Given a diffeomorphism of the disk that preserves the standard symplectic form, I will introduce the asymptotic action associated to this map. I will then show a pointwise formula relating the asymptotic action to the asymptotic winding number of pairs of points. As a corollary one obtains a new proof for a well known result by A. Fathi which gives a formula for the Calabi invariant of a disk map in terms of its mean winding numbers. Additionally this formula can be used to study symplectic dynamical information for irrational pseudo-rotations of the disk. This talk includes joint work with Patrice Le Calvez and Abror Pirnapasov.