  Bell inequalities rest on three fundamental assumptions: realism, locality,
and free choice, which lead to nontrivial constraints on correlations in very
simple experiments. If we retain realism, then violation of the inequalities
implies that at least one of the remaining two assumptions must fail, which can
have profound consequences for the causal explanation of the experiment. We
investigate the extent to which a given assumption needs to be relaxed for the
other to hold at all costs, based on the observation that a violation need not
occur on every experimental trial, even when describing correlations violating
Bell inequalities. How often this needs to be the case determines the degree
of, respectively, locality or free choice in the observed experimental
behavior. Despite their disparate character, we show that both assumptions are
equally costly. Namely, the resources required to explain the experimental
statistics (measured by the frequency of causal interventions of either sort)
are exactly the same. Furthermore, we compute such defined measures of locality
and free choice for any nonsignaling statistics in a Bell experiment with
binary settings, showing that it is directly related to the amount of violation
of the so-called Clauser-Horne-Shimony-Holt inequalities. This result is theory
independent as it refers directly to the experimental statistics. Additionally,
we show how the local fraction results for quantum-mechanical frameworks with
infinite number of settings translate into analogous statements for the measure
of free choice we introduce. Thus, concerning statistics, causal explanations
resorting to either locality or free choice violations are fully
interchangeable.
