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Equation 6 · Part 2 · From Origins to Frontier: A History of Frontier AI Model Comparisons

Symbol A

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

What this part means

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

Its job in the formula

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

The passage around this formula

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…

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Learn the underlying idea

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

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