Multiplexed proteomics has emerged as a powerful tool to measure protein expression levels across multiple conditions. The relative protein abundances are inferred by comparing the signal generated by isobaric tags, which encode the samples origins. Intuitively, the trust associated with a protein measurement depends on the similarity of ratios from different peptides and the signal level of these measurements. Up to this point in the field, peptide-level information has not typically been integrated into confidence, and only the most likely results for relative protein abundances are reported. If confidence is reported, it is based on protein-level measurement agreement between replicates. Here we present a mathematically rigorous approach that integrates peptide intensities and peptide-measurement agreement into confidence intervals for protein ratios (BACIQ). The main advantages of BACIQ are: 1) it removes the need to threshold reported peptide signal based on an arbitrary cut-off, thereby reporting more measurements from a given experiment; 2) confidence can be assigned without replicates; 3) for repeated experiments BACIQ provides confidence intervals for the union, not the intersection, of quantified proteins; 4) for repeated experiments, BACIQ confidence intervals are more predictive than confidence intervals based on protein measurement agreement. Therefore, our method drastically increases the value obtained from quantitative proteomics experiments and will help researchers to interpret their data and prioritize resources. To make our approach easily accessible we distribute it via an R/Stan package.