Area under the curve as a measure of discounting.

The authors built a simple ruler for delay-discounting curves. They call it area-under-the-curve (AUC).

You draw the curve, count the squares under it, and get one clean number. No math models. No theory fights.

They show the steps in Excel so any BCBA can copy the sheet and go.

The ruler works on any curve shape. Steeper curves give smaller AUC. Flatter curves give bigger AUC.

One number tells you how much the person devalues delayed rewards.

Odum et al. (2020) pooled 20 years of studies that now use this ruler. Their review says non-money rewards are discounted more steeply than money, and AUC captures the gap in one glance.

Holt et al. (2018) took the ruler to pigeons. Key-peck, treadle-press, or lever-push—every curve stayed hyperbolic and the AUC stayed stable. The metric travels across species.

McKerchar et al. (2019) tweaked how we ask the questions—variable delays vs. double rewards. Curves changed shape, but AUC still tracked the shift. Your procedure matters, yet the ruler still reads it.

If you run delay-discounting probes with clients, stop wrestling with k-values that refuse to converge. Plug the choices into the free AUC sheet and you have a score you can graph across sessions. It takes two minutes and needs no stats degree.