We study ensembles of 1/2-BPS bound states of fundamental strings and NS-fivebranes (NS5-F1) in the decoupling limit. We revisit a solution corresponding to an ensemble average of these bound states, and find that the appropriate duality frame for describing the near-source structure is the T-dual NS5-P frame.
When members of the ensemble spin with two fixed angular potentials about two orthogonal planes, our main result is that an ensemble average of them gives rise to a smooth horizonless solution characterized by an ellipsoidal structure. This contrasts with ring structures obtained when fixing the angular momenta instead of the angular potentials\DSEMIC we trace this difference of ensembles to large fluctuations of the angular momentum in the ensemble of fixed angular potential.