What is this all about?

The Brier score is a mathematical representation that reflects the accuracy of a prediction at a given time interval. It is essentially the squared error of a probabilistic forecast. The lower the Brier Score, the more accurate the prediciton. A score of 0 indicates perfect predictions, while a score of 1 indicates that the predictions are always incorrect.

To calculate the Brier Score, we divide the forecasted prediction (0-100%) by 100 so that the probabilities are converted into a range between 0 (0%) and 1 (100%).

Next, we define the Ground Truth as either 0 (if the event did not happen) or 1 (if the event did happen).

We then subtract the actual outcome (0 or 1) from the predicted forecast (a number from 0 to 1).

The result of the subtraction is squared and the final result is the Brier Score for that prediction.

If the user made several predictions at different time intervals, the squared errors are averaged to provide a final Brier Score result.

Example: A user predicts that there is a 20% probability that GE stock will exceed $20 by MM/DD/YYYY. On day MM/DD/YYYY, the stock has not exceeded the threshold value.

• The Ground Truth (ο) is "0". The event did NOT occur.
• The Predicted Outcome (ƒ) is then 20 ÷ 100 → 0.2
• Then, 0.2 - 0 → 0.2
• Finally, (0.2)² → 0.04
• The Brier Score for this single instance would be: 0.04