A pressing problem for supersymmetry (SUSY) phenomenologists is how to incorporate Large Hadron Collider search results into parameter fits designed to measure or constrain the SUSY parameters. Owing to the computational expense of fully simulating lots of points in a generic SUSY space to aid the calculation of the likelihoods, the limits published by experimental collaborations are frequently interpreted in slices of reduced parameter spaces. For example, both ATLAS and CMS have presented results in the Constrained Minimal Supersymmetric Model (CMSSM) by fixing two of four parameters, and generating a coarse grid in the remaining two. We demonstrate that by generating a grid in the full space of the CMSSM, one can interpolate between the output of an LHC detector simulation using machine learning techniques, thus obtaining a superfast likelihood calculator for LHC-based SUSY parameter fits. We further investigate how much training data is required to obtain usable results, finding that approximately 2000 points are required in the CMSSM to get likelihood predictions to an accuracy of a few per cent. The techniques presented here provide a general approach for adding LHC event rate data to SUSY fitting algorithms, and can easily be used to explore other candidate physics models.