Direction-of-arrival (DoA) estimation of a speaker in a room using microphone arrays is an important task in audio signal processing in general, and robot audition in particular. Recently, a novel DoA estimation method developed for spherical arrays presented accurate performance even under real-world conditions with strong reverberation. The method identifies time-frequency bins dominated by the direct signal from the source, and employs only these bins for DoA estimation. A recent extension allowed the use of shorter time frames by employing Gaussian mixture model based clustering to the DoA statistics. However, performance still degrades under challenging acoustical conditions, such as close to a reflecting surface. In this paper, a novel analysis is presented that provides insight into the acoustic significance of the individual Gaussians in the mixture, clearly showing the distinctiveness of the Gaussian corresponding to the direct path signal. The results presented here can be employed in the design of acoustically robust DoA estimation under strong reverberation.