mRNA contexts containing a 'slippery' sequence and a downstream secondary structure element stall the progression of the ribosome along the mRNA and induce its movement into the -1 reading frame. In this study we build a thermodynamic model based on Bayesian statistics to explain how -1 programmed ribosome frameshifting can work. As training sets for the model, we measured frameshifting efficiencies on 64 dnaX mRNA sequence variants in vitro and also used 21 published in vivo efficiencies. With the obtained free-energy difference between mRNA-tRNA base pairs in the 0 and -1 frames, the frameshifting efficiency of a given sequence can be reproduced and predicted from the tRNA-mRNA base pairing in the two frames. Our results further explain how modifications in the tRNA anticodon modulate frameshifting and show how the ribosome tunes the strength of the base-pair interactions.