Symbol P
P is part of the quantity the equation computes from the expression on the right.
Read this term in its guide →Published equation contexts
Why this formula appears here
The response, arriving in 2023, was to stop checking against a fixed answer and start recording a preference between two outputs instead. Chatbot Arena built an open platform in which users submit a prompt, receive responses from two anonymized models side by side, and vote for the one they prefer, without knowing which model produced which response; its authors reported collecting more than 240,000 such votes from a broad user base and validated that crowdsourced preferences agreed well with those of a separate panel of expert raters [ 12 ] . Pairwise votes of this kind are naturally converted into a single continuous rating using a Bradley–Terry-style model — the same functional form used…
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Symbol A
A occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Read this term in its guide →Symbol B
modeled as a logistic function of the difference between two scalar ratings: [displayed formula].
Read this term in its guide →Symbol R_A
occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Read this term in its guide →Symbol R_B
occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Read this term in its guide →Denominator: 1 + 10^-(R_A - R_B)/400
The complete quantity below the fraction bar; it must be nonzero for this division.
Read this term in its guide →How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
Research cited beside this formula
Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 6 · Model Evaluation
From Origins to Frontier: A History of Frontier AI Model Comparisons
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
The response, arriving in 2023, was to stop checking against a fixed answer and start recording a preference between two outputs instead. Chatbot Arena built an open platform in which users submit a prompt, receive responses from two anonymized models side by side, and vote for the one they prefer, without knowing which model produced which response; its authors reported collecting more than 240,000 such votes from a broad user base and validated that crowdsourced preferences agreed well with those of a separate panel of expert raters [ 12 ] . Pairwise votes of this kind are naturally converted into a single continuous rating using a Bradley–Terry-style model — the same functional form used…