Modern DNA sequencing methods produce vast amounts of data that often requires mapping to a reference genome. Most existing programs use the number of mismatches between the read and the genome as a measure of quality. This approach is without a statistical foundation and can for some data types result in many wrongly mapped reads. Here we present a probabilistic mapping method based on position-specific scoring matrices, which can take into account not only the quality scores of the reads but also user-specified models of evolution and data-specific biases.