James Madison · 6-0
53.5 − 59.6 = -6.1
Final component: 0.0 · clamped at zero
Account
What changes between these views?
Beta changes only the 15% performance component. Quality-win grades, loss costs and other inputs remain at current NRR values. Both views use the same games and cutoff; Beta is experimental, not an official NRR release.
Beta formula and limitations
Efficiency-only prototype. No separate turnover, special-teams, field-position or weather adjustment. Both seasons use the same scale, fixed at the first 2024 CFP checkpoint without fitting to teams or polls.
Offense and defense each receive 50% of the game’s raw difference. References weight every play equally; the season averages every game equally. Φ is the standard normal cumulative distribution, used as a smooth 0–100 display scale.
Later 2024 checkpoints share calibration games; these are not independent holdouts. Later-retrieved sources make this retrospective checkpoint repricing, not a vintage-data backtest. Full-game boxes include overtime and late plays; sacks remain in rushing totals. Any held game holds its team’s entire component—there is no zero fill or selective replacement.
Opponent schedule composition, cross-division comparisons and style of play still need validation. This cannot reliably separate great opposing offense from poor defense. Only the direct 15% component changes: other component values, opponent valuations, record foundation and head-to-head credit remain archived. This is not an official NRR release or a complete formula rebuild.
Overlap and outlier checks
Correlation measures resemblance, not accuracy. NRR correlation covers all FBS teams. The poll comparison uses only its 25 ranked teams—AP for the 2026 early-season preview, CFP for historical Selection Sunday—with no invented rank for unranked teams.
Performance remains embedded in other NRR components. Full dependency and incremental-value testing is still pending. These published trial numbers are for inspection, not automatic promotion into official NRR.
Why do 37 teams have zero performance? · Week 7 audit
All 138 performance scores reproduced exactly. No missing season EPA inputs. In Current NRR, 37 schedule deductions exceed the starting play estimate. Those results clamp to zero. This describes the October 10 cutoff—not every season or the Beta formula.
The starting estimate standardizes adjusted net EPA across FBS, bounded from 5 to 95. The schedule deduction uses the model’s validated schedule caliber, including its two strongest opponent connections. This is our formula, not an ESPN schedule rating.
Miami · 5-0
77.5 − 47.1 = 30.4
Final component: 30.4
Oregon · 3-2
64.0 − 0.9 = 63.1
Final component: 63.1
Uniform sensitivity test—not a proposed change
Halving the deduction factor from 4.5 to 2.25 leaves 10 zeroes; using 3.375 leaves 24. Removing it leaves none. These are all-team diagnostic comparisons, not school-specific exceptions.
Only the direct 15% component is varied. Other dependencies remain fixed. The download includes the mean direct Index effect, all 138 calculation traces, input hashes and the snapshot hash. It is not a full model rebuild or evidence that a weaker penalty is correct.
Lost distinction: these 37 teams start between 21.3 and 60.6, yet all finish at zero in this component. Other components still separate their overall rankings. That alone does not prove their order is wrong.
Where schedule difficulty stacks up · 9 formula tests
The record multiplier deserves testing alongside performance. Nine all-team reruns use the same Week 7 inputs. The unchanged formula reproduces every component, multiplier and published ranking exactly. No experiment below changes the live rankings.
Half the performance deduction
101 teams move · up to 11 places
24/25 same Top 25 teams · 10 performance zeroes
No extra multiplier penalty
118 teams move · up to 32 places
24/25 same Top 25 teams · 37 performance zeroes
No opponent schedule connection
86 teams move · up to 7 places
25/25 same Top 25 teams · 37 performance zeroes
These are sensitivity checks, not proof that any alternative is more accurate. The multiplier test removes only its extra schedule penalty; schedule-adjusted record and the other schedule routes remain. The opponent-connection test removes only one schedule term—not all opponent adjustment.
Follow schedule difficulty through the formula
Schedule-adjusted record. Opponent challenge affects benchmark record value; 30% component.
Direct performance. Validated schedule caliber deducts from standardized EPA; 15% component.
Win control. Full-slate soft schedule shortfall decays game-control average; 7.5% component.
Record foundation. Soft schedule shortfall lowers the multiplier when losses are present; undefeated teams have no loss-dependent penalty.
Opponent value → wins and losses. Schedule contributes directly (10%) and through connected performance (30%); opponent record value also uses schedule. Quality-win and loss-integrity evidence use those values.
Peer head-to-head gate. Provisional composite, including performance, determines whether same-record direct winners qualify for the small credit.
The direct performance deduction does not feed the final Opponent Value calculation. Opponent Value uses a separate schedule-connected EPA estimate. Changing the deduction can still alter the provisional résumé used by the peer head-to-head gate.
Repeated inputs can serve different purposes. This map establishes overlap, not harmful double counting. That requires testing incremental value against untouched outcomes.
All nine results and the connection-gate check
Current formula: 37 zeroes; 25/25 shared Top 25; 0 teams move, at most 0 places. Mean absolute Index change: 0.00.
Performance deduction ×3.375: 24 zeroes; 25/25 shared Top 25; 79 teams move, at most 7 places. Mean absolute Index change: 0.20.
Performance deduction ×2.25: 10 zeroes; 24/25 shared Top 25; 101 teams move, at most 11 places. Mean absolute Index change: 0.48.
No performance schedule deduction: 0 zeroes; 24/25 shared Top 25; 124 teams move, at most 18 places. Mean absolute Index change: 1.24.
Broader connection gate: scale 2: 33 zeroes; 24/25 shared Top 25; 59 teams move, at most 11 places. Mean absolute Index change: 0.14.
Broader connection gate: scale 4: 28 zeroes; 24/25 shared Top 25; 82 teams move, at most 13 places. Mean absolute Index change: 0.25.
Remove record-foundation schedule penalty: 37 zeroes; 24/25 shared Top 25; 118 teams move, at most 32 places. Mean absolute Index change: 3.87.
Remove win-control schedule decay (limit): 37 zeroes; 25/25 shared Top 25; 73 teams move, at most 10 places. Mean absolute Index change: 0.35.
Remove opponent-performance schedule connection: 37 zeroes; 25/25 shared Top 25; 86 teams move, at most 7 places. Mean absolute Index change: 0.48.
The current two-opponent connection gate is continuous but narrow (scale 0.5). Broader gates at scales 2 and 4 were also rerun uniformly. The download contains a controlled schedule sweep with a fixed starting estimate of 60 and connection average of 70—not a forecast for a real team.
In that controlled sweep, one schedule-caliber point can change the performance score by up to 18.3 points with the current gate, versus 8.2 with scale 2. This measures sensitivity, not predictive accuracy.
What must pass before a formula change?
Freeze candidate parameters before evaluation.
Reserve genuinely untouched outcomes or data vintages; these retrospective snapshots are development inputs.
Evaluate held-out game performance against a simple baseline, not agreement with AP.
Test FCS, blowouts, close losses and small-sample cases with uniform rules.
Audit dependency changes and stability before publishing a new formula.
This uses retrospective development data. We have not established an independent holdout or selected a replacement formula. Better agreement with AP is not the success criterion.
Beta stress checks · FCS, blowouts and close losses
FCS reference comparability is the next priority. This checks 777 team-game views from 448 games. A game between two FBS teams has two views; the groups below can overlap. These are development checks—not proof of accuracy or changes to the rankings.
FCS matchups
85/119 grade 90 or higher
Median Beta game grade: 96.1
Close losses
13/114 grade 90 or higher
A performance grade can be positive in a loss. Loss integrity remains separate.
One-game influence
Up to 30.1 component points
Change when one game is omitted. Not a forecast or confidence interval.
High FCS grades are not automatically wrong, but opponent averages may come from very different schedule pools. Test that comparability before adding any blanket FCS cap or exclusion.
All groups and uniform sensitivity results
FCS opponents: 119 team-game views. Median grade 96.1; 85 grades of 90 or higher.
Wins by 28 or more: 164 team-game views. Median grade 96.9; 124 grades of 90 or higher.
Losses by 1–7: 114 team-game views. Median grade 58.5; 13 grades of 90 or higher.
Losses by 28 or more: 82 team-game views. Median grade 17.8; 0 grades of 90 or higher.
Opponent reference of 1–2 games: 0 team-game views. No observed cases; not validated by this snapshot.
Bound each raw game difference to ±3: 6 teams move, by at most 3 places; 25/25 shared Top 25 teams. Only the direct performance component changes.
Exclude FCS games from performance only: 77 teams move, by at most 12 places; 24/25 shared Top 25 teams. Only the direct performance component changes.
Every team has at least 5 games; every opponent reference has at least 4. We cannot claim the one- or two-game reference problem is solved from these results.
Omitting a game is an influence diagnostic, not a missing-data policy. The FCS exclusion is a counterfactual, not a recommendation. These calculations retain the named provisional Beta scenario; they do not independently certify source statistics.
Held-out validation: ready to design, not yet evaluated
Freeze parameters and data versions before obtaining held-out outcomes.
Use only opponent references available before each held-out kickoff; no end-of-season repricing.
Compare held-out adjusted efficiency error against a simple prior-game mean; report sample size and uncertainty.
Report FCS, margin and reference-size strata even when a stratum is empty.
Do not promote based on AP resemblance or this development snapshot alone.
A test guard rejects previously used games, outcomes before the freeze and references obtained after it. No independent holdout has been evaluated and no new formula has been promoted.
Download stress groups, sensitivity results and all team influence checks (JSON) →
2024–25 replay: where current NRR and Beta diverge
The top 25 is mostly stable; the performance floor is not. At Selection Sunday, swapping only the 15% performance component leaves 24 of the current top 25 teams in place in both seasons. The larger changes occur among teams with weaker schedules. This comparison is a diagnostic, not a proposed formula update.
2024 Selection Sunday
27 of 134 current performance scores were zero; Beta averaged 41.1 for those same teams.
The lowest schedule-strength quarter gained 46.7 component points on average under Beta, versus 8.0 for the highest quarter.
Top-25 overlap with the official CFP list: current 22/25; Beta 21/25. Poll agreement alone does not establish accuracy.
2025 Selection Sunday
33 of 136 current performance scores were zero; Beta averaged 41.5 for those same teams.
The lowest schedule-strength quarter gained 47.7 component points on average under Beta, versus 6.9 for the highest quarter.
Top-25 overlap with the official CFP list: current 21/25; Beta 22/25. Poll agreement alone does not establish accuracy.
Show the uniform replacement steps
Each step blends the archived current and Beta performance scores for every FBS team. All other components, opponent values, the record multiplier and head-to-head credit stay fixed.
| Beta share | 2024 teams moving | 2025 teams moving | 2024 shared top 25 | 2025 shared top 25 |
|---|---|---|---|---|
| 0% | 0 | 0 | 25/25 | 25/25 |
| 25% | 83 | 90 | 25/25 | 25/25 |
| 50% | 93 | 99 | 24/25 | 24/25 |
| 75% | 98 | 110 | 24/25 | 24/25 |
| 100% | 110 | 113 | 24/25 | 24/25 |
Batch 2 · How much score correction is enough?
We also capped each team’s Beta–current performance difference at 10, 20, or 30 points before reranking. Even a 10-point cap removes every zero performance score in these two replays, while keeping the same top-25 membership. It still changes many positions lower down.
| Maximum score change | 2024 teams moving | 2025 teams moving | 2024 shared top 25 | 2025 shared top 25 |
|---|---|---|---|---|
| ±0 points | 0 | 0 | 25/25 | 25/25 |
| ±10 points | 70 | 76 | 25/25 | 25/25 |
| ±20 points | 105 | 101 | 24/25 | 25/25 |
| ±30 points | 105 | 109 | 24/25 | 24/25 |
| Uncapped Beta | 110 | 113 | 24/25 | 24/25 |
Read this as sensitivity, not a recommendation. A cap on archived scores is not a rerun of the schedule-deduction formula. The raw 2024–25 game inputs are not retained here, so we cannot yet measure its full knock-on effects or claim better predictions.
Next validation gate: recover and hash the historical raw game inputs, rerun the full formula at several deduction strengths, then check outcomes not used to choose the candidate. The published NRR formula remains unchanged.
Record + loss overlap: four formula stress tests
Nothing here changes published NRR. Each replay uses the same games, opponents, win evidence and 2024–25 checkpoint cutoffs. It changes one scoring relationship at a time, then reranks every FBS team.
Half record-foundation penalty
Keep every component fixed; halve only the gap between the record foundation and 1.
24.2/25 average Top-25 membership retained · 1.5 average rank move
134 team-checkpoints move at least five places across 12 replays.
Half loss-integrity deficit
Keep the weights fixed; halve only the gap between Loss Integrity and 100.
24.8/25 average Top-25 membership retained · 0.5 average rank move
3 team-checkpoints move at least five places across 12 replays.
Adjusted-record weight 20
Reduce SAR from 25 to 20 relative-weight points; the unchanged other weights renormalize over 95.
24.8/25 average Top-25 membership retained · 0.9 average rank move
29 team-checkpoints move at least five places across 12 replays.
Both penalties halved
Combine the first two stress tests, leaving adjusted record, QWD and game evidence fixed.
24.0/25 average Top-25 membership retained · 1.6 average rank move
125 team-checkpoints move at least five places across 12 replays.
The milder loss-only test retains all 25 teams at both Selection Sundays, but that does not prove it predicts results better. Halving the record foundation moves substantially more teams, particularly those with multiple losses. No variant is selected for NRR.
Next gate: compare each fixed variant against later games using only earlier checkpoints, then inspect schedule cohorts, source uncertainty and the full Index before considering a change.
Path to the default NRR
Beta needs a future test.
The Lab is still a trial; published NRR has not changed. The Beta-versus-current comparison is now frozen at the same checkpoint and cutoff, but no future forecasts or results have been filed.
What must pass before promotion?
Both formulas must forecast the same eligible games with identical training and résumé controls. The only swapped input is the 15% performance component. Forecasts must be issued before kickoff; held or missing games never become zeros.
The registered forecast gate calls for at least 200 games on 8 dates, a positive paired improvement over current NRR, and a 95% date-resampling range above zero. This tests next-game yards per play—not whether the full ranking order is correct.
Source authenticity, missing-data coverage, full-Index and subgroup behavior, weekly refresh reliability, and rollback remain separate requirements. Passing the forecast gate will not flip the default automatically.
Download the frozen Beta test protocol → · See the separate Candidate test →