  Simple quantitative measures of indeterminism and signalling, $I$ and $S$,
are defined for models of statistical correlations. It is shown that any such
model satisfies a generalised Bell-type inequality, with tight upper bound
B(I,S). This upper bound explicitly quantifies the complementary contributions
required from indeterminism and signalling, for modelling any given violation
of the standard Bell-CHSH inequality. For example, all models of the maximum
quantum violation must either assign no more than 80% probability of occurrence
to some underlying event, and/or allow a nonlocal change of at least 60% in an
underlying marginal probability of one observer in response to a change in
measurement setting by a distant observer. The results yield a corresponding
complementarity relation between the numbers of local random bits and nonlocal
signalling bits required to model a given violation. A stronger relation is
conjectured for simulations of singlet states. Signalling appears to be a
useful resource only if a `gap' condition is satisfied, corresponding to being
able to nonlocally flip some underlying marginal probability $p$ to its
complementary value 1-p.
