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Equation 6 · Part 12 · From Origins to Frontier: A History of Frontier AI Model Comparisons

Numerator: 1

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

What this part means

The complete quantity above the fraction bar.

Its job in the formula

1 is one of the signed contributions combined to compute the quantity on the left.

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.

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Sources cited in the surrounding passage

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