  We explore four approaches to the question of defectivity for a complex
projective toric variety $X_A$ associated with an integral configuration $A$.
The explicit tropicalization of the dual variety $X_A^\vee$ due to Dickenstein,
Feichtner, and Sturmfels allows for the computation of the defect in terms of
an affine combinatorial invariant $\rho(A)$. We express $\rho(A)$ in terms of
affine invariants $\iota(A)$ associated to Esterov's iterated circuits and
$\lambda(A)$, an invariant defined by Curran and Cattani in terms of a Gale
dual of $A$. Thus we obtain formulae for the dual defect in terms of iterated
circuits and Gale duals. An alternative expression for the dual defect of $X_A$
is given by Furukawa-Ito in terms of Cayley decompositions of $A$. We give a
Gale dual interpretation of these decompositions and apply it to the study of
defective configurations.
