  Let $S(t) =
\frac{1}{\pi}\operatorname{Im}\log\zeta\left(\frac{1}{2}+it\right)$. Using
Soundararajan's resonance method we prove an unconditional lower bound on the
size of the tails of the distribution of $S(t)$. In particular we reproduce the
best unconditional $\Omega$ result for $S(t)$ which is due to Tsang, \[ S(t) =
\Omega_\pm\left(\left(\frac{\log t}{\log \log t}\right)^{1/3}\right), \] and
get a bound on how often large values of $S(t)$ occur. We also give a
probabilistic argument for why this $\Omega$ result may be the best possible
given our current knowledge of the zeros of the zeta function.
