Constrained SUSY models like the CMSSM might look less attractive nowadays because of fine tuning arguments. They also might look less probable in terms of Bayesian statistics. The question how well the model under study describes the data, however, is answered by frequentist p-values. Thus, for the first time, we calculate p-values for the CMSSM by performing dedicated toy experiments. We combine constraints from low-energy and astrophysical observables, Higgs mass and rate measurements as well as the non-observation of new physics in searches for supersymmetry at the LHC. Using the framework Fittino, we perform global fits of the CMSSM to the toy data. In this way we also derive estimates of the allowed ranges of parameters and observables in this model. Results using the well-established profile likelihood technique are shown in comparison.