Recent field observations of the statistical distribution of turbidite and debris flow deposits are discussed. In some cases one finds a good fit over 1.5-2 orders of magnitude to the scaling law <i>N(h)</i> α <i>h<sup>-B</sup></i>, where <i>N(h)</i> is the number of layers thicker than <i>h</i>. Observations show that the scaling exponent <i> B</i> varies widely from deposit to deposit, ranging from about 1/2 to 2. Moreover, one case is characterized by a sharp crossover in which <i> B</i> increases by a factor of two as <i> h</i> increases past a critical thickness. We propose that the variations in <i>B</i>, either regional or within the same deposit, are indicative of the geometry of the sedimentary basin and the rheological properties of the original gravity-driven flow. The origin of the power-law distribution remains an open question.