# Forecast skill

Skill in forecasting (or skill score,[1] forecast skill, prediction skill) is a scaled representation of forecast error that relates the forecast accuracy of a particular forecast model to some reference model.

 Mean squared error (MSE) $\ \mathit{MSE} = \frac{\sum_{t=1}^N {E_t^2}}{N}$ Forecast skill (SS) $\ \mathit{SS} = 1- \frac{\mathit{MSE}_\text{forecast}}{\mathit{MSE}_\text{ref}}$

A perfect forecast results in a forecast skill of 1.0, a forecast with similar skill to the reference forecast would have a skill of 0.0, and a forecast which is less skillful than the reference forecast would have negative skill values.[2][3]

## References

1. ^ Glossary of Meteorology, American Meteorological Society
2. ^ Roebber, Paul J. (1998), "The Regime Dependence of Degree Day Forecast Technique, Skill, and Value", American Meteorological Society -- Weather and Forecasting (Allen Press) 13 (3): 783–794, Bibcode:1998WtFor..13..783R, doi:10.1175/1520-0434(1998)013<0783:TRDODD>2.0.CO;2, retrieved 2009-01-19
3. ^ Murphy, Allen H. (1988), "Skill Scores Based on the Mean Square Error and Their Relationships to the Correlation Coefficient", American Meteorological Society -- Monthly Weather Review (Allen Press) 116 (12): 2417–2424, Bibcode:1988MWRv..116.2417M, doi:10.1175/1520-0493(1988)116<2417:SSBOTM>2.0.CO;2, retrieved 2009-01-19