  The deviations of a graded algebra are a sequence of integers that determine
the Poincare series of its residue field and arise as the number of generators
of certain DG algebras. In a sense, deviations measure how far a ring is from
being a complete intersection. In this paper we study extremal deviations among
those of algebras with a fixed Hilbert series. In this setting, we prove that,
like the Betti numbers, deviations do not decrease when passing to an initial
ideal and are maximized by the Lex-segment ideal. We also prove that deviations
grow exponentially for Golod rings and for certain quadratic monomial algebras.
