Let S be a hyperbolic surface and f a pseudo-Anosov map on S. I will describe a result that predicts the number of fixed points of f, up to constants that depend only on the surface S. If f satisfies a mild condition called “strongly irreducible,” then the log of the number of fixed points of f is coarsely equal to the log of the dilatation. Without this mild condition, there is still a coarse formula. One application of our result is a relationship between the volume of a fibered hyperbolic 3-manifold and the rank of its Heegaard Floer homology. This is joint work with Tarik Aougab and Sam Taylor.