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Equation 2 · Part 6 · What Claude's Capability Evaluations Actually Measure

fraction

p(t)=11+exp⁡(a+blog⁡t),p(t) = \frac{1}{1 + \exp\left(a + b \log t\right)},
fraction

What this part means

Divide the expression above the line by the one below it.

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

The passage around this formula

The method is a curve fit, not a lookup table, and stating it plainly exposes the assumption it rests on. For a task of human-expert duration t , METR fits a logistic curve to the model’s observed success rate across many tasks of varying length: p(t)=11+exp⁡(a+blog⁡t)p(t) = \frac{1}{1 + \exp\left(a + b \log t\right)}. with b > 0 , so predicted success falls as human-equivalent task length grows. The reported time horizon TxT_x at success level x is then the duration at which the fitted curve crosses that threshold, i.e. the t solving p(t) = x . Two things follow directly from this formulation that a single reported number obscures: the curve, not the crossing point, is the actual result, and a different chosen threshold x produces a different…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

Open the illustrated fractions: division written vertically guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.