We contribute a novel, ball-histogram approach to DNA-binding propensity prediction of proteins. Unlike state-of-the-art methods based on constructing an ad-hoc set of features describing physicochemical properties of the proteins, the ball-histogram technique enables a systematic, Monte-Carlo exploration of the spatial distribution of amino acids complying with automatically selected properties. This exploration yields a model for the prediction of DNA binding propensity. We validate our method in prediction experiments, improving on state-of-the-art accuracies. Moreover, our method also provides interpretable features involving spatial distributions of selected amino acids.