Premise of the Study—Phylogenetic support has been difficult to evaluate within the green plant tree of life partly due to a lack of specificity between conflicted versus poorly informed branches. As datasets continue to expand in both breadth and depth, new support measures are needed that are more efficient and informative. Methods— We describe the Quartet Sampling (QS) method, a quartet-based evaluation system that synthesizes several phylogenetic and genomic analytical approaches. QS characterizes discordance in large-sparse and genome-wide datasets, overcoming issues of alignment sparsity and distinguishing strong conflict from weak support. We test QS with simulations and recent plant phylogenies inferred from variously sized datasets. Key Results— QS scores demonstrate convergence with increasing replicates and are not strongly affected by branch depth. Patterns of QS support from different phylogenies lead to a coherent understanding of ancestral branches defining key disagreements, including the relationships of Ginkgo to cycads, magnoliids to monocots and eudicots, and mosses to liverworts. The relationships of ANA grade angiosperms, major monocot groups, bryophytes, and fern families are likely highly discordant in their evolutionary histories, rather than poorly informed. QS can also detect discordance due to introgression in phylogenomic data. Conclusions— Quartet Sampling is an efficient synthesis of phylogenetic tests that offers more comprehensive and specific information on branch support than conventional measures. The QS method corroborates growing evidence that phylogenomic investigations that incorporate discordance testing are warranted when reconstructing complex evolutionary histories, in particular those surrounding ANA grade angiosperms, monocots, and non-vascular plants.