It is well known that the size (peak count rate of emission, or inferred en
ergy) distribution of flares observed on the Sun follows a power law. Howev
er, the distributions that are constructed include flares from different ac
tive regions that have a variety of physical properties. In this paper cumu
lative peak count rate distributions are constructed for individual active
regions using events listed in the WATCH solar X-ray burst catalog. The ind
ividual distributions are found to be consistent with the distribution cons
tructed from events in all active regions named in the catalog. This result
suggests that the flare power-law size distribution reflects an intrinsic
property of the flare mechanism and is not a product of the distributions o
f physical parameters between active regions. The result is consistent with
the avalanche model for flares and more generally argues against macroscop
ic flare models.