Photochemical upconversion is a promising way to boost the efficiency of solar cells using triplet-exciton annihilation. Currently, predicting the performance of photochemical upconversion devices is challenging. We present an open-source software package that takes experimental parameters as inputs and gives the figure of merit of an upconversion system, enabling theory-driven design of better solar-energy devices. We incorporate the statistical distribution of triplet excitons between the sensitizer and the emitter. Using the dynamic quenching effect of the sensitizer on emitter triplet excitons, we show that the optimal sensitizer concentration can be below the sensitizer solubility limit in liquid devices. These theoretical contributions can explain, without the use of heavy-atom-induced triplet-exciton formation or phenyl-group rotation, the experimental failure of zinc octaethylporphyrin to effectively sensitize diphenylanthracene, where platinum octaethylporphyrin succeeds. Our predictions indicate a change in direction for device design that will reduce triplet-exciton losses.