A pressing statistical challenge in the field of mass spectrometry proteomics is how to assess whether a given software tool provides accurate error control. Each software tool for searching such data uses its own internally implemented methodology for reporting and controlling the error. Many of these software tools are closed source, with incompletely documented methodology, and the strategies for validating the error are inconsistent across tools. In this work, we identify three different methods for validating false discovery rate (FDR) control in use in the field, one of which is invalid, one of which can only provide a lower bound rather than an upper bound, and one of which is valid but under-powered. The result is that the field has a very poor understanding of how well we are doing with respect to FDR control, particularly for the analysis of data-independent acquisition (DIA) data. We therefore propose a theoretical formulation of entrapment experiments that allows us to rigorously characterize the behavior of the various entrapment methods. We also propose a more powerful method for evaluating FDR control, and we employ that method, along with other existing techniques, to characterize a variety of popular search tools. We empirically validate our entrapment analysis in the fairly well-understood DDA setup before applying it in the DIA setup. We find that none of the DIA search tools consistently controls the FDR at the peptide level, and the tools struggle particularly with analysis of single cell datasets.