Statistical sequence comparison techniques, such as hidden Markov models and generalized profiles, calculate the probability that a sequence was generated by a given model. Log-odds scoring is a means of evaluating this probability by comparing it to a null hypothesis, usually a simpler statistical model intended to represent the universe of sequences as a whole, rather than the group of interest. Such scoring leads to two immediate questions: what should the null model be, and what threshold of log-odds score should be deemed a match to the model.This paper analyses these two issues experimentally. Within the context of the Sequence Alignment and Modeling software suite (SAM), we consider a variety of null models and suitable thresholds. Additionally, we consider HMMer's log-odds scoring and SAM's original Z-scoring method. Among the null model choices, a simple looping null model that emits characters according to the geometric mean of the character probabilities in the columns modeled by the hidden Markov model (HMM) performs well or best across all four discrimination experiments.