$$\kappa_i = \rho_i = 1$$

Equation 19 · Model Evaluation

Comparing Frontier Model Pricing Without Comparing Apples to Oranges

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Reading $p^{\text{in}}_i$ and $p^{\text{out}}_i$ off a rate card and comparing them directly across vendors is equivalent to assuming $\kappa_i$ , $\gamma_i$ , and $\rho_i$ are all equal to each other and to 1 across every vendor in the comparison. This article has just shown that one of those three, $\gamma_i$ , genuinely does converge close to 0.1 across all three companies’ published cards — the one term a naive comparison happens to get right by accident. The other two do not converge, are not published as clean multipliers by any vendor, and vary by content type and by task in ways that only measurement on the caller’s own workload can pin down. A price comparison that reports $p^{\text{in}}_i$ and…

Meanings in this article

• $\rho_i$: all equal to each other and to 1 across every vendor in the comparison.

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