Credible tests of hypotheses about power require credible measures of power. Roll rates purport to measure the relative power of the parties in legislatures. This article develops and employs a baseline model to assess roll rates. Although 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-governed voting within nominal but behaviorally inconsequential parties suggests that inferences based on roll rates overstate party influence and exaggerate the influence of the majority party relative to the minority. Analysis of data from the U.S. House of Representatives produces findings consistent with the nonpartisan model.