Matrix of optimal factors

Matrix of optimal factors was a central element of Algorithm SM-5 used in SuperMemo 5 (1989). This matrix was composed of 20 rows corresponding with the repetition number, and 20 columns corresponding with item difficulty expressed as E-Factor. Each entry of the matrix held the optimum factor (O-Factor) for a given difficulty and repetition number. The O-Factor would increase with good performance or be reduced otherwise.

In SuperMemo 19, the matrix can still be inspected with Toolkit : Statistics : Analysis : Matrices : O-Factors. It no longer plays a role in Algorithm SM-18; however, it helps illustrating how optimal factors change in time depending on item difficulty. Note that repetition number has been replaced with repetition category, and E-Factors with A-Factors.

The role of the matrix of optimum factors in the evolution of SuperMemo algorithms is described here: First fast-converging spaced repetition algorithm: Algorithm SM-5

In Algorithm SM-17, the role of the 2-dimensional OF matrix is played by the 3-dimensional stability increase matrix (SInc[]) with an added dimension of retrievability.

This glossary entry is used to explain "History of spaced repetition" by Piotr Wozniak (June 2018)

Figure: Matrix of optimal factors is no longer used by Algorithm SM-18. However, it can still be generated with procedures inherited from Algorithm SM-15. The columns correspond with easiness of the material expressed as A-Factor. The rows correspond with memory stability expressed as repetition category. Individual entries represent the current best estimate of the optimal factor that can be used to compute the increase in intervals in spaced repetition