  We present a detailed study of the collapse of a spherical perturbation in
DGP braneworld gravity for the purpose of modeling simulation results for the
halo mass function, bias and matter power spectrum. The presence of evolving
modifications to the gravitational force in form of the scalar brane-bending
mode lead to qualitative differences to the collapse in ordinary gravity. In
particular, differences in the energetics of the collapse necessitate a new,
generalized method for defining the virial radius which does not rely on strict
energy conservation. These differences and techniques apply to smooth dark
energy models with w unequal -1 as well. We also discuss the impact of the
exterior of the perturbation on collapse quantities due to the lack of a
Birkhoff theorem in DGP. The resulting predictions for the mass function, halo
bias and power spectrum are in good overall agreement with DGP N-body
simulations on both the self-accelerating and normal branch. In particular, the
impact of the Vainshtein mechanism as measured in the full simulations is
matched well. The model and techniques introduced here can serve as practical
tools for placing consistent constraints on braneworld models using
observations of large scale structure.
