Transcription factors play a crucial role in gene regulation by binding to specific regulatory sequences. The sequence motifs recognized by a transcription factor can be described in terms of position frequency matrices. When scanning a sequence for matches to a position frequency matrix, one needs to determine a cut-off, which then in turn results in a certain number of hits. In this paper we describe how to compute the distribution of match scores and of the number of motif hits, which are the prerequisites to perform motif hit enrichment analysis.