THE APP’S MODEL, EXPLAINED
Inside the mind of Rityvo
Every percentage Rityvo displays comes from a few formulas. Explore Rityvo’s documented model: each step is explained mathematically, then in plain language. The simulators on this page illustrate those formulas.
- Only an unaided answer counts.
Rereading, highlighting or spending hours on a chapter does not increase mastery. Recalling it on your own can.
- An estimate, never a certainty.
The figure is called “estimated mastery”. It comes with a confidence level.
- Recalculated whenever you open it.
The app keeps your actual recall history. Forgetting is calculated when you look at it.
What the app remembers
Three values at the heart of the mastery calculation.
The maths
A concept is an idea from your course, with a definition you have written yourself. The mastery calculation uses three main values for each concept:
- A
- The anchor : your level immediately after your last recall attempt, between 0 and 1.
- t₀
- The date of that last recall attempt.
- H
- The half-life : the number of days it takes for half of that level to fade. It starts at 3 days, before the first recall update.
These values are used to recalculate mastery. Status, priorities and planning also use your history, deadlines and the settings described below. No task runs in the background.
In plain language
For each thing you learn, Rityvo writes down three things in a little notebook:
- how full your bucket was the last time you recalled it;
- which day that was;
- the size of the hole in the bottom of the bucket.
With those three pieces of information, it can estimate how much water is left at any moment.
Forgetting
Estimated mastery decreases over time, halving with each half-life.
The maths
Δ is the number of days since the last recall attempt. Every H days, estimated mastery is halved.
Example. With A = 85% and H = 20 days, it is about 79.3% two days later and 42.5% twenty days later.
This is inspired by Half-Life Regression (Settles and Meeder, 2016). The anchor keeps the estimated level reached, rather than assuming a return to 100% after every review. And H is not universal: each concept, for each learner, has its own value.
In plain language
Think of your memory as a bucket with a small hole in the bottom.
The water level represents estimated mastery. The water leaking out represents the forgetting calculated by the model.
The half-life is the time it takes for half the water to drain away. A half-life of 3 days halves the estimate in 3 days. This is an initial model setting, not a universal law of memory.
Recall
Answer from memory, then compare with your definition. Your rating changes two numbers.
The maths
You rate your own answer: Missed it · P = 0 Partly · P = 0.5 Got it · P = 1
The recall weight E determines its influence in the model. It is 1 for the very first attempt, then depends on the time since the previous one (Δ in days):
In this calculation, an attempt made very soon after the last one receives a weight close to one quarter. After 24 hours, its weight reaches 1. This setting gives greater weight to spaced recall attempts.
The new anchor is a weighted average: the previous level has a weight of 1.6 and the new answer has a weight of E :
One good session therefore does not take a concept from 20% to 95%. Starting from zero, five “Got it” ratings at least 24 hours apart give 38, 62, 77, 86 and then 91%. The same five ratings on the same evening stop at about 66%.
The new half-life increases when you succeed, and more so when you have waited longer:
z = min(1 + Δ/H ; 3) after a success. After a failure, z = 1: in this rule, failing after three weeks does not carry a larger penalty than failing straight away. E moderates the change: a low-weight recall attempt barely shifts the half-life. H stays between 1 and 365 days.
| Answer | Straight away | After 1 half-life | After 2 or more |
|---|---|---|---|
| Got it | × 1.08 | × 1.87 | × 2.55 |
| Partly | × 1 | × 1 | × 1 |
| Missed it | × 0.93 | × 0.73 | × 0.73 |
“Straight away”: the previous recall attempt was only a few minutes ago, so E ≈ 0.25. The two right-hand columns assume at least one day has passed, so E = 1.
Spacing therefore acts twice: an attempt repeated too soon counts for less, while success after a longer delay increases the half-life faster.
In plain language
When you successfully recall something without looking at your notes, two things happen in this model.
- Water is added gradually. It is like an average where the old score carries more weight than the new one. Filling the bucket takes several successful attempts.
- The hole gets a little smaller. Especially if you waited a few days: recalling after a break gives the model more evidence of lasting knowledge.
An answer recalled five minutes after studying may still be fresh. The model therefore gives it less weight. After 24 hours, that weight reaches 1.
If you get it wrong, the hole gets a little larger. It is not a punishment: it simply suggests coming back sooner.
Status and confidence
What the number means, and how much confidence to place in it.
The maths
Concept status
- Not started : never tested.
- Mastered : M ≥ 80 %.
- Review needed : the anchor has previously reached 80%, but M has dropped below it.
- Learning : all other cases.
Confidence for a concept : low if all recall attempts happened on the same day; high after attempts on at least 4 different days, including an attempt after a wait of at least one day; medium in between.
Confidence for a chapter or subject :
Low = 1, medium = 2, high = 3, with a minimum of “low”. A chapter at 90% with only one of its four concepts tested still has low confidence.
In plain language
The orange line at 80% is the “I know it” line. Above it, the concept is mastered. If it drops below again, it needs review.
The confidence level reflects the recall history used to check the bucket.
If you have checked only once, or always on the same day, there is limited evidence. Checks on several different days give the model more information.
From concept to subject
A subject is worth 100 points. The missing points can be traced to its chapters.
The maths
Chapter mastery : the average mastery of its concepts. Subject mastery : the average mastery of its chapters, weighted by their exam weight w (from 1 to 5).
A chapter split into 20 concepts does not carry more weight than one with 4: its exam weight decides.
Missing points for a chapter :
Subject mastery plus the missing points across all chapters always equals 100. “Material covered” is a separate measure: the proportion of concepts tested at least once.
In plain language
A subject is a cake worth 100 points, divided among the chapters.
Chapters that matter more for the exam get a larger slice.
What you know colours part of your slice green. The rest represents points still to work on, and Rityvo can identify which chapters they belong to.
Today’s priority
Four factors multiplied together. The highest score becomes “Your priority today”.
The maths
- U
- Urgency = 14 / (14 + days until the exam). It equals 1 on exam day, 0.5 two weeks before, 0.25 six weeks before, and 0.25 when no date is set.
- B
- Need for review = 1 − 2−Δ/H, the proportion of the anchor that has faded. A concept never tested is assigned 0.6. For a chapter, this is averaged across its concepts.
- I
- Importance of the subject, from 1 to 5, chosen by the student.
The reasons displayed below the priority come directly from these factors: “Exam in N days”, “Important subject” (I ≥ 4), “X points to recover” (missing ≥ 1), “What you knew is starting to fade” (B ≥ 0.5).
In plain language
To choose what to study, Rityvo asks four questions about each chapter, then multiplies the answers.
In this model, any factor of zero makes the score zero. For example, a chapter with no missing points receives zero priority. This is a ranking rule, not a claim that reviewing it would be pointless.
The chapter with the highest score becomes your priority for the day.
The study plan
No interval is fixed in advance: estimated forgetting determines when a chapter returns.
The maths
Two durations follow directly from the forgetting curve:
- “Starting to fade” (B ≥ 0.5) exactly one half-life after the last recall attempt.
- A concept stays mastered for t = H · log₂(A / 0.8) days. After the 4th “Got it” in the example, 2.6 days; after the 5th, 9.4 days.
The plan simulates the next 14 days.
- Blocks per day = ⌊ minutes per day ÷ block length ⌋. Minutes come from your weekly hours converted to minutes, divided by 7 (at least one block; two if you have not set your available time).
- On each simulated day, priorities are recalculated. Chapters scoring above 0.5 are considered, yesterday’s chapters are excluded, and those with the highest scores are selected.
- For each selected chapter, the simulation assumes a correct but imperfect recall rating (P = 0.75) for its 6 most forgotten concepts, in a working copy of the data.
- Next day. A studied chapter drops in priority, then rises again as estimated forgetting increases.
In plain language
Think of the plan as Rityvo imagining the next two weeks.
Each evening in the simulation, it acts as though you completed that day’s studying: it adds a little water to the reviewed buckets and makes their holes slightly smaller. The next day, it asks the same four questions about every chapter again.
One extra rule: never the same chapter on two consecutive days in the proposed plan. This is a design choice for distributing work, not proof that reviewing the next day would be unhelpful.
That is how a chapter returns: its bucket has drained enough to move it back up the ranking.
What is set manually
These values are design choices, not measurements. Each recall attempt is recorded with mastery before and after it, so the settings can later be recalibrated using real data.
| Weight of the previous level in the anchor | 1.6 |
| Weight of an immediate repeat attempt | 0.25 |
| Delay before a recall attempt receives full weight | 1 d |
| Half-life consolidation rate | 0.45 |
| Maximum spacing bonus | × 3 |
| Initial half-life, before the first recall | 3 d |
| “Mastered” threshold | 80 % |
| Urgency horizon | 14 d |
| Need for review of an untested concept | 0.6 |
| Assumed success rating in the plan | 0.75 |
| Threshold for inclusion in the plan | 0.5 |
What Rityvo does not claim
The default values and thresholds are design choices. The confidence level is an internal indicator, not a statistical probability of passing an exam.
- To know a forgetting rate that applies to everyone. Half-life is specific to each concept and each learner.
- That a small part of the course is “worth” most of the grade. The student sets the importance of a chapter.
- That time spent proves mastery. It counts as an achievement, not as evidence of knowledge.
- To know what you know. It estimates this from what you have recalled and provides a confidence indicator based on your recall history.
The research behind it
Active recall and spacing are studied principles. Half-life decay draws inspiration from Settles and Meeder’s model, whose parameters are learned from data. The coefficients presented here are Rityvo’s own choices: they do not reproduce that trained model and are not validated by these publications.
- Roediger, H. L. and Karpicke, J. D. (2006). Test-enhanced learning. ↗ Psychological Science.
- Yang, C. et al. (2021). Testing (quizzing) boosts classroom learning: a systematic and meta-analytic review. ↗ Psychological Bulletin.
- Cepeda, N. J., Pashler, H., Vul, E., Wixted, J. T. and Rohrer, D. (2006). Distributed practice in verbal recall tasks. ↗ Psychological Bulletin.
- Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J. and Willingham, D. T. (2013). Improving students' learning with effective learning techniques. ↗ Psychological Science in the Public Interest.
- Settles, B. and Meeder, B. (2016). A trainable spaced repetition model for language learning. ↗ ACL.
Model v2 · Rityvo documentation · September 2026