  We compare the diversity of spectral line velocities in a large sample of
type IIb supernovae (SNe IIb) with the expected asphericity in the explosion,
as measured from the light echoes of Cassiopeia A (Cas A), which was a
historical galactic SN IIb. We revisit the results of Rest et al. (2011a), who
used light echoes to observe Cas A from multiple lines of sight and hence
determine its asphericity, as seen in the velocity of three spectral lines (He
I $\lambda$5876, H$\alpha$ and the Ca II NIR triplet). We confirm and improve
on this measurement by reproducing the effect of the light echoes in the
spectra of several extragalactic SNe IIb found in the literature as well as
mean SN IIb spectra recently created by Liu et al. (2016), and comparing these
to the observed light echo spectra of Cas A, including their associated
uncertainties. In order to quantify the accuracy of this comparison we smooth
the light echo spectra of Cas A using Gaussian processes and use a Monte Carlo
method to measure the absorption velocities of these three features in the
spectra. We then test the hypothesis that the diversity of ejecta velocities
seen in SNe IIb can be explained by asphericity. We do this by comparing the
range of velocities seen in the different light echoes, and hence different
lines of sight, of Cas A to that seen in the population of SNe IIb. We conclude
that these two ranges are of the same order and thus asphericity could be
enough to explain the diversity in the expansion velocity alone.
