# A-Factor (Supermemo)

In Supermemo algorithms before SM-17, a key parameter for each task is its “absolute factor” (A-Factor or AF). For recall tasks, this maps to an absolute measure of item difficulty: the estimated optimal increase in review interval between the first and second repetition.

A new estimate is recomputed after each repetition by finding the entry in a precomputed matrix which best explains the current estimated forgetting index. This new A-Factor depends only on the most recent response, so to smooth out changes, the item’s stored A-Factor is shifted by weighted average with the new estimate. This approach probably depends to a high degree on SuperMemo’s responses being “grades” 1-5.

This parameter is related to (but distinct from) “ease” as used in Anki (which was called E-Factor in early versions of Supermemo). Ease is a dynamic state variable: each response modulates ease upwards or downwards, and the current ease value is multiplied by the current interval to produce the next interval. So ease represents not an absolute measure of item difficulty, but a momentary, contingent measure of item difficulty. The A-Factor is also updated on every repetition, but it’s always trying to represent the optimal interval growth between first and second interval, rather than an ongoing growth ratio.

A-Factors are also used for topics and tasks in SuperMemo (e.g. for Incremental reading). In this context, the A-Factor represents subjective priority.

It’s interesting to note that the rough, approximating nature of this approach is necessitated by the fact that SuperMemo users don’t share the same questions, so it’s not possible to aggregate user data to create external estimates of item difficulty.

Q. What’s the difference between Supermemo’s A-Factor and Anki’s ease factor?
A. The A-Factor is meant to be an absolute measure of item difficulty, while the ease factor estimates the item’s “current” difficulty.

Q. Mathematically, how is Supermemo’s A-Factor defined?
A. The optimal increase in review interval between the first and second repetitions.

Q. How is Supermemo’s A-Factor estimated?
A. It estimates the user’s current forgetting index and finds the A-Factor value which best explains the forgetting index at the current repetition.

Q. What’s an example of an A-Factor for an easy question in SuperMemo?
A. 5

Q. What’s an example of an A-Factor for a hard question in SuperMemo?
A. 1.2

Q. What did SuperMemo call its equivalent of Anki’s “ease” value?
A. E-Factor

## References

Algorithm SM-15 - supermemo.guru