chance level concept
| Definition | The value a rank statistic reaches on average under a random ranking. Zero for a correlation, one half for AUROC. Chapter 0 section 0.8. Also chance overlap, times chance. |
|---|---|
| Example | A constant score has AUROC 0.5, and recall at 10 from 100000 rows at random is 0.0001. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id chance-level, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation 0.38. |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/ChanceLevel.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation 0.38.
\[w=\max\big(0,\ 2\cdot\mathrm{AUROC}-1\big).\]
Conditions
- The value a rank statistic reaches under a ranking that carries no information. A constant score ties every pair, so its AUROC is one half when both classes are present, its Kendall correlation with any score is zero, and its reliability weight is zero.
- Every reading the probe reports comes with its chance overlap beside it, and a gate subtracts the chance level before it counts a margin.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Chapter 0 section 0.8 of Data Mining as Observation, with
the program’s chance-overlap reporting in
readscope/readscope/metrics.py:31-99.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/ChanceLevel.lean,
theorems aurocNum_const, auroc_const,
weight_const, tau_const, at
observation-data-mining f3914f0; what the check covers is stated in the
book’s appendix
C.
Used in
Data Mining as Observation primer S, chapters 0, 3, 6, 11.
Related
reliability weight; cross-corpus gate; Kendall correlation; harness.
See also
Book equations stated beside the entry’s terms, not defining it: 0.16, 0.15.
Status
Generated 2026-09-10 by encyclopedia/generate.py; book
at observation-data-mining f3914f0; the commit of every record is listed
in the encyclopedia’s provenance.