  The Shapley value provides a natural means of quantifying the contributions
of facts to database query answers. In this work, we seek to broaden our
understanding of Shapley value computation (SVC) in the database setting by
revealing how it relates to Fixed-size Generalized Model Counting (FGMC), which
is the problem of computing the number of sub-databases of a given size and
containing a given set of assumed facts that satisfy a fixed query. Our focus
will be on explaining the difficulty of SVC via FGMC, and to this end, we
identify general conditions on queries which enable reductions from FGMC to
SVC. As a byproduct, we not only obtain alternative explanations for most
existing results on SVC, but also new complexity results. In particular, we
establish FP-#P complexity dichotomies for constant-free connected UCQs and
homomorphism-closed connected graph queries. We further explore variants of
SVC, either in the absence of assumed facts, or where we measure the
contribution of constants rather than facts.
