of measure preserving transformations -- and most likely it can be modeled as the orbit equivalence relation of a Polish group acting on a Polish space. By using the tools of invariant descriptive set theory, we can measure the complexity of this orbit equivalence relation and conclude meaningful things about what kind of solution one can expect, if any, to the corresponding classification problem. One such measure of complexity is potential Borel complexity. We will develop the theory of this notion, and show how one can find elementary proofs of lower bound results using ideas of the Scott analysis and its generalization by Hjorth.