Previous observations that suggest a substantial role for nondiffusive energy transport in tokamaks subjected to off-axis electron cyclotron heating (ECH) are compared to the output from a sandpile model. The observations considered include local and global aspects of temperature profile evolution in the DIII-D [for example, C. C. Petty and T. C. Luce, Nucl. Fusion 34 , 121 (1994) and RTP (Rijnhuizen Tokamak Project) [for example, M. R. de Baar, M. N. A. Beurskens, G. M. D. Hogeweij, and N. J. Lopes Cardozo, Phys. Plasmas 6 , 4645 (1999)] tokamaks. The sandpile model employed is an extension, to incorporate noncentral fueling, of one used previously to address tokamak physics issues [S. C. Chapman, R. O. Dendy, and B. Hnat, Phys. Rev. Lett. 86 , 2814 (2001)]. It is found that there are significant points of resemblance between the phenomenology of the noncentrally fueled sandpile and of the tokamaks with off-axis ECH. This suggests that the essential ingredient of the sandpile model, namely avalanching conditioned by a local critical gradient, may be one of the key transport effects generated by the tokamak plasma physics.