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Equation 1 · Part 11 · Futures Methods and Technological Scenarios in Practice: An Advanced Technical Guide

Numerator: 1

B=1N∑i=1N(pi−oi)2B = \frac{1}{N}\sum_{i=1}^{N} (p_i - o_i)^2
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What this part means

The complete quantity above the fraction bar.

Its job in the formula

1 occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

The Brier score is the mean squared error between a stated probability and the binary outcome (1 if it happened, 0 if it did not): B=1N∑i=1N(pi−oi)2B = \frac{1}{N}\sum_{i=1}^{N} (p_i - o_i)^2. where pip_i is the forecaster’s stated probability on question i and oio_i ∈\in \{0,1\} is the realized outcome. Lower is better; a perfectly calibrated coin-flip forecaster scores 0.25 on a 50/50 question, and a forecaster who says 100 percent and is wrong scores the maximum possible 1.0.

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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 article section

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