Ly α emission lines are typically found to be redshifted with respect to the systemic redshifts of galaxies, likely due to resonant scattering of Ly α photons. Here, we measure the average velocity offset for a sample of 96 z ≍ 3.3 Ly α emitters (LAEs) with a median Ly α flux (luminosity) of ${\approx}10^{-17}~\rm erg~cm^{-2}~s^{-1}$ ( ${\approx}10