  In this work, we present a new technique to measure the longitudinal and
transverse polarization fractions of hadronic decays of boosted $W$ bosons. We
introduce a new jet substructure observable denoted as $p_\theta$, which is a
proxy for the parton level decay polar angle of the $W$ boson in its
rest-frame. We show that the distribution of this observable is sensitive to
the polarization of $W$ bosons and can therefore be used to reconstruct the $W$
polarization in a model-independent way. As a test case, we study the efficacy
of our technique on vector boson scattering processes at the high luminosity
Large Hadron Collider and we find that our technique can determine the
longitudinal polarization fraction to within $\pm 0.15$. We also show that our
technique can be used to identify the parity of beyond Standard Model scalar or
pseudo-scalar resonances decaying to $W$ bosons with just 20 events.
