Reliability decomposition and its closure check

Read the components only after the closure check. The direct Brier score and the published ten-bin reconstruction do not close exactly. The reliability, resolution and uncertainty components are shown beside that remainder.

no packet verdict (descriptive exhibit)n = 27,351 MLB rows, 4,265 soccer rowsno intervalas of 2026-09-16murphy_decomposition.jsonas of 2026-09-16descriptive_only

quoted on 20 pages

Findings are exploratory unless a pre-registration file, date and hash are shown on the page.

How it was tested

Gate: descriptive: Murphy decomposition with a ten-bin reconstruction remainder
Corpora: data/cache/ingame_grade_joined/{mlb_segmented,soccer_intl_segmented}
Folds: none

Replication

single corpus

Inspector

Calibration inspector (bins and checkpoints)

This exhibit reports the direct Brier score alongside the published ten-bin reconstruction for each source. It does not assign the model-to-reference score difference to recalibration or any other single cause.

The published ten-bin reconstruction does not close identically for every measured sport, so its components do not establish a cause for the model-to-reference Brier difference.

Each reconstructed Brier is the published reliability minus resolution plus uncertainty. The signed remainder is derived as direct Brier minus reconstructed Brier; it is shown to make the ten-bin closure check inspectable.

MLB

Published denominators: 27,351 rows; each source has its own n below.

MLB published decomposition audit
Source	Direct Brier	Reconstructed Brier	Remainder (derived)	n rows	n	Reliability vs resolution
Model	0.166759	0.168327	-0.001568	27,351	27,351	Reliability is smaller than resolution (0.005619 vs 0.087187).
Market	0.151008	0.151258	-0.000250	27,351	27,351	Reliability is smaller than resolution (0.003425 vs 0.102062).

A non-zero remainder means the published ten-bin identity does not close for this sport. The artifact alone does not identify why; binning, population differences, rounding, or another published-data limitation are possible.

International soccer

Published denominators: 4,265 rows; each source has its own n below.

International soccer published decomposition audit
Source	Direct Brier	Reconstructed Brier	Remainder (derived)	n rows	n	Reliability vs resolution
Model	0.332522	0.366753	-0.034231	4,265	4,265	Reliability is larger than resolution (0.191982 vs 0.038714).
Market	0.195157	0.230310	-0.035153	4,265	4,265	Reliability is larger than resolution (0.088088 vs 0.071263).

Inspect the score decomposition and the calibration inspector for the related published views.

Limitations

Sample and independence: in-game rows repeat within games; counts are rows, not games.
Scope: MLB and international soccer in-game corpora.
Does not establish the cause of the model-to-reference score gap.

Verdict history

2026-09-16: current: no packet verdict (descriptive exhibit)

Findings