Immersion is the only method that gets better as you improve

"Just move there" is the standard advice, and the model agrees with it — but not at the point in the journey when people usually act on it.

The coefficients

Every method here has a multiplier at the bottom of the range and one at the top:

Read the last row against the others. Self-study gets 36% worse from A1 to C1. App-only gets 169% worse. Immersion gets 17% better.

It is the only entry in the table that improves, and that asymmetry is the whole story.

Why it improves

Immersion supplies one thing in unlimited quantity: unpredictable input from people who are not adjusting for you.

At A1 that is nearly worthless. You know two hundred words. A conversation between two native speakers at full speed is noise, and noise does not teach. What you need at A1 is graded, sequenced, repeated material — which is exactly what a textbook or an app is for, and which a foreign country conspicuously does not provide. Hence 0.9×: better than studying at home, but only slightly.

At C1 the same input is the only thing that works. You need the constructions nobody teaches, the register shifts, the speed, the accents, the vocabulary that appears once a month. No curriculum contains that, because it is not a finite list. Hence 0.75×.

Concretely, Spanish to B2 at an hour a day: 345 hours living in-country against 460 with a tutor and 695 by self-study.

The mistake this explains

People move abroad as beginners and are disappointed. The standard interpretation is that they failed — did not push themselves, stayed in the expat bubble, lacked discipline.

Sometimes. But the model says something less moralistic: at A1, immersion is only marginally better than staying home, and the marginal gain is easily wiped out by the practical friction of a new country. You are spending enormous life resources for a 10% discount on the cheapest part of the project.

The same six months, taken at B1 instead, buys a 25% discount on the most expensive part — and by then you can actually participate, which is what makes it work at all.

The caveat that matters most

These coefficients are estimates. FSI publishes hours for its own intensive classes and does not publish an immersion comparison, because it does not run immersion programmes.

The direction is well attested and not seriously disputed. The specific values are ours, set conservatively, and marked as estimates in the code and in the caveats under every result.

There is also a substitution the model cannot see: "living in-country" assumes you actually use the language daily and unavoidably. Living abroad while working in English is not this method, and the model has no way to tell the difference. Dutch is the extreme case — a country where the local population will kindly switch to English, which converts immersion into ordinary self-study with a better view.

Using it

If a stay abroad is available to you, the model's advice is: arrive at B1, not at A1. Build the base where a base is cheap to build, and spend the expensive resource on the expensive part.

Run both scenarios — same language, same target, immersion against your current method — and the gap it shows is the argument for going, at the level where the argument is strongest.