Statistical analysis is applied to a set of electron micrographic images (Kocsis, E., B. L. Trus, C. J. Steer, M. E. Bisher, and A. C. Steven. 1991. J. Struct. Biol. 107:6-14), from which quantitative measures are obtained to support the notion that the three arms of a triskelion have statistically identical properties and exhibit independent structural fluctuations. Additionally, a study of local contour fluctuations, which indicates that the elastic properties of a triskelion arm are approximately constant over the entire arm length, is used along with a small deformation statistical mechanics theory to derive an effective, average flexural rigidity for the arms. This result is used to estimate the bending energy necessary to deform a clathrin patch, and comparison is made with the deformation energy of an equivalent area of non-clathrin-coated membrane. We estimate that the rigidity of the clathrin lattice is at least comparable to that of a typical membrane. Hence, the natural curvature of a clathrin cage can stabilize, and perhaps propel, the formation of intracellular coated vesicles.