Discounting is a fundamental process in human and non-human decision making. Although various quantitative models have been proposed to describe how people make trade-off decisions between reward magnitude, and delay or probability, there is no definitive answer as to the best model. Based on studies conducted in the past 25 years, a residual meta-analysis was conducted to provide a comprehensive evaluation of six prominent models of discounting. Two-parameter generalised-hyperbola and exponential models described delay and probability discounting very well, but systematic residual patterns were evident in the pooled residuals of all models. The bounded nature of the present value scale was excluded as a confound, and neither best-fitting model could be identified as the true model underlying the data. A weighted function suggested that a hyperboloid-constant sensitivity composite may better describe the decline of subjective present value. Notably, the same underlying functional form was identified for delay and probability discounting. Together, these findings suggest a novel model is required, that re-examines how delay (or odds-against) and reward magnitude are scaled, so that the true underlying discount function is accurately described.