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
A different style of evaluation sidesteps fixed question sets altogether by asking humans which of two anonymized model outputs they prefer, on real conversational prompts, and aggregating millions of these paired judgments into a ranking. Chatbot Arena, the platform behind this approach, describes itself as using “a pairwise comparison approach” that “leverages input from a diverse user base through crowdsourcing,” with the underlying statistics resting on a standard paired-comparison model rather than a raw win count [ 6 ] . The relevant object is a Bradley–Terry model: each system i is assigned a latent strength , and the estimated probability that system A ’s output is preferred…
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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
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 →Symbol e^-(theta_A - theta_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 + e^-(theta_A - theta_B)
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 5 · Model Evaluation
Frontier AI Model Comparisons: A First-Principles Introduction
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
A different style of evaluation sidesteps fixed question sets altogether by asking humans which of two anonymized model outputs they prefer, on real conversational prompts, and aggregating millions of these paired judgments into a ranking. Chatbot Arena, the platform behind this approach, describes itself as using “a pairwise comparison approach” that “leverages input from a diverse user base through crowdsourcing,” with the underlying statistics resting on a standard paired-comparison model rather than a raw win count [ 6 ] . The relevant object is a Bradley–Terry model: each system i is assigned a latent strength , and the estimated probability that system A ’s output is preferred…
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