  Bell's Theorem from 1964 and the (Strong) Free Will Theorem of Conway and
Kochen from 2009 both exclude deterministic hidden variable theories (or, in
modern parlance, `ontological models') that are compatible with some small
fragment of quantum mechanics, admit `free' settings of the archetypal Alice &
Bob experiment, and satisfy a locality condition called Parameter Independence.
We clarify the relationship between these theorems by giving reformulations of
both that exactly pinpoint their resemblance and their differences. Our
reformulation imposes determinism in what we see as the only consistent way, in
which the `ontological state' initially determines both the settings and the
outcome of the experiment. The usual status of the settings as `free'
parameters is subsequently recovered from independence assumptions on the
pertinent (random) variables. Our reformulation also clarifies the role of the
settings in Bell's later generalization of his theorem to stochastic hidden
variable theories.
