  The main goal of this paper is to size up the minimal graded free resolution
of a homogeneous ideal in terms of its generating degrees. By and large, this
is too ambitious an objective. As understood, sizing up means looking closely
at the two available parameters: the shifts and the Betti numbers. Since, in
general, bounds for the shifts can behave quite steeply, we filter the
difficulty by the subadditivity of the syzygies. The method we applied is
hopefully new and sheds additional light on the structure of the minimal free
resolution. We use the Boij-S\"oderberg techniques for the Betti numbers to get
polynomial upper bounds for them.
  It is expected that the landscape of hypersurface singularities already
contains most of the difficult corners of the arbitrary case. In this regard,
we treat some facets of this case, including an improvement of one of the basic
results of a recent work by Bus\'e--Dimca--Schenck--Sticlaru.
