Previous LHC forecasts for the constrained minimal supersymmetric standard model (CMSSM), based on current astrophysical and laboratory measurements, have used priors that are flat in the parameter tan beta, while being constrained to postdict the central experimental value of MZ. We construct a different, new and more natural prior with a measure in mu and B (the more fundamental MSSM parameters from which tan beta and MZ are actually derived). We find that as a consequence this choice leads to a well defined fine-tuning measure in the parameter space. We investigate the effect of such on global CMSSM fits to indirect constraints, providing posterior probability distributions for Large Hadron Collider (LHC) sparticle production cross sections. The change in priors has a significant effect, strongly suppressing the pseudoscalar Higgs boson dark matter annihilation region, and diminishing the probable values of sparticle masses. We also show how to interpret fit information from a Markov Chain Monte Carlo in a frequentist fashion; namely by using the profile likelihood. Bayesian and frequentist interpretations of CMSSM fits are compared and contrasted.