Equation 1 · Part 12 · Futures Methods and Technological Scenarios in Practice: An Advanced Technical Guide

Starting index or lower bound: i=1

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

i=1

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

i=1 appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Full expressionStarting index or lower bound: i=1Article meaning

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.

Read this part in the article →

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 →

Sources cited in the article section

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