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This paper introduces a random statistical scan over the high-energy initialparameter space of the minimal SUSY $B-L$ model--denoted as the $B-L$ MSSM.Each initial set of points is renormalization group evolved to the electroweakscale--being subjected, sequentially, to the requirement of radiative $B-L$ andelectroweak symmetry breaking, the present experimental lower bounds on the$B-L$ vector boson and sparticle masses, as well as the lightest neutral Higgsmass of $\sim$125 GeV. The subspace of initial parameters that satisfies allsuch constraints is presented, shown to be robust and to contain a wide rangeof different configurations of soft supersymmetry breaking masses. Thelow-energy predictions of each such "valid" point - such as the sparticle massspectrum and, in particular, the LSP - are computed and then statisticallyanalyzed over the full subspace of valid points. Finally, the amount offine-tuning required is quantified and compared to the MSSM computed using anidentical random scan. The $B-L$ MSSM is shown to generically require lessfine-tuning.

The Minimal SUSY $B-L$ Model: From the Unification Scale to the LHC