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Equation 6 · Part 7 · From Origins to Frontier: A History of Frontier AI Model Comparisons

fraction

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

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