protok

Value ranking methodology

protok ranks models by how much Artificial Analysis (AA) capability you get per dollar of output tokens. Raw benchmark scores are not treated as linear in difficulty, so the ranking uses an exponential linearization before dividing by price.

Eligibility

• Output price must be greater than zero.
• The selected AA composite score must be present and at least 40.

Why scores are not linear

AA composite indices compress a wide range of model capability into a bounded score. Moving from 40 to 60 is generally easier than moving from 70 to 90: higher scores represent disproportionately harder capability gains. Ranking by raw score / output$ therefore over-rewards mid-tier models relative to frontier ones.

Exponential fit

For each scan and metric, protok fits an exponential curve from the eligible scores in that scan:

• a = minimum eligible score
• b = ln(max / min) / 2 (floored at 0.01)

If fewer than three eligible scores are available, or the score range is tiny, the fit falls back to a near-identity mapping so rankings remain defined.

Linearization and value ratio

• Linearized score: L(s) = ln(s / a) / b (clamped at zero)
• Value ratio: L(s) / output price per 1M tokens

Models are sorted by value ratio descending. Input price and provider discount are shown for context; they do not change the ranking denominator.

Discount column

When OpenRouter reports a fractional pricing.discount, protok stores it and shows it as a percent off list. Applied input/output prices already include that discount (applied = base × (1 − discount)).