  The Higgs boson discovery stirred interest in next-to-minimal supersymmetric
models, due to the apparent fine-tuning required to accommodate it in minimal
theories. To assess their naturalness, we compare fine-tuning in a
$\mathbb{Z}_3$ conserving semi-constrained Next-to-Minimal Supersymmetric
Standard Model (NMSSM) to the constrained MSSM (CMSSM). We contrast popular
fine-tuning measures with naturalness priors, which automatically appear in
statistical measures of the plausibility that a given model reproduces the weak
scale. Our comparison shows that naturalness priors provide valuable insight
into the hierarchy problem and rigorously ground naturalness in Bayesian
statistics. For the CMSSM and semi-constrained NMSSM we demonstrate qualitative
agreement between naturalness priors and popular fine tuning measures. Thus, we
give a clear plausibility argument that favours relatively light superpartners.
