Study Schedule Optimizer Spaced Repetition

Spaced repetition rests on two robust findings: memory for a newly learned item decays roughly exponentially with time, and each successful effortful recall flattens that decay. The exponential form R = e raised to minus t over S follows from assuming a constant hazard of forgetting per unit time, so S, the stability, is the time constant at which retention falls to about 37 percent. The scheduler here multiplies stability by 2.5 after each review, the default ease factor from the SM-2 algorithm, and walks an interval ladder of 1, 3, 7, 14, 30, and 60 days. Practitioners generally aim to review when predicted retrievability has fallen to roughly 80 to 90 percent, since reviewing too early wastes time and reviewing too late forces relearning at close to first-exposure cost. Difficulty scales the base stability by 1.3 for easy material, 1.0 for medium, and 0.7 for hard, and sets per-topic budgets of roughly 20, 30, or 45 minutes for first learning against 8, 12, or 18 minutes per review. Several simplifications matter. The model treats all topics as equally hard, whereas real schedulers such as Anki track difficulty per item and lengthen or shorten intervals from actual grading. The interval ladder is fixed rather than adaptive, so a failed recall does not reset it. Minutes per topic are stipulated constants, not measurements of your own pace. Feasibility is a bare comparison of required minutes against days multiplied by daily hours, with no allowance for attention decay past three or four hours of concentrated study, context switching, or the sleep-dependent consolidation that makes two 90-minute sessions outperform one 3-hour block.

Hermann Ebbinghaus established the field almost single-handedly with Ueber das Gedaechtnis, published in Leipzig in 1885. Working as his own sole subject, he memorised lists of nonsense syllables to eliminate prior associations and measured how much relearning time he saved at intervals from 20 minutes to 31 days, producing both the forgetting curve and the savings method for quantifying it. He also noted that repetitions distributed across days were markedly more efficient than the same number crammed into one sitting, the spacing effect in its original form. Application came slowly. Cecil Alec Mace advocated deliberately spaced rehearsal in The Psychology of Study in 1932. Paul Pimsleur described graduated interval recall for language learning in 1967, and Sebastian Leitner popularised a physical implementation in 1972 with a box system in which cards recalled correctly move to a less frequently reviewed compartment. Piotr Wozniak began systematic experiments on interval growth in the mid-1980s and released SuperMemo for DOS in 1987; his SM-2 algorithm, with its per-item ease factor starting at 2.5, remains the most copied scheduling rule in the field. Damien Elmes released Anki in 2006 on an SM-2 variant, taking the method to a mass audience. Laboratory support consolidated in parallel, notably the 2006 meta-analysis of spacing studies by Nicholas Cepeda and colleagues and the retrieval-practice work of Henry Roediger and Jeffrey Karpicke the same year. More recent schedulers such as FSRS replace fixed ease factors with fitted difficulty, stability, and retrievability parameters.