The cubic-to-tetragonal antiferrodistortive transition at 105 K in the most widely studied perovskite, SrTiO3, is perhaps the preeminent example of a second-order structural phase transition. Extensive investigations since the 1960s have tracked the softening of the phonon mode associated with this transition, the development of octahedral rotations, and the interplay with incipient ferroelectricity and superconductivity. It is less well known that modest ionic substitutions alter the transition temperature (Ta) over a remarkable range in SrTiO3, from 0 K to above ambient. Here, we first study the thermodynamics of the transition via specific heat and determine a Ta shift of +10.9 K/atomic % in Nb-substituted crystals, the most heavily studied in terms of electronic transport. We then present the first quantitative rationalization of the trends in Ta with substitution in SrTiO3. We demonstrate that the apparently complex behavior versus tolerance factor occurs simply due to a nonlinear dependence of the rate of change of Ta with substituent concentration. We then connect this to ionic valence mismatch, using bond valence concepts to establish a new parameter, «ϵ4», which exhibits a universal linear dependence with Ta for all known substitutions. This provides the first unified view of the substituent-dependent Ta in SrTiO3, deepens our understanding of the phase transition (including a theoretical maximum in the rate of Ta suppression), and demonstrates predictive power via a simply computed parameter.