Speed of learning vs. acquisition rate

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From: Robyn
Country: Nov 28, 2000
Sent: {{{Sent}}}
Subject: Speed in statistics

Question:

I like your formula for knowledge acquisition rate. I made some estimations and was disappointed with my result (I learn philosophy and my items are a bit hard). Only some time later I discovered the parameter Speed in statistics, and this displays even a lower speed value. Is Speed and acquisition rate the same? Can you provide exact formulas?

Answer:

The overall formula is always the same:

  AcquisitionRate = Memorized/(Days/365.25)/Workload

where: Memorized is the total number of memorized items, Days is the number of days devoted to learning, and Workload is the average time spent for answering questions per day.

AcquisitionRate is always expressed in items per minute per year.

However, the way Workload is determined may affect the ultimate result. Originally, Workload was supposed to stand for time devoted to learning per day (in minutes). When the Speed parameter was introduced, SuperMemo did not have time per day statistic. However, it had Burden (items per day) and Avg time (average repetition time). This is why SuperMemo 9.5 (1999) used Workload=Burden*AverageTime. This formula survived until today.

Also in 1999, SuperMemo introduced Total time, which estimates total time devoted to answering questions. For older collections that value could only be estimated. This is why Total time could not be used for Speed estimations. Now, in 2016, most users have never used SuperMemo 9 (1998) or earlier. Moreover, in 17 years, total learning time would now be computed pretty accurately (estimated for the period 1987-1999 and computed exactly for the period 1999-2016).

This is why, future SuperMemos will used Workload=TotalRepetitionTime/Days to accurately express Speed.

All users who substantially overload their learning process will now see a boost to their learning speed parameter. This is not because of the better algorithm (Algorithm SM-17), but because Speed based on Burden would underestimate the speed of learning. The underestimate is caused by the fact that not all scheduled items are reviewed by the end of the day.

To better account for material overload, Speed will also be multiplied by Retention to truly reflect knowledge possessed (rather than auto-memorized in SuperMemo).

To sum it up:

  • SuperMemo 9..16: AcquisitionRate = Memorized/(Days/365.25)/(Burden*AverageTime)
  • SuperMemo 17..: AcquisitionRate = Memorized/(Days/365.25)/(TotalRepetitionTime/Days)*Retention