What is the memory curve actually calculating? Understanding the three keys: stability, retrievability, and difficulty
In the previous article Why We Always Forget the Words We Memorized, we discussed a very practical conclusion: reviewing right when you are about to forget, but haven't completely forgotten, requires the least effort and makes the memory stick the best. You already know that "timing" is crucial. This article aims to answer a deeper question—how exactly does the system calculate that perfect timing?
The answer lies in three key variables: retrievability, stability, and difficulty. While they sound highly academic, they can actually be understood in very plain terms. After reading this article, when you open Loopy's memory curve, you will understand why each flashcard pops up to remind you on "that exact day."
Quick review: Memories decline over time
After we learn a new word, our memory of it naturally decays over time. You remember it best the moment you finish learning it. An hour later, it drops a bit; a day later, it's even lower; and a week later, only a vague impression might remain. This downward-sloping line is the forgetting curve.
To give you a concrete sense of the numbers: for a word that hasn't been reviewed, memory retention drops to about half just a few days after learning, and continues to go lower the longer you wait.
- I learned the word "bright" yesterday. (I learned the word "bright" yesterday.)
You remembered it very clearly at the moment of learning, but if you don't encounter it again for the whole week, by the weekend, this word will have quietly faded away. What the system needs to do is bring it back in front of you just before it fades. The question is—how do we know how much it has faded "right now"? This is where the first variable comes in.
Variable 1: retrievability — The probability that you can recall it "at this moment"
Retrievability answers the question: "If you were tested on this word right now, what is the probability that you would be able to recall it?"
It is a value that decreases over time:
- Just after review: Retrievability is very high; you are almost certain to recall it.
- After a few days of no contact: It slowly drops.
- Long time no review: It drops to a very low level, meaning you have likely forgotten most of it.
You can think of it as the "battery level" of a flashcard. It is fully charged when you just finish reviewing, and drops bar by bar if left unused. Retrievability is the system's estimate of "how many bars of battery are left right now."
Key takeaway: Retrievability is an instantaneous value "at this very moment," and it changes every day. The retrievability of bright today is different from the retrievability of bright three days from now—for the same word, the longer it goes without being reviewed, the lower this value becomes.
Variable 2: stability — How long this memory "can last" before needing a review
If retrievability is "how many bars of battery are left now," then stability is "how durable this battery is."
Stability answers the question: "How long can this memory last before it drops to the level where it needs to be reviewed?"
- Newly learned words: Stability is very low; it might drop in just a day or two.
- After one successful review: Stability increases, perhaps lasting four or five days.
- After another successful review: It can last one or two weeks.
- After several rounds: It can last one or two months, or even longer.
This is exactly the magic of spaced repetition: every time you successfully recall a word, its stability jumps up a level, meaning it can last longer next time. In other words, each time you answer correctly, you "flatten" the forgetting curve a little bit, making it decline more slowly.
- She is a kind person. (She is a kind person.)
When you first learn kind, you might need to review it two days later; but after you successfully recall it several times in a row, its stability becomes high enough that you only need to be tested on it once every two weeks or a month—you spend less and less effort, yet remember it more and more firmly.
How to remember them: Retrievability is the "current state," which drops; stability is the "ability to last," which gets stronger with practice. One is the current battery level, while the other is the battery capacity.
Variable 3: difficulty — How challenging this word is for you personally
With the exact same amount of review, why do some words stick instantly while others just won't stay in your head no matter how hard you try? This is the third variable: difficulty.
Difficulty measures "how hard this item itself is for you." It affects the speed at which stability grows:
- Low-difficulty words: Every time you successfully review them, stability grows quickly, and you can rapidly extend the review interval.
- High-difficulty words: With each review, stability only climbs a little bit, so they need to be reviewed more frequently with shorter intervals.
Short and concrete words like cat and book usually have low difficulty and become stable after learning them just two or three times. In contrast, words that look similar and are abstract, like though, although, and thorough, have high difficulty. The system will present them to you more frequently to help you gradually make them stick.
By the way, here is a common misunderstanding: difficulty refers to "how hard this word is for you to remember," not whether the word "is spelled correctly." For example, with past tense verbs, actually remembering them is what matters—I went ✓, I goed ✗. For these forms that are easily remembered incorrectly, the system will show them to you more often with shorter intervals.
This is exactly where the fairness lies: The system doesn't treat all words with the same interval. It extends the interval for easy words so as not to waste your time, and keeps a closer eye on difficult words so your effort doesn't go to waste. Every word gets its own customized review rhythm based on its actual difficulty to you.
Putting the three variables together: The health status of a flashcard
Translating retrievability into something you can actually see gives you the health status of each flashcard. Loopy uses three statuses to help you understand at a glance:
- Solid (solid): Retrievability is still very high, you can probably recall it now, so there's no need to rush to review.
- Review (review): Retrievability has dropped to the middle, which is exactly the golden window of "about to forget but haven't completely forgotten"—this is the most efficient time to review.
- Fading (fading): Retrievability is already very low; if you don't review it now, you'll have to relearn it from scratch.
Just by glancing at the distribution of these three types of words, you can tell whether your overall review rhythm is healthy: a lot of solid words and few fading ones means you are keeping up; a massive block of fading words means it's time to come back and catch up.
Summary: A review rhythm tailored just for you
Many people think reviewing is just about following a fixed schedule like "3 days, 7 days, 14 days." The memory curve is much smarter than that: for every single word you have learned, it tracks all three of the above values simultaneously—
- It uses retrievability to determine "how far it has dropped right now";
- It uses stability to determine "how long it can last after this review";
- It uses difficulty to determine "how much to extend or shorten the interval."
Then, it dynamically calculates the optimal review timing unique to each word. Difficult words come back sooner, while familiar words are spaced further and further apart. You don't have to calculate any of this yourself—just follow the reminders and practice the words due today.
How to apply this in Loopy
These three variables might sound complicated, but the actual operation is very simple for you—because Loopy's memory curve has calculated everything for you.
- For every word you learn in the graded courses, the system quietly records your response each time: whether you answered instantly, took a moment to recall, or got completely stuck. These responses are used to update its retrievability, stability, and difficulty.
- Reviewing uses active recall: it first asks you to think of the meaning, then reveals the answer. Every "effort to recall" pushes up the stability of that word, flattening the curve even more.
- All words live in real course sentences and listening contexts, naturally encountered again and again alongside listening and shadowing practice. When you come across something you don't understand, simply tapping the dictionary to look it up also counts as another review.
All you need to do is practice a little bit each day following the review reminders; leave the calculations behind those three variables to the memory curve. Looking back a week or two later, you'll find that words you used to forget right after memorizing have climbed all the way from "fading" to "solid," quietly making their home in your long-term memory.