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Millimeter-wave (mmWave) communication systems require narrow beams to increase communication range. If the dominant communication direction is blocked by an obstacle, an alternative and reliable spatial communication path should be quickly identified to maintain connectivity. In this paper, we introduce a new metric to quantify the effective multipath richness (EMR) of a directional communication channel by considering the strength and spatial diversity of the resolved paths, while also taking into account beamwidth and blockage characteristics. The metric is defined as a weighted sum of the number of multipath component (MPC) clusters, where clustering is performed based on the cosine-distance between the MPCs that have power above a certain threshold. This process returns a single scalar value for a transmitter (TX)/receiver (RX) location pair in a given environment. It is also possible to represent the EMR of the whole environment with a probability distribution function of the metric by considering a set of TX/RX locations. Using this proposed metric, one can assess the scattering richness of different communication environments to achieve a particular quality of service (QoS). This metric is especially informative and useful at higher frequencies, such as mmWave and terahertz (THz), where the propagation path loss and penetration loss are high, and directional non-light-of-sight (NLOS) communication is critical for the success of the network. We evaluate the proposed metric using our channel measurements at 28 GHz in a large indoor environment at a library setting for LOS and NLOS scenarios.