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Pyrochlores have attracted considerable interest lately due to their ability to host a variety of interesting phenomena, often derived from their geometrically frustrated interpenetrating sublattices. The triangular arrangement of cations tends to disfavor the coordinated displacements necessary to realize polar structures, but there are a few materials which overcome this frustration and exhibit ferroelectricity. Here we examine the origin and nature of the distortion mechanisms in the oxysulfide series Cd₂Nb₂O_7-xS_x. Using density functional theory, group theoretical methods, and diffraction techniques, we characterize changes in the phase transition under sulfur substitution. We ultimately identify the role of covalent bonding on the Cd-X’ sublattice in shifting the ferroelectric phase transition from proper (x=0) to improper (x=0.25) and eventual elimination (x=0.7). This work sheds light on the origin of polar distortion mechanisms in the pyrochlore structure family, in addition to providing insight into the off-centering mechanisms of complex oxides in general.