  We consider curvature invariants in the context of black hole collision
simulations. In particular, we propose a simple and elegant combination of the
Weyl invariants I and J, the {\sl speciality index} ${\cal S}$. In the context
of black hole perturbations $\cal S$ provides a measure of the size of the
distortions from an ideal Kerr black hole spacetime. Explicit calculations in
well-known examples of axisymmetric black hole collisions demonstrate that this
quantity may serve as a useful tool for predicting in which cases perturbative
dynamics provide an accurate estimate of the radiation waveform and energy.
This makes ${\cal S}$ particularly suited to studying the transition from
nonlinear to linear dynamics and for invariant interpretation of numerical
results.
