Strictly Proper Scoring Rules, Prediction, and Estimation

Main finding

Explains why strictly proper scores such as the Brier and logarithmic scores reward honest probability forecasts.

Limitations

Theory; does not address betting returns.

Study details

Authors

Tilmann Gneiting, Adrian E. Raftery

Published

2007

Venue

Journal of the American Statistical Association 102(477), 359–378

Status

Published

Evidence type

Peer-reviewed theory

Evidence strength

Strong (our assessment of how much weight the finding can bear)

Sport

None

Markets

None

Method

A unified review and theory of proper scoring rules for probabilistic forecasts.

Sample

Not applicable.

Replication

Standard reference.

Read the original

doi:10.1198/016214506000001437 (opens in a new tab)

Our summary is an original paraphrase for education. Verification: Bibliographic record checked against publisher, index or author listings. Checked 2026-10-25.