Squared Error
Squared error is the squared difference between predicted probability and outcome. It is the per forecast loss used in Brier score.
Definition
Squared error is (p - o)^2, where p is the predicted probability and o is the outcome (0 or 1).
Why it is used
Squaring makes large mistakes much more costly than small mistakes. That is why Brier score strongly penalizes confident wrong calls, especially when you are overconfident.
Examples
• p = 0.60, o = 1 -> squared error = 0.16
• p = 0.90, o = 0 -> squared error = 0.81
Related
Squared error is the building block of Brier score and connects to calibration analysis via bucket summaries.