Credible tests of hypotheses about power require credible measures of power. Roll rates purport to measure the power of the majority party in legislatures. This paper develops and employs a baseline model to assess roll rates. While on the surface roll rates have some intuitively satisfying properties, beneath the surface they have several previously unrecognized shortcomings. Analysis based on stochastic, strictly preference-based voting within parties suggests that inferences based on roll rates overstate party influence generally, and they exaggerate the influence of the majority party relative to the minority. Data from the U.S. House of Representatives are consistent with the fully nonpartisan model.