Statistical energy analysis (SEA) is a method for estimating structural acoustic transfer functions based on a statistical model of the system. The SEA model assumes random noise excitation in frequency bands and an underlying ensemble of “similar” systems. However, since the results of a SEA calculation are nearly always applied to a single system, there is a natural question of in what sense a single system can be random. A particular structural acoustics system is considered that displays both deterministic and random behavior with a distinct transition between the two. System parameters (damping, modal density, and coupling factors) are examined to see how they might be controlling the transition from deterministic to random.