Equation 1 · Part 4 · Futures Methods and Technological Scenarios in Practice: An Advanced Technical Guide

Symbol p_i

B = \frac{1}{N}\sum_{i=1}^{N} (p_i - o_i)^2

p_i

What this part means

the forecaster’s stated probability on question i and $o_i$ $\in$ \{0,1\} is the realized outcome.

Its job in the formula

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

Full expressionSymbol p_iArticle meaning

Where the article explains it

where $p_i$ is the forecaster’s stated probability on question i and $o_i$ $\in$ \{0,1\} is the realized outcome.

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): $B = \frac{1}{N}\sum_{i=1}^{N} (p_i - o_i)^2$ . where $p_i$ is the forecaster’s stated probability on question i and $o_i$ $\in$ \{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 subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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