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Equation 6 · Part 3 · From Origins to Frontier: A History of Frontier AI Model Comparisons

Symbol B

P(A≻B)=11+10−(RA−RB)/400.P(A \succ B) = \frac{1}{1 + 10^{-(R_A - R_B)/400}}.
BB

What this part means

modeled as a logistic function of the difference between two scalar ratings: [displayed formula].

Its job in the formula

B occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Where the article explains it

Pairwise votes of this kind are naturally converted into a single continuous rating using a Bradley–Terry-style model — the same functional form used for chess Elo ratings — in which the probability that a rater prefers system A over system B is modeled as a logistic function of the difference between two scalar ratings: P(A≻B)=11+10−(RA−RB)/400P(A \succ B) = \frac{1}{1 + 10^{-(R_A - R_B)/400}}.

The passage around this formula

…kind are naturally converted into a single continuous rating using a Bradley–Terry-style model — the same functional form used for chess Elo ratings — in which the probability that a rater prefers system A over system B is modeled as a logistic function of the difference between two scalar ratings: P(A≻B)=11+10−(RA−RB)/400P(A \succ B) = \frac{1}{1 + 10^{-(R_A - R_B)/400}}. That formula encodes a specific, testable assumption: that pairwise preference between any two systems can be explained by each system’s position on one shared scale, and that preferences are…

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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