Conjugated organic polymers have substantial potential for multiple applications but their properties are strongly influenced by structural defects such as homocoupling of monomer units and unexpected end-groups. Detecting and/or quantifying these defects requires complex experimental techniques, which hinder the optimization of synthesis protocols and fundamental studies on the influence of structural defects. Mass spectrometry offers a simple way to detect these defects but a manual analysis of many complex spectra is tedious and provides only approximate results. In this work, we develop a computational methodology for analyzing complex mass spectra of organic copolymers. Our method annotates spectra similarly to a human expert and provides quantitative information about the proportions of signal assigned to each ion. Our method is based on the open-source Masserstein algorithm, which we modify to handle large libraries of reference spectra required for annotating complex mass spectra of polymers. We develop a statistical methodology to analyze the quantitative annotations and compare the statistical distributions of structural defects in polymer chains between samples. We apply this methodology to analyze commercial and lab-made samples of a benchmark polymer and show that the samples differ both in the amount and in the types of structural defects.