Research

Findings, with
the script attached.

Every hypothesis that was registered, the verdict it came back with, and the committed script that produces it. The nulls are published with the rest.

Brier gap, model − market · positive is worse

+0.0142

The interval excludes zero, only just: its low end is +0.0007.

95% interval 0.0007 to 0.0263.

Calibration

925 predictions over 14 games, scored against what happened in 20 bins, with the counts shown.

Brier score, model

0.1845

Calibration error, model

0.0658

Predictions, settled

925

Games

Log loss, the calibration slope and the week-by-week record: coming once research/calibration.json carries them.

Calibration, model against market

On the common set the Brier strip on Studies scores, the model’s expected calibration error is 0.0658 and the exchange mid’s is 0.0502.

How this is computed

Expected calibration error: how far a stated probability sits from the rate that followed it. Lower is closer.

Model and market calibration

Brier on this set: model 0.1845, market 0.1703, naive 0.1833.

Reliability, model against market

research/score.py (brief 021) · Wilson 95% · generated Tue, Oct 13, 9:27 AM ET

NFL week 1 2026, KXNFLREC + KXNFLRSHATT, common set n=925, 14 games. All three scores and both intervals are computed on this one set of 925 predictions.

model (ECE 0.0658)market (ECE 0.0502) identityhollow = n < 30, not a data point

Wilson 95% intervals. Brier: model 0.1845, market 0.1703, naive 0.1833; model − market +0.0142 [0.0007, 0.0263]. Source: research/score.py (brief 021).

Series	Bin	n	Forecast	Realized	Wilson 95%
model	0.0–0.1	235	0.049	0.102	[0.070, 0.147]
model	0.1–0.2	142	0.147	0.232	[0.171, 0.308]
model	0.2–0.3	134	0.250	0.269	[0.201, 0.349]
model	0.3–0.4	95	0.351	0.474	[0.376, 0.573]
model	0.4–0.5	83	0.446	0.530	[0.424, 0.634]
model	0.5–0.6	80	0.547	0.512	[0.405, 0.619]
model	0.6–0.7	63	0.647	0.619	[0.496, 0.729]
model	0.7–0.8	39	0.749	0.590	[0.434, 0.729]
model	0.8–0.9	43	0.833	0.907	[0.784, 0.963]
model	0.9–1.0	11	0.924	0.818	[0.523, 0.949]	not a data point
market	0.0–0.1	289	0.043	0.073	[0.048, 0.108]
market	0.1–0.2	114	0.148	0.219	[0.153, 0.304]
market	0.2–0.3	89	0.237	0.281	[0.198, 0.382]
market	0.3–0.4	71	0.350	0.479	[0.367, 0.593]
market	0.4–0.5	133	0.454	0.556	[0.472, 0.638]
market	0.5–0.6	85	0.550	0.553	[0.447, 0.654]
market	0.6–0.7	58	0.639	0.638	[0.509, 0.750]
market	0.7–0.8	50	0.746	0.760	[0.626, 0.857]
market	0.8–0.9	36	0.836	0.889	[0.747, 0.956]
market	0.9–1.0	0	—	—	—	not a data point