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Equation 1 · Part 13 · Futures Methods and Technological Scenarios in Practice: An Advanced Technical Guide

Ending index or upper bound: N

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

What this part means

This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.

Its job in the formula

N 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 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

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

Open the illustrated sums and products: repeat an operation over an index guide →

See this notation across published equations →

Sources cited in the article section

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