  Standard video encoders developed for conventional narrow field-of-view video
are widely applied to 360{\deg} video as well, with reasonable results.
However, while this approach commits arbitrarily to a projection of the
spherical frames, we observe that some orientations of a 360{\deg} video, once
projected, are more compressible than others. We introduce an approach to
predict the sphere rotation that will yield the maximal compression rate. Given
video clips in their original encoding, a convolutional neural network learns
the association between a clip's visual content and its compressibility at
different rotations of a cubemap projection. Given a novel video, our
learning-based approach efficiently infers the most compressible direction in
one shot, without repeated rendering and compression of the source video. We
validate our idea on thousands of video clips and multiple popular video
codecs. The results show that this untapped dimension of 360{\deg} compression
has substantial potential--"good" rotations are typically 8-10% more
compressible than bad ones, and our learning approach can predict them reliably
82% of the time.
