  We propose a holistic framework for constructing sensitivity measures for any
elicitable functional $T$ of a response variable. The sensitivity measures,
termed score-based sensitivities, are constructed via scoring functions that
are (strictly) consistent for $T$. These score-based sensitivities quantify the
relative improvement in predictive accuracy when available information, e.g.,
from explanatory variables, is used ideally. We establish intuitive and
desirable properties of these sensitivities and discuss advantageous choices of
scoring functions leading to scale-invariant sensitivities.
  Since elicitable functionals typically possess rich classes of (strictly)
consistent scoring functions, we demonstrate how Murphy diagrams can provide a
picture of all score-based sensitivity measures. We discuss the family of
score-based sensitivities for the mean functional (of which the Sobol indices
are a special case) and risk functionals such as Value-at-Risk, and the pair
Value-at-Risk and Expected Shortfall. The sensitivity measures are illustrated
using numerous examples, including the Ishigami--Homma test function. In a
simulation study, estimation of score-based sensitivities for a non-linear
insurance portfolio is performed using neural nets.
