CRISPR screens are powerful tools to identify key genes that underlie biological processes. One important type of screen uses fluorescence activated cell sorting (FACS) to sort perturbed cells into bins based on the expression level of marker genes, followed by guide RNA (gRNA) sequencing. Analysis of these data presents several statistical challenges due to multiple factors including the discrete nature of the bins and typically small numbers of replicate experiments. To address these challenges, we developed a robust and powerful Bayesian random effects model and software package called Waterbear. Furthermore, we used Waterbear to explore how various experimental design parameters affect statistical power to establish principled guidelines for future screens. Finally, we experimentally validated our experimental design model findings that, when using Waterbear for analysis, high power is maintained even at low cell coverage and a high multiplicity of infection. We anticipate that Waterbear will be of broad utility for analyzing FACS-based CRISPR screens.