The total, triplet, and pair contributions to the entropy with increasing tetrahedrality are mapped out for the Stillinger-Weber liquids to demonstrate the qualitative and quantitative differences between triplet-dominated, tetrahedral liquids and pair-dominated, simple liquids with regard to supercooling and crystallization. The heat capacity anomaly of tetrahedral liquids originates in local ordering due to both pair and triplet correlations. The results suggest that structural correlations can be directly related to thermodynamic anomalies, phase changes, and self-assembly in other atomic and colloidal fluids.