  We consider the effect of disorder on the tight-binding Hamiltonians with a
flat band and derive a common mathematical formulation of the average density
of states and inverse participation ratio applicable for a wide range of them.
The system information in the formulation appears through a single parameter
which plays an important role in search of the critical points for disorder
driven transitions in flat bands [1]. In weak disorder regime, the formulation
indicates an insensitivity of the statistical measures to disorder strength,
thus confirming the numerical results obtained by our as well as previous
studies.
