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DEFINITION OF THE BRIER SCORE

Suppose it is required to give a probability Pi forecast of a binary event – such as a forecast of rain. The forecast issued says that there is a probability Pi that the event will occur. Let Xi = 1 if the event occurs and Xi = 0 if it doesn’t.

Then the Brier score is given by: B = (Pi-Xi)^2.

  • If you forecast 100% (Pi = 1) and there is at least 0.01 inches of rain in the bucket, your Brier Score is 0, or "perfect".

  • If you forecast 100% Pi and there is no rain in the bucket, your Brier Score is 1, or "awful".

  • If you forecast 70% Pi and there is at least 0.01 inches of rain in the bucket, your Brier Score is (0.70-1)^2 = 0.09, or "not too shabby".

  • If you forecast 30% Pi and there is at least 0.01 inches of rain in the bucket, your Brier Score is (0.30-1)^2 = 0.49, or "needs work".

  • If you hedge your forecast with a 50% Pi and whether or not there is at least 0.01 inches of rain in the bucket, your Brier Score is 0.25, or "no courage".


In weather forecasting, a trace (<0.01) is considered "0.0"


REFERENCES

  • [http://armstrong.wharton.upenn.edu/dictionary/definitions/brier%20score.html J. Scott Armstrong, ''Principles of Forecasting''].

  • [http://amsglossary.allenpress.com/glossary/browse?s=b&p=43 AMS Glossary of Meteorology]