  We study the kinematics of multigrid Monte Carlo algorithms by means of
acceptance rates for nonlocal Metropolis update proposals. An approximation
formula for acceptance rates is derived. We present a comparison of different
coarse-to-fine interpolation schemes in free field theory, where the formula is
exact. The predictions of the approximation formula for several interacting
models are well confirmed by Monte Carlo simulations. The following rule is
found: For a critical model with fundamental Hamiltonian H(phi), absence of
critical slowing down can only be expected if the expansion of <H(phi + psi)>
in terms of the shift psi contains no relevant (mass) term. We also introduce a
multigrid update procedure for nonabelian lattice gauge theory and study the
acceptance rates for gauge group SU(2) in four dimensions.
