Symbol B
B is part of the quantity the equation computes from the expression on the right.
Read this term in its guide →Published equation contexts
Why this formula appears here
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): . where is the forecaster’s stated probability on question i and \{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 the representative guide
Symbol N
N occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Read this term in its guide →Symbol i
i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Read this term in its guide →Symbol p_i
the forecaster’s stated probability on question i and \{0,1\} is the realized outcome.
Read this term in its guide →Symbol o_i
is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Starting index or lower bound: i=1
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.
Read this term in its guide →Ending index or upper bound: N
This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.
Read this term in its guide →How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
Research cited beside this formula
- [2] Expert Political Judgment: How Good Is It? How Can We Know? ↗
- [3] Strictly Proper Scoring Rules, Prediction, and Estimation ↗
- [7] A Primer on the Metaculus Scoring Rule ↗
- [1] Identifying and Cultivating Superforecasters as a Method of Improving Probabilistic Predictions ↗
- [4] Aggregative Contingent Estimation (ACE) Program ↗
Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 1 · Future Studies
Futures Methods and Technological Scenarios in Practice: An Advanced Technical Guide
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
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): . where is the forecaster’s stated probability on question i and \{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.