While web applications expand in usage and complexity, testing demands are growing without corresponding automated support. One promising approach to automatic test generation is statistical model-based testing, where logged user behavior is used to build a usage-based model of web application navigation, from which abstract test cases are generated. Executable test cases are then created by adding parameter values to the abstract test cases. Several researchers have proposed variations of this approach; however, no one has empirically examined the tradeoffs and implications of the different ways to represent user behavior in a navigation model and the characteristics of the automatically generated test cases from different models. We report on our exploratory study of automatically generated abstract test cases and the underlying usage-based navigation models constructed from over 3500 user sessions across five publicly deployed web applications. Our results suggest how web testers can easily tune statistical model-based automatic test case generators for web applications toward generating tests closely related to user behavior or toward new navigations without using large additional test resources.