Extreme Probabilities
Extreme probabilities are forecasts near 0% or 100%. They can be valuable when justified, but they create large penalties when wrong.
Definition
Extreme probabilities are forecasts close to 0 or 1, such as 0.98 or 0.02. They represent very high confidence.
Why they are risky
Extreme calls amplify scoring penalties when you are wrong:
• In Brier score, squared error grows quickly.
• In log loss, penalties can explode without probability clipping.
When they are appropriate
• The base rate is truly extreme (for example, an event almost never happens).
• You have strong direct evidence that shifts odds far away from the prior.
Related
Extreme probabilities are closely tied to overconfidence and to the tradeoff between sharpness and calibration.