Dexterity is a central yet ambiguously defined concept in the design and evaluation of anthropomorphic robotic hands. In practice, the term is often used inconsistently, with different systems evaluated under disparate criteria, making meaningful comparisons across designs difficult. This highlights the need for a unified, performance-based definition of dexterity grounded in measurable outcomes rather than proxy metrics. In this work, we introduce POMDAR, a comprehensive dexterity benchmark that formalizes dexterity as task performance across a structured set of manipulation and grasping motions. The benchmark was systematically derived from established taxonomies in human motor control. It is implemented in both real-world and simulation and includes four manipulation configurations: vertical and horizontal configurations, continuous rotation, and pure grasping. The task designs contain mechanical scaffolding to constrain task motion, suppress compensatory strategies, and enable metrics to be measured unambiguously. We define a quantitative scoring metric combining task correctness and execution speed, effectively measuring dexterity as throughput. This enables objective, reproducible, and interpretable evaluation across different hand designs. POMDAR provides an open-source, standardized, and taxonomy-grounded benchmark for consistent comparison and evaluation of anthropomorphic robot hands to facilitate a systematic advancement of dexterous manipulation platforms. CAD, simulation files, and evaluation videos are publicly available at https://srl-ethz.github.io/POMDAR/.