Athletic Vector Rankings: A Fixed Ensemble and Its Potential Predictive Edge

1. The fixed rating

Let L_i be team i’s neutral Lean C1 strength, I_i its role-adjusted strength, and H_i its robust scoreboard strength on the same scale. The frozen 2026 issue is:

The output is a scalar ordering of estimated team strength. A display transformation or tier does not turn it into a calibrated win probability or a rule for awarding playoff places. The name Athletic Vector Rankings describes the multivariate inputs and their projection into this ordering; the published team rating itself remains scalar.

Lean C1

Lean C1 uses 247 encoded inputs and regularized pairwise logistic learning. Inputs cover opponent-adjusted team performance, internal strength components and observed personnel descriptors. Training gives greater weight to games between teams of similar prior strength. Neutral published strength omits the fitted venue term. The Lean C1 paper specifies its encoding, earlier-only annual learning and exact fallback policy. Bradley–Terry-style pairwise modeling is an established approach [1]; no novelty is claimed for this general model class.

Observed role correction

I_i = L_i + x_i^Tc uses eight descriptors: quarterback performance Q; offensive-line true-pass protection P; gap and zone run-blocking performance G and Z; a soft-minimum protection descriptor B; observed gap share v; interaction QP; and scheme-weighted blocking vG + (1 − v)Z. Native quarterback and guard/tackle/center records, their facet exposures and source identities define these quantities.

Player performance uses the current and two preceding seasons, with exposure weighting and a 180-day half-life. Deployment shares use the last three observed admissible team games within 365 days. This is an observed-source window, not a guarantee of a complete three-game schedule. Ambiguous latest team membership or missing positive exposure in any required facet suppresses the correction. A regularized logistic fit learns c with Lean’s pairwise gap as an offset; its venue coefficient is omitted from the neutral issued rating.

These descriptors concern measured performance and deployment. PFF explicitly distinguishes its grades from innate talent, and season grades are not simple averages of game grades [2]. Recent observed participation does not certify availability for the next game. This frozen correction adds no new injury-based replacement-share adjustment.

Robust scoreboard component

The scoreboard model estimates point strengths θ and a venue term h by minimizing:

Here m is the uncapped final scoreboard margin, v indicates a nonneutral venue, σ is an earlier-fitted residual scale, and ρ is Huber’s quadratic loss near zero with linear tails. The frozen current rule uses δ = 2, τ = 12 and no time-evolving latent strength. All admitted games have unit weight. Team means μ come from a frozen earlier strength reference converted to points; additional lower-division nodes use the declared earlier population rule. The prior and likelihood do not overlap.

Only explicitly completed games with authenticated identities, final scores, venue and admissible clocks enter the current likelihood. A 24-hour completion buffer supplements the source clock; it does not prove a historical publication time. H_i = θ_i/b uses the positive earlier point-conversion slope b. Unsupported calibration retains Lean exactly; declared source-support fallbacks suppress a component rather than manufacturing values. Numerical failure is preserved as failure, not relabeled as missing-source fallback. Positive quadratic penalties give a unique mathematical minimizer, but approximate stationarity cannot certify the ordering of nearly tied teams.

2. Why an edge is plausible

The potential advantage is that three partially different measurements may correct one another: Lean summarizes a broad team profile, role inputs describe quarterback/protection and run-blocking deployment, and robust scoreboard fitting connects actual scoring performance across opponents while limiting the influence of extreme residuals. Partial weights constrain the departure from the broad baseline.

This is a hypothesis, not a demonstrated causal explanation. Components share games and personnel observations; their errors need not be independent. A scoreboard component can be useful inside a combination even when it performs worse alone, but that possibility must be tested. The external rating values themselves are comparators, not inputs to this ensemble.

3. Historical evaluation

The frozen evaluation bank contains 7,717 decisive FBS-versus-FBS games from August 27, 2016 through September 20, 2026, including only 157 games from 2026. Each game is associated with its original weekly origin. Ordering loss is one when the higher-rated team loses, one-half for an exact rating tie, and zero otherwise. It evaluates neutral strength ordering; it is not a venue-adjusted betting forecast.

The historical ensemble is an earlier-selected annual procedure. Each year selects α and β from {0, 0.1, 0.25} using the preceding year’s ordering errors; ties prefer smaller total correction, then smaller β, then smaller α. Unsupported years retain Lean. Historical Huber settings and component heads likewise retain their original earlier-qualified choices. Consequently, the reported 2,109 errors do not measure imposing the 2026 quarter/quarter settings on every historical season.

Both teams must come from the same admitted external edition. Matching retains exact game identity, origin, teams and raw outcome. Editions require qualified clocks and at most ten days’ information age. Newly recovered editions require availability strictly before the origin; the original qualified legacy bank retains its existing inclusive boundary. Source rejections and exclusions remain recorded. Massey Power has zero eligible pairs in this bank and is distinct from MAS; this is not a claim that no Massey Power data exist elsewhere.

Uncertainty uses paired losses and two declared 20,000-draw resampling schemes: UTC calendar-week clusters and football-season/week hierarchical clusters. Individual intervals exclude zero in the favorable direction against MAS, Colley, FEI and CFBD Elo. Both schemes leave the smaller FPI, SP+ and Sagarin-family differences unresolved. These individual comparisons do not establish simultaneous superiority over every external system, and their intervals do not include the uncertainty of the preceding adaptive research program.

Colley uses wins, losses and schedule adjustment and explicitly emphasizes championship deservedness rather than pure predictiveness [3]. Its ordering result therefore does not settle whether AVR better assigns playoff places.

4. Adverse evidence and tested alternatives

Earlier alternatives remain part of the record. The static/dynamic Student-t scoreboard variants each recorded 2,197 errors, and standalone Huber recorded 2,199, versus Lean’s 2,128. The ensemble’s separate FCS transport evaluation recorded 1,637 errors over 5,991 matched games, versus 1,633 for Lean; both uncertainty schemes include zero. This supplies no demonstrated FCS gain or full-FCS coverage claim.

The first intervention preserves each annual choice and halves its corrections. The second zeroes team prior means while retaining quadratic regularization, the original other settings and annual ensemble choices; it does not remove all historical information from Lean. Neither improves the observed ordering or margin measures. Both paired uncertainty schemes include zero, so neither clear harm nor equivalence is established. Six AI expert-lens result ballots recommend retaining the ensemble; these are recorded analytical reviews, not human industry endorsements or external peer review.

5. Prospective evaluation and publication

The prospective model carries its frozen 2026 Lean coefficients, component-selector weights, role coefficients, calibration and team-prior reference forward into 2027. There is no annual coefficient refit or weight reselection during this study. New admissible observations refresh strengths under those equations; the Huber likelihood accumulates completed games since the frozen 2026 prior, rather than resetting to a newly learned 2027 prior. This is deliberately different from the earlier-selected annual procedure evaluated in the historical tables.

The prospective question is whether the frozen current ensemble improves future ordering on identical games relative to each external product. The historical bank cannot answer it. A valid issue must be durably captured before kickoff with model identity, source identities, exact team strengths, matchup identity and issue time. External editions require the same treatment. The issue selects the first successful capture within 60 minutes before kickoff. The ensemble is a published weekly board, with both its original computation and source cutoff at most ten days old; external editions have the same ten-day age limit. Capturing that board again preserves its original clocks and does not imply a new fit before every kickoff. A provider gap stays a documented gap; a post-kickoff capture cannot be backdated into eligibility. Coverage and exclusions must accompany performance.

The prospective protocol was frozen in the normal database on October 14, 2026 at 21:49:49 UTC, before the first eligible kickoff. Its SHA-256 identifier is c8b949b882362630fbfe1ae631ce3b967cc720597480ea3947b4ce394ab3407c. Earlier unused protocols are preserved; no predictions were issued under them.

The primary outcome remains neutral ordering loss. Margin error is secondary where a genuine native point prediction exists; ordinal vendor ranks are not converted into invented point margins. The prospective design freezes 12 external products, including Massey Power even when coverage is missing, requires at least a 0.5-percentage-point advantage for a meaningful superiority claim, and permits the final analysis only on or after February 1, 2028, following the 2027 season’s playoffs. Both calendar-week bootstrap and crossed-team sensitivity upper bounds must clear that threshold using one-sided Bonferroni adjustment across all 12 products. A comparator also needs at least 500 paired games, 20 calendar weeks and 30 teams; otherwise its result remains inconclusive. There is no stop-on-significance rule; progress reports do not permit weight changes or repeated opportunities to declare success. This paper reports no prospective outcomes. Operational capture, scheduling and deployment receipts are distinct from evidence that the model has gained accuracy.

Site archives regenerated with this release are reconstructed editions of this model. They are useful for a consistent site history, but their present-day computation and source vintages must remain visible. They cannot be counted as predictions sealed before the original kickoff. The immutable prospective ledger must remain separate from those regenerated archives.

6. Limitations and conclusion

All reported historical seasons are development evidence. Many retained provider records were recovered or captured after their nominal historical week. Event-time filtering and completion buffers reduce outcome leakage but cannot reconstruct a publication clock that was never preserved. Model selection on finite data can itself overfit [4]. The enhanced comparator bank improves coverage without eliminating those limitations.

The evidence supports a narrower conclusion than universal superiority: the ensemble is a reproducible candidate with favorable historical point estimates and no successful replacement among the two tested interventions. Prospective validation remains necessary, especially against the closest predictive comparators. Ratings near a boundary should not be presented as certain, and strength should remain distinct from résumé merit. Production adoption is an operational choice, not a statistical finding.

Disclosure

Andy Volpe develops AVR. This owner-directed working paper uses immutable normal-database research evidence and independent computational checks. AI expert-lens reviews are disclosed as such. Provider raw records and proprietary grades are not reproduced. Version: October 14, 2026.

References and evidence

1. Turner, H., and Firth, D. (2012). Bradley–Terry Models in R: The BradleyTerry2 Package. Journal of Statistical Software, 48(9).
2. PFF. Player grades: methodology, facets and interpretation.
3. Colley, W. N. The Colley Matrix Method.
4. Cawley, G. C., and Talbot, N. L. C. (2010). On Over-fitting in Model Selection and Subsequent Selection Bias in Performance Evaluation. Journal of Machine Learning Research, 11, 2079–2107.
5. Volpe, A. (2026). Lean C1: A Regularized Team-Strength Rating for College Football.

Private reproducibility record: normal DuckDB immutable family private:rating-thinktank-overnight:20261013:, objects enhanced-external:v3:results and :verification, panel-tweaks:v1:results and :verification, enhanced-panel:v2:result-ballots, and enhanced-owner-review:v1:report. These are evidence identifiers, not public download links.