Missing values weaken the power of label-free quantitative proteomic experiments to uncover true quantitative differences between biological samples or experimental conditions. Match-between-runs (MBR) has become a common approach to mitigate the missing value problem, where peptides identified by tandem mass spectra in one run are transferred to another by inference based on m/z, charge state, retention time, and ion mobility when applicable. Though tolerances are used to ensure such transferred identifications are reasonably located and meet certain quality thresholds, little work has been done to evaluate the statistical confidence of MBR. Here, we present a mixture model-based approach to estimate the false discovery rate (FDR) of peptide and protein identification transfer, which we implement in the label-free quantification tool IonQuant. Using several benchmarking datasets generated on both Orbitrap and timsTOF mass spectrometers, we demonstrate that IonQuant with FDR-controlled MBR results in superior performance compared to MaxQuant. We further illustrate the need for FDR-controlled MBR in sparse datasets such as those from single-cell proteomics experiments.