The Acquisition Potential Equation

I made this equation as I wanted a framework for thinking and talking about immersion content/activities for language acquisition:

AcquisitionPotential = ∛(A × C × D)

OR

AcquisitionPotential = (A × C × D)^(1/3)

Where:

• Attention (A): How focused you are on the content (0-100)
• Comprehensibility (C): How much you understand (regardless of whether you know the words or not) (0-100)
• Density (D): How frequently language is being used (0-100)

The equation uses the geometric mean (calculated as the cube root of the product of the three components), which has several important properties:

• It ensures all three components must be reasonably high to achieve a good score. Unlike an arithmetic mean, the geometric mean prevents one high score from compensating for a very low score in another area.
• If any single component equals zero, the entire equation equals zero, regardless of how high the other components are.
• It values all three components equally, giving them the same weight in determining the final score.

Why This Equation Matters for Language Learners

The Acquisition Potential equation provides a balanced framework for evaluating language learning activities, moving beyond the common debates in language learning communities.

Many language learners fall into camps that prioritize just one factor:

• "Only watch engaging content" (prioritizing attention)
• "Only use comprehensible input" (prioritizing comprehensibility)
• "Only use content-rich materials" (prioritizing density)

The equation demonstrates why all three factors matter simultaneously. A high score in one area cannot compensate for severe deficiencies in another.

Evaluating Efficiency

Acquisition Potential provides a single metric to compare different learning activities:

• High AP activities (like watching comprehensible, dense content with full attention) deliver maximum language acquisition per hour invested
• Medium AP activities might include passive listening to highly comprehensible content or active engagement with partially comprehensible materials

Making Strategic Decisions

The equation helps learners make informed choices about:

1. Content selection: Choose materials that balance all three factors rather than excelling in just one
2. Time allocation: Prioritize higher AP activities when time is limited
3. Improvement focus: Identify which factor is your limiting component and work to improve it

Understanding Passive Immersion

Rather than debating whether passive immersion "works," the equation quantifies its effectiveness:

• Passive immersion with 30% attention to highly dense, comprehensible content might have a moderate AP
• While not as efficient as full attention, high volume can compensate (AP × Hours = Total Acquisition)

Additional Notes

• Anki and focused study increase comprehensibility, raising the AP of all immersion activities
• Focused listening practice helps you acquire more, which increases the AP of future passive immersion
• Activities that improve any component have compound effects across your entire learning system

By using this equation, you can make objective decisions about what to watch, listen to, or read based on your current level and available time.