The resolution of four controversial topics in phylogenetic experimental design hinges upon the informativeness of characters about the historical relationships among taxa. These controversies regard the power of different classes of phylogenetic character, the relative utility of increased taxonomic versus character sampling, the differentiation between lack of phylogenetic signal and a historical rapid radiation, and the design of taxonomically broad phylogenetic studies optimized by taxonomically sparse genome-scale data. Quantification of the informativeness of characters for resolution of phylogenetic hypotheses during specified historical epochs is key to the resolution of these controversies. Here, such a measure of phylogenetic informativeness is formulated. The optimal rate of evolution of a character to resolve a dated four-taxon polytomy is derived. By scaling the asymptotic informativeness of a character evolving at a nonoptimal rate by the derived asymptotic optimum, and by normalizing so that net phylogenetic informativeness is equivalent for all rates when integrated across all of history, an informativeness profile across history is derived. Calculation of the informativeness per base pair allows estimation of the cost-effectiveness of character sampling. Calculation of the informativeness per million years allows comparison across historical radiations of the utility of a gene for the inference of rapid adaptive radiation. The theory is applied to profile the phylogenetic informativeness of the genes BRCA1, RAG1, GHR, and c-myc from a muroid rodent sequence data set. Bounded integrations of the phylogenetic profile of these genes over four epochs comprising the diversifications of the muroid rodents, the mammals, the lobe-limbed vertebrates, and the early metazoans demonstrate the differential power of these genes to resolve the branching order among ancestral lineages. This measure of phylogenetic informativeness yields a new kind of information for evaluation of phylogenetic experiments. It conveys the utility of the addition of characters a phylogenetic study and it provides a basis for deciding whether appropriate phylogenetic power has been applied to a polytomy that is proposed to be a rapid radiation. Moreover, it provides a quantitative measure of the capacity of a gene to resolve soft polytomies.