  The $\tau$ polarization in semileptonic $B$ decays provides probes of new
physics complementary to decay rate distributions of the three-body final
state. Prior calculations for inclusive decays used a definition for the
polarization axis that is different from the choice used in calculations (and
the only measurement) for exclusive channels. To compare inclusive and
exclusive predictions, we calculate the $\tau$ polarization in inclusive $B\to
X\tau\bar\nu$ using the same choice as in the exclusive decays, and construct a
sum rule relating the inclusive $\tau$ polarization to a weighted sum of
exclusive decay polarizations. We use this relation, experimental data, and
theoretical predictions for the decays to the lightest charm or up-type hadrons
to make predictions for excited channels.
