Significance One-tenth of human genes produce proteins called transcription factors (TFs) that bind to our genome and read the local DNA sequence. They work together to regulate the degree to which each gene is expressed. The affinity with which DNA is bound by a particular TF can vary more than a thousand-fold with different DNA sequences. This study presents the first computational method able to quantify the sequence-affinity relationship almost perfectly over the full affinity range. It achieves this by analyzing data from experiments that use massively parallel DNA sequencing to comprehensively probe protein–DNA interactions. Strikingly, it can accurately predict the effect in vivo of DNA mutations on gene expression levels in fly embryos even for very-low-affinity binding sites.