  In string theory with flux compactifications, anthropic selection for
structure formation from a discretuum of vacuum energy values provides at
present our only understanding of the tiny yet positive value of the
cosmological constant. We apply similar reasoning to a toy model of the
multiverse restricted to vacua with the MSSM as the low energy effective
theory. Here, one expects a statistical selection favoring large soft SUSY
breaking terms leading to a derived value of the weak scale in each pocket
universe (with appropriate electroweak symmetry breaking) which differs from
the weak scale as measured in our universe. In contrast, the SUSY preserving
\mu parameter is selected uniformly on a log scale as is consistent with the
distribution of SM fermion masses: this favors smaller values of \mu. An
anthropic selection of the weak scale to within a factor of a few of our
measured value -- in order to produce complex nuclei as we know them (atomic
principle) -- provides statistical predictions for Higgs and sparticle masses
in accord with LHC measurements. The statistical selection then more often
leads to (radiatively-driven) {\it natural} SUSY models over the Standard Model
or finely-tuned SUSY models such as mSUGRA/CMSSM, split, mini-split, spread,
high scale or PeV SUSY. The predicted Higgs and superparticle spectra might be
testable at HL-LHC via higgsino pair production but is certainly testable at
higher energy hadron colliders with \sqrt{s}~ 30-100 TeV.
