The 12C(α ,γ )16O reaction, an important component of stellar helium burning, plays a key role in nuclear astrophysics. It has direct impact on the evolution and final state of massive stars, while also influencing the elemental abundances resulting from nucleosynthesis in such stars. Providing a reliable estimate for the energy dependence of this reaction at stellar helium burning temperatures has been a major goal for the field. In this work, we study the role of potential new measurements of the inverse reaction, 16O(γ ,α )12C , in reducing the overall uncertainty. A multilevel R -matrix analysis is used to make extrapolations of the astrophysical S factor for this reaction to the stellar energy of 300 keV. The statistical precision of the S -factor extrapolation is determined by performing multiple fits to existing E 1 and E 2 ground-state capture data, including the impact of possible future measurements of the 16O(γ ,α )12C reaction. In particular, we consider a proposed Jefferson Laboratory (JLab) experiment that will make use of a high-intensity low-energy bremsstrahlung beam that impinges on an oxygen-rich single-fluid bubble chamber in order to measure the total cross section for the inverse reaction. The importance of low-energy data as well as high-precision data is investigated.