In TTFT, Michael Nielsen and I plotted readers’ Demonstrated retention, which depicts a pleasing exponential for repetitions vs. retention. These plots align with the story we’d like to tell (Spaced repetition yields (what feel like) exponential returns for small increases in effort)—and I still think that story is true. But I fear the plots themselves are misleading.
The trouble is that they’re really (approximating) a lower bound on demonstrated retention. The samples are over-determined by when we ask the reader to recall. We know from Quantum Country users seem to forget most prompts quite slowly that at the first repetition, many people probably could successfully recall at much longer intervals. If we had enough data from 2021-04 Quantum Country schedule experiment to plot a similar curve, we’d see a ton of points much higher up the y axis in early repetitions. The median might still grow exponentially, but the dispersion would be much higher.
What we “really” want to plot is something like a “safe retention interval”, which would describe the number of days you can recall with P > 0.9. I do think this curve is probably still exponential, but I’m not sure.