Athletic Vector Rankings: A Framework for Rating Division I Football

Abstract

Athletic Vector Rankings (AVR) combines game results, drive performance and team-unit evidence on a common Division I strength scale, with fixed tiers for interpretation. We evaluate its current rating framework through a retrospective, completion-buffered reconstruction and qualified historical editions of FPI, Massey’s published ranking (MAS), Sagarin Rating and SP+/S&P+. The principal weekly arm made 123 fewer ordering errors than MAS on 7,045 matched games, an advantage retained under season-level resampling. On the 3,465-game all-four common sample, AVR made 942 errors versus 921, 1,003, 936 and 935 respectively. The evidence does not establish performance within one percentage point of all four products. Separate rating-derived margin comparisons favor FPI and Sagarin; the Massey advantage is sensitive to resampling, and author SP+ is inconclusive. AVR has a defensible measurement and classification framework, with a specific historical ordering advantage rather than demonstrated universal superiority.

Keywords: college football; team ratings; opponent adjustment; tiers; matched evaluation

1. Rating framework

A strength rating estimates performance relative to opposition. Record alone cannot distinguish programs facing unequal schedules. AVR combines regularized, opponent-adjusted estimates informed by results, drive observations and offensive–defensive unit grading. Recent evidence receives greater emphasis; earlier seasons support sparse current-season estimates. Component selection uses earlier evaluated outcomes.

These complementary measurements can reduce reliance on a noisy final score, but correlated inputs and repeated selection can also amplify historical noise. Cross-division games connect FBS and FCS teams on a shared scale; sparse connections limit certainty. These are methodological reasons to investigate AVR, rather than proof of accuracy. This paper addresses team ratings and their direct ordering and point interpretations; player ratings, résumé rankings and the game simulator are outside its scope.

2. Scale and tiers

AVR’s underlying rating is expressed in point-scaled strength units centered on the rated Division I population. The separate 0–100 display index aids readability and is not a win probability. Fixed v1.1 tiers classify the underlying points. Interior subtiers are six points wide, with open-ended extremes.

Tiers communicate broad separation while discarding information. Nearly equal ratings can fall on opposite boundaries; a one-tier difference does not always imply a six-point team gap. Tier labels are neither confidence intervals nor calibrated probabilities.

3. Comparators and study design

The four named products are ESPN FPI, Massey’s own published ordinal ranking (MAS), Sagarin’s overall Rating and Connelly’s SP+, including historical S&P+. FPI’s published objective is predictive strength. Massey’s description distinguishes résumé-oriented Rating from predictive Power; our MAS ordering comparison does not establish superiority to Power. Sagarin Rating is distinct from Predictor. General opponent adjustment is established practice; this paper makes no novelty claim for it.

The target comprises 7,717 FBS-versus-FBS games from 2016 through September 20, 2026. The weekly reconstruction was designated principal before corrected scoring; daily and calendar-postseason reconstructions are sensitivities. The latter addresses a literal postseason-week convention that can hold one board for 21–37 days. No arm was selected for favorable results.

Training results, game observations, grades and selector outcomes require a conservative 24-hour completion buffer. Each comparator uses its latest qualified edition available at the common evaluation origin, with an information age of at most ten days. Unknown publication clocks and four Sagarin Starting Ratings editions with unknown information dates are excluded explicitly. Genuine recovered records and native source bytes were stored in the normal database and verified through the actual consumer.

The primary endpoint is raw published-ordering error, without a venue adjustment: a stronger team losing contributes one error, an exact rating tie one-half, and scoreboard ties are excluded. Uncertainty uses 20,000 paired UTC calendar-week resamples, with season-then-week resampling as sensitivity. Four-family upper bounds govern superiority and a predeclared one-percentage-point noninferiority tolerance. A bound below zero supports fewer errors; below +1 pp supports practical noninferiority. An interval including zero does not prove equality.

4. Ordering results

On the all-four common cohort, AVR’s error rate was 27.19%. Differences against FPI, Sagarin and SP+ were small, but their simultaneous upper bounds exceeded +1 pp. Thus neither all-four noninferiority nor all-four superiority is established. The ordinary Massey advantage on this cohort loses its superiority designation under hierarchical resampling.

The larger pairwise cohorts give a stronger, product-specific Massey result: AVR made 1,941 errors versus 2,064 for MAS, or 123 fewer (−1.75 pp). Both upper bounds remain below zero. FPI and Sagarin meet the one-point tolerance under ordinary week resampling, but fail it under hierarchical sensitivity. SP+ fails the ordinary criterion as well.

The Massey advantage is not uniform across years. In 2025 AVR made 233 errors versus 230 across 808 matched games; in partial 2026 it made 35 versus 27 across 157. Both sensitivities retain the broad pattern of a Massey ordering advantage and no all-four noninferiority conclusion.

5. Point-consumer results

A separate analysis compares AVR’s fixed, earlier-only point conversion with genuine published game margins. AVR’s weekly MAE is higher than FPI and Sagarin, with both individual paired and hierarchical intervals above zero. The smaller Massey MAE favors AVR under ordinary resampling but becomes inconclusive hierarchically. Author SP+ margins are inconclusive under both approaches.

The author SP+ comparison covers five seasons. The four-consumer common sample contains only 1,154 games, versus 7,492 for the three other consumers. Cohort differences preclude ranking the maximal-sample MAEs against each other. Complete common-sample and per-season results, RMSE, signed bias, winner errors, both sensitivities, exploratory variants and historical conference coverage are in the aggregate evidence supplement.

6. Limitations

This is retrospective development evidence, not independent prospective validation. Reconstruction applies the current method to historical inputs; the reported intervals omit uncertainty from earlier model development and selection. The completion buffer does not certify exact historical PFF publication times. Publisher edition ages differ, so eligibility does not establish identical information horizons. PredictionTracker and author-margin records also lack exact individual game-row issue times; verified workbook release is a separate fact.

Source coverage is uneven. The all-four ordering cohort represents ten seasons and excludes 2021; 2026 is partial. Results apply to matched FBS games, not FCS or cross-division accuracy. Tier readability and wider Division I coverage do not remedy these limitations. Independent file-only reviews reproduced all six arms’ arithmetic and uncertainty and checked native values, product identity, timing, exclusions and revisions.

The earlier 2,156-versus-2,231 daily comparison and incumbent v1 claims remain quarantined because some origins admitted evidence from games still underway. Their artifacts are preserved, but they support no accuracy claim here. The completed comparisons above use the repaired, separately registered reconstruction.

7. Conclusion

AVR provides a coherent, opponent-adjusted Division I scale with complementary evidence and explicit strength tiers. Its qualified historical weekly ordering outperforms Massey’s published MAS ranking on the maximal matched cohort. The study does not establish parity or superiority to all four incumbents, and point-consumer results favor FPI and Sagarin. A prospective, untouched evaluation is needed before making broader claims.

Disclosure

Andy Volpe develops AVR. This working paper reports owner-directed research, with independent AI-agent checks and an AI expert-panel synthesis; these are not external peer review. Unpublished implementation details are outside the public scope. Revised October 12, 2026.

References and evidence

1. ESPN (2017). Football Power Index terminology.
2. Massey, K. (n.d.). Rating-system description. NCAA.
3. Sagarin, J. (n.d.). College football ratings and named components.
4. Connelly, B. (2026). SP+ ratings. ESPN.
5. The PredictionTracker. Archived published football predictions.
6. Volpe, A. (2026). AVR rating-comparison aggregate evidence, clean24 / source v12. Six arms, immutable result identifiers, coverage and uncertainty.