Sequence-specific interactions of transcription factors (TFs) with genomic DNA underlie many cellular processes. High-throughput in vitro binding assays coupled with machine learning have made it possible to accurately define such molecular recognition in a biophysically interpretable way for hundreds of TFs across many structural families, providing new avenues for predicting how the sequence preference of a TF is impacted by disease-associated mutations in its DNA binding domain. We developed a method based on a reference-free tetrahedral representation of variation in base preference within a given structural family that can be used to accurately predict the effect of mutations in the protein sequence of the TF. Using the basic helix-loop-helix (bHLH) and homeodomain families as test cases, our results demonstrate the feasibility of accurately predicting the shifts ({Delta}{Delta}{Delta}G/RT) in binding free energy associated with TF mutants by leveraging high-quality DNA binding models for sets of homologous wild-type TFs.