The rational design of heterogeneous catalysts relies on the efficient survey of mechanisms by density functional theory (DFT). However, massive reaction networks cannot be sampled effectively as they grow exponentially with the size of reactants. Here we present a statistical principal component analysis and regression applied to the DFT thermochemical data of 71 C1–C2 species on 12 close-packed metal surfaces. Adsorption is controlled by covalent (d-band center) and ionic terms (reduction potential), modulated by conjugation and conformational contributions. All formation energies can be reproduced from only three key intermediates (predictors) calculated with DFT. The results agree with accurate experimental measurements having error bars comparable to those of DFT. The procedure can be extended to single-atom and near-surface alloys reducing the number of explicit DFT calculation needed by a factor of 20, thus paving the way for a rapid and accurate survey of whole reaction networks on multimetallic surfaces.