  The pion multiplicity distribution is widely believed to reflect the
statistical aspects of $\bar{p}p$ annihilation at rest. We try to reproduce it
in a grand canonical picture with explicit conservation of electric charge,
isospin, total angular momentum, and the parity quantum numbers $P$, $C$, and
$G$ via the projection operator formalism. Bose statistics is found to be
non-negligible, particularly in fixing the interaction volume. The calculated
pion multiplicity distribution for $\left\langle n_{\pi} \right\rangle = 5$
turns out to depend strongly on the conservation of the angular momentum and
connected quantum numbers, as well as on the spin state occupation in S-wave
annihilation. However, the empirical Gaussian pion multiplicity distribution
cannot be reproduced. This calls in question either the statistical ansatz or
the rather old data themselves.
