Horizontal scale represents 50 words, sampled at intervals of 100 from a frequency-sorted list of vocabulary. Black tick marks just help me identify which of the 50 is where.

Top shimmery rainbow band represents 7 language learners' progress. Red marks the first 5 words they learn (well, the first 5 that are in our sample, so at the red stage they've learned ~500 words overall), orange the next 5, etc. Each of them has learned a respectable ~3500 words so far.

Each person learns some rare vocabulary early because all topical vocabulary, all vocabulary that is about something, is rare. Interests in different topics mean they each learn vocabulary in a different sequence.

The rainbow-ish bar below them shows their median judgement about when you would learn each word. This generic learning sequence does more or less just march down the frequency list, unlike any individual learner. But even that breaks down lower on the list, where the frequency decline is flatter and many many words are all around the same rarity.

Black bands below show the vocabulary content of some stories. They are simulated to each be limited to a considerably smaller vocabulary than any of the learners. Again, though, to be about something, each one has to use some rare vocabulary. You can compare their demands to the 7 people and see if anybody is competent to read the story.

The top story band has a vocabulary limit of 1500 words, and the bottom one only 1000 words.

Can you learn words from context? Really, only if you understand the context really well to begin with. Conventionally, it's considered that you need to have 98% token coverage in order to grasp the rest from context. Common words make up more than their share of the tokens, so missing even more than one of the rare topical words can be coped with. But missing any of the more common words is disastrous for your token coverage, so that doesn't help our readers much.

If there is just one rare word type in a story that the person doesn't understand,