The affine stratification number of a variety is a measure of how far a variety is from being affine and how close it is to being projective. I shall talk about a certain filtration on the moduli space of curves and the affine stratification number of the open sets occurring in the filtration. This will lead to some cohomology computations where we shall make use of the natural operad structure on the homology of the moduli spaces as well as the some mixed hodge theory.