Rankings by format — specification

This specification was written before fitting the new format tables. The earlier ODI forecast comparison and its historical coefficients have already been seen. This is an exploratory extension, not a blinded confirmatory analysis.

Population and quantity

Estimate a regularized, player-only lineup association with match outcome for Tests, ODIs, and T20 internationals, separately for men and women. The first release uses matches starting after 26 October 2021 and completed by 26 October 2026. Every match has equal weight. All observed players in that window remain eligible, including players who have since retired. Scores summarize the window; they are not instantaneous form, causal effects, or wins above replacement.

Use official Cricsheet international archives and stable registry IDs. Require exactly eleven listed players per side and no recorded match replacements. Exclude no-results and incomplete matches. Retain Test draws and ties; restrict ODIs and T20Is to decisive outcomes. Source coverage and withheld matches limit the population. Record exclusions, match IDs, dates, hashes, and acquisition receipts.

Estimation

The predictor is the sum of side A’s player coefficients minus side B’s, plus signed toss-winner and batting-first controls. No team coefficients, interactions, venue adjustments, recency weights, or role-specific terms are included.

For decisive matches use ridge logistic regression with no intercept. For Tests with draws use a symmetric three-outcome multinomial model (the Davidson form):

\[ P(A\text{ wins}):P(\text{draw}):P(B\text{ wins}) = \exp(\eta/2):\nu:\exp(-\eta/2). \]

Implement symmetry by supplying both orientations of each match, each with weight one half. Multinomial logistic regression has opposite win/loss coefficient vectors, zero draw slopes, equal win/loss intercepts, and a free draw intercept. The published score is the win-minus-loss coefficient: additive in log win/loss odds, conditional on a decisive result. Draws affect estimation and predicted outcomes. A draw-free cohort uses the binary model. A cohort containing only draws cannot identify directional strength and receives no ranking.

Test ties share the draw category. Use half the stated C in the three-outcome estimator: its win/loss slopes are ±half the published score. This matches the binary model’s ridge penalty on the published score, \(\|\beta\|^2/(2C)\). The exported model records both the stated C and the estimator’s C. This convention was clarified during independent design review, before fitting the format tables.

Tune C over 0.01, 0.1, 1, 10 using the final year of the window as chronological validation and earlier completed matches as training. Exclude matches crossing the validation boundary from tuning. Use mean outcome log loss, preferring the smaller C on a tie; refit the selected model on the entire five-year window. Require at least 20 training and 10 validation matches and a decisive training outcome; when a cohort contains draws, require a training draw too. Otherwise use C=0.1, explicitly labeled untuned. These counts are operational tuning rules, not claims about adequate inferential precision. No new untouched test set is claimed.

Reporting and checks

Rank coefficients within each format, gender, and connected comparison group. Link groups through matches or shared players, and never rank disconnected groups against each other. Use competition ranks for numerical ties to twelve decimals. Publish all players, appearances, teams, last appearance, regularization, and identical-lineup diagnostics. Flag fewer than twenty appearances; this flag is descriptive and is not a selection threshold. Report sample sizes and tuning status beside each table. No rank intervals or significance claims are produced.

Player-only models avoid the additional team-versus-player allocation ambiguity, but stable teammates and unmeasured team conditions still confound attribution. Connectedness is necessary, not sufficient, for independently identifying players. Scores have meaning within a fit, not across formats or genders. A larger player coefficient is a model association, not proof of superiority in every context. The Test model uses a common draw propensity; weather and playing conditions can also cause draws and are not modeled separately.

The T20 preparation starts at the ranking window boundary. This excludes an older source identity conflict (match 1229824, 21 August 2020, the same J Butler ID on both sides) without assigning an invented identity. Every excluded file retains its hash and date-exclusion status in the preparation manifest. Included records still fail validation on identity conflicts.

Before publication test side-swapping symmetry, preservation of match weight, binary agreement with the existing estimator, recovery in synthetic draw data, chronological boundaries, format/gender separation, disconnected groups, and provenance integrity. Obtain an independent review of the design and code. Preserve the earlier ODI experiment and publication unchanged.

References: Cricsheet JSON, Davidson (1970), and scikit-learn logistic regression.