Per-Outcome Baseline Normalization Makes Proper Forecast Scores Improper

We show that dividing a forecast’s score by a baseline’s score on the same realized outcome makes a proper scoring rule improper: in expectation, a forecaster who knows the true distribution can score better by reporting a different one. Agenthon 2026 Track 2 scores probabilistic financial forecasts with the continuous ranked probability score (CRPS), a variogram score and tail quantile losses, each divided by the same component of a text-blind random-walk baseline, whose method is published, on the same outcome. That division weights each outcome by the inverse of the baseline’s error, so the best report shifts probability toward out- comes the baseline happened to predict well, and it can be computed by any entry that rebuilds the baseline. We test this in two pre-registered analyses. In a one- dimensional simulation where the belief is the truth and the truth is twice as wide as the baseline, the truthful forecast scores 1.22, worse than the baseline’s 1.00, while the tilted forecast scores 0.99; on a scale fixed before the outcome the order reverses (2.00 against 2.44). On 67 practice tasks, our entry’s reporting rule beats its own honest report by 0.137 on the leaderboard’s scale and loses by 0.578 on the fixed scale, though a few tasks carry most of the gain. We propose normaliz- ing each task by a scale fixed before the outcome, such as the baseline’s expected score under its own distribution.