  String theory realisations of the QCD axion are often said to belong to the
anthropic window where the decay constant is around the GUT scale and the
initial misalignment angle has to be tuned close to zero. In this paper we
revisit this statement by studying the statistics of axion physics in the
string landscape. We take moduli stabilisation properly into account since the
stabilisation of the saxions is crucial to determine the physical properties of
the corresponding axionic partners. We focus on the model-independent case of
closed string axions in type IIB flux compactifications and find that their
decay constants and mass spectrum feature a logarithmic, instead of a
power-law, distribution. In the regime where the effective field theory is
under control, most of these closed string axions are ultra-light axion-like
particles, while axions associated to blow-up modes can naturally play the role
of the QCD axion. Hence, the number of type IIB flux vacua with a closed string
QCD axion with an intermediate scale decay constant and a natural value of the
misalignment angle is only logarithmically suppressed. In a recent paper we
found that this correlates also with a logarithmic distribution of the
supersymmetry breaking scale, providing the intriguing indication that most, if
not all, of the phenomenologically interesting quantities in the string
landscape might feature a logarithmic distribution.
