Probability & Forecasting Glossary

Base Rate

A base rate is the background frequency of an event occurring within a reference class of similar situations, before any case-specific evidence is considered. It serves as the starting probability for Bayesian reasoning.

Brier Score

The Brier score is a numerical measure of the accuracy of probabilistic predictions, calculated as the mean squared difference between a forecast probability and the actual binary outcome. Lower scores indicate better forecasts, with 0 being perfect and 1 being maximally wrong.

Calibration

Calibration measures how well a forecaster's stated probabilities match the actual frequency of outcomes. A forecaster who assigns 70% probability to events should see those events occur approximately 70% of the time.

Forecast Aggregation

Forecast aggregation is the process of combining multiple individual probability estimates into a single composite forecast, typically to improve accuracy by canceling out individual errors and incorporating diverse information.

Log Score

The log score is a strictly proper scoring rule that evaluates probabilistic forecasts by taking the negative logarithm of the probability assigned to the outcome that actually occurred. Higher (less negative) scores indicate better forecasts.

Overround

Overround is the amount by which the sum of implied probabilities across all outcomes in a market exceeds 100%, representing the bookmaker's or platform's built-in margin. An overround of 110% means the house has a 10% edge embedded in the prices.

Posterior Probability

Posterior probability is the updated probability of an event after incorporating new evidence into a prior belief, calculated using Bayes's theorem. It reflects the rational revision of confidence in light of new information.

Prior Probability

Prior probability is a forecaster's initial estimate of an event's likelihood before incorporating new evidence, typically anchored to historical base rates or expert knowledge. It is the starting point for Bayesian probability updating.

Vig

Vig (short for vigorish, also called juice) is the fee or margin built into market odds that ensures the house or platform profits over time, regardless of which outcome occurs. It is the cost of participating in a market.

Wisdom of the Crowd

Wisdom of the crowd is the phenomenon where the aggregated judgments of a large, diverse group of independent individuals produce more accurate estimates than most or all of the individual members. It is a core theoretical justification for prediction markets.