Bracket study · October 15, 2026 · Counterfactual
What does a double bye buy?
Compare the proposal with one complete alternative: two opening games and fourteen single byes. Both use the same eighteen entrants and five dates. Fewer games for the highest-benefit teams comes with a longer wait before they begin.
Read this before the percentages
Actual field. Hypothetical strengths and effects.
The field, underlying ranks, protection allocation and last-game dates come from the existing 2024 historical reconstruction. The probability model uses invented strength profiles so the format can be examined separately. Team names identify entrants; these percentages are not forecasts of their ability. No NRR Index is converted to a point spread.
The alternative is a research comparison, not an adopted policy. It removes protected double byes and requires eight neutral-site round-two games rather than the proposal’s six. Its venues, rights, staffing and athlete arrangements are not approved.
Same field · Different entry rewards
Both brackets close. Their obligations differ.
| Round and illustrative date | Proposal | Single-bye alternative |
|---|---|---|
| Opening · Dec 14, 2024 | 4 games · 8 playing | 2 games · 4 playing |
| Round two · Dec 21 | 6 games · 12 playing | 8 games · 16 playing |
| Quarterfinals · Jan 1, 2025 | 4 games · 8 playing | 4 games · 8 playing |
| Semifinals · Jan 11 | 2 games · 4 playing | 2 games · 4 playing |
| Neutral final · Jan 18 | 1 games · 2 playing | 1 games · 2 playing |
Proposal: double byes for underlying ranks 1 and 3; eight single byes; eight opening entrants. Texas remains rank 3 but keeps the double bye earned by entering its required conference title game at rank 2. Protection changes entry, not reseeding rank.
Alternative: fourteen single byes include every selected champion and all protected pre-title top-ten entrants, then fill in underlying order. The four remaining entrants are ranks 14, 15, 17, 18. The higher two host the lower two: 14–18 and 15–17. All double-bye guarantees are deliberately removed for this test.
Both redraw highest against lowest before round two and again before quarterfinals, using unchanged underlying rank. Quarterfinals feed fixed semifinal paths; there is no third redraw. The higher underlying rank hosts opening games, quarterfinals and semifinals; round two and the final are neutral. Both eliminate seventeen teams and produce one champion.
The same dates leave Christmas week without a game. The quarterfinal-to-semifinal and semifinal-to-final gaps are ten and seven days. These placements do not certify academic access, broadcast windows, practice exposure or medical recovery.
18 sensitivity settings · 20,000 runs per format per setting
Rewarding earned rank and selecting strength are different objectives.
In the illustrative profile where strength follows earned rank, with no home or rest effect, the combined title share for earned ranks 1–2 is 55.25% in the proposal and 54.74% in the alternative. Ranks 14–18 receive 0.07% and 0.07% respectively. These are model outcomes under declared assumptions, not measured competitive benefits.
When all teams are equal and games are neutral with no rest effect, the exact title chance is 1 ÷ 2 raised to the number of wins required. A double-bye entrant needs three wins (12.5%); a single-bye entrant needs four (6.25%); an opening entrant needs five (3.125%). The simulation agrees within its stated numerical tolerance. This isolates the entry-round advantage without claiming that any real teams are equally strong.
| Underlying rank and entrant | Assumed strength rank | Proposal title chance | Alternative title chance |
|---|---|---|---|
| 1. Oregon | 1 | 33.31% | 31.93% |
| 2. Georgia | 2 | 21.95% | 22.81% |
| 3. Texas | 3 | 17.23% | 15.89% |
| 4. Penn State | 4 | 10.58% | 10.74% |
| 5. Notre Dame | 5 | 6.87% | 7.16% |
| 6. Ohio State | 6 | 4.37% | 4.50% |
| 7. Tennessee | 7 | 2.35% | 2.90% |
| 8. Indiana | 8 | 1.33% | 1.67% |
| 9. Boise State | 9 | 0.97% | 1.10% |
| 10. SMU | 10 | 0.58% | 0.64% |
| 11. Alabama | 11 | 0.22% | 0.29% |
| 12. Arizona State | 12 | 0.14% | 0.19% |
| 13. Miami | 13 | 0.03% | 0.11% |
| 14. Ole Miss | 14 | 0.03% | 0.04% |
| 15. South Carolina | 15 | 0.01% | 0.01% |
| 16. Clemson | 16 | 0.01% | 0.01% |
| 17. BYU | 17 | 0.01% | 0.01% |
| 18. Iowa State | 18 | 0.00% | 0.00% |
Compare every declared strength, home and rest setting
“Swapped” exchanges the assumed strengths of earned ranks 1 and 8, without changing their earned ranks or benefits. That makes the strongest pair ranks 8 and 2, so strongest-team and earned-top-two shares need not move together. All-equal strength has no unique strongest pair.
| Setting | Earned top two title share | Strongest two title share | Earned ranks 14–18 title share |
|---|---|---|---|
| All teams equalNo rest effect · home coefficient 0 | 18.79% → 12.25% | All strengths tied | 18.45% → 18.77% |
| All teams equalNo rest effect · home coefficient 0.2 | 23.22% → 15.77% | All strengths tied | 14.85% → 15.76% |
| All teams equalExtra-rest benefit · home coefficient 0 | 20.70% → 13.16% | All strengths tied | 15.90% → 17.85% |
| All teams equalExtra-rest benefit · home coefficient 0.2 | 24.64% → 15.72% | All strengths tied | 11.92% → 14.37% |
| All teams equalLong-layoff cost · home coefficient 0 | 18.23% → 12.63% | All strengths tied | 19.18% → 18.29% |
| All teams equalLong-layoff cost · home coefficient 0.2 | 21.46% → 14.76% | All strengths tied | 14.58% → 14.77% |
| Strength follows earned rankNo rest effect · home coefficient 0 | 55.25% → 54.74% | 55.25% → 54.74% | 0.07% → 0.07% |
| Strength follows earned rankNo rest effect · home coefficient 0.2 | 59.55% → 58.81% | 59.55% → 58.81% | 0.03% → 0.04% |
| Strength follows earned rankExtra-rest benefit · home coefficient 0 | 56.45% → 55.68% | 56.45% → 55.68% | 0.04% → 0.10% |
| Strength follows earned rankExtra-rest benefit · home coefficient 0.2 | 59.61% → 58.82% | 59.61% → 58.82% | 0.02% → 0.03% |
| Strength follows earned rankLong-layoff cost · home coefficient 0 | 54.89% → 54.60% | 54.89% → 54.60% | 0.07% → 0.08% |
| Strength follows earned rankLong-layoff cost · home coefficient 0.2 | 58.90% → 58.37% | 58.90% → 58.37% | 0.03% → 0.05% |
| Strength of ranks 1 and 8 swappedNo rest effect · home coefficient 0 | 28.45% → 28.82% | 40.92% → 44.40% | 0.10% → 0.17% |
| Strength of ranks 1 and 8 swappedNo rest effect · home coefficient 0.2 | 32.50% → 32.61% | 41.20% → 44.07% | 0.08% → 0.11% |
| Strength of ranks 1 and 8 swappedExtra-rest benefit · home coefficient 0 | 28.60% → 28.67% | 39.63% → 44.67% | 0.10% → 0.14% |
| Strength of ranks 1 and 8 swappedExtra-rest benefit · home coefficient 0.2 | 33.30% → 32.75% | 40.33% → 44.76% | 0.06% → 0.08% |
| Strength of ranks 1 and 8 swappedLong-layoff cost · home coefficient 0 | 27.75% → 28.85% | 41.63% → 44.30% | 0.13% → 0.14% |
| Strength of ranks 1 and 8 swappedLong-layoff cost · home coefficient 0.2 | 32.46% → 32.63% | 41.91% → 43.94% | 0.11% → 0.10% |
The logistic win model uses strength differences plus a home coefficient of 0 or 0.2. The extra-rest scenario adds 0.02 logit units per day above seven, capped at fourteen extra days; the layoff scenario subtracts 0.03 per day above twenty-one. These coefficients are not estimated from football outcomes. The named scenarios show sensitivity to assumptions, not confidence bounds on real rest effects.
At 20,000 runs, a single simulated proportion has a Monte Carlo standard error no larger than 0.36 percentage points. Model uncertainty is much larger and is not captured by that number. Paired differences and standard errors for the ranks 14–18 group are in the result download; tiny movements should not be treated as findings.
Calendar days · Game burden · Travel assumptions
A shorter path can mean a longer initial wait.
Oregon and Texas would first play January 1 after 25 idle days under the proposal. The alternative starts them December 21 after 14 days but requires four wins instead of three. The example therefore trades one avoided game for eleven more calendar days before entry. Idle days are elapsed days between games, not days free from training or travel.
| Entrant · last game | Proposal: first date / idle / wins needed / season total if finalist | Alternative: same measures |
|---|---|---|
| 1. Oregon2024-12-07 · 13-0 · played title game | 2025-01-01 25 days · 3 wins · 16 total | 2024-12-21 14 days · 4 wins · 17 total |
| 2. Georgia2024-12-07 · 11-2 · played title game | 2024-12-21 14 days · 4 wins · 17 total | 2024-12-21 14 days · 4 wins · 17 total |
| 3. Texas2024-12-07 · 11-2 · played title game | 2025-01-01 25 days · 3 wins · 16 total | 2024-12-21 14 days · 4 wins · 17 total |
| 4. Penn State2024-12-07 · 11-2 · played title game | 2024-12-21 14 days · 4 wins · 17 total | 2024-12-21 14 days · 4 wins · 17 total |
| 5. Notre Dame2024-11-30 · 11-1 · no title game | 2024-12-21 21 days · 4 wins · 16 total | 2024-12-21 21 days · 4 wins · 16 total |
| 6. Ohio State2024-11-30 · 10-2 · no title game | 2024-12-21 21 days · 4 wins · 16 total | 2024-12-21 21 days · 4 wins · 16 total |
| 7. Tennessee2024-11-30 · 10-2 · no title game | 2024-12-14 14 days · 5 wins · 17 total | 2024-12-21 21 days · 4 wins · 16 total |
| 8. Indiana2024-11-30 · 11-1 · no title game | 2024-12-14 14 days · 5 wins · 17 total | 2024-12-21 21 days · 4 wins · 16 total |
| 9. Boise State2024-12-06 · 12-1 · played title game | 2024-12-21 15 days · 4 wins · 17 total | 2024-12-21 15 days · 4 wins · 17 total |
| 10. SMU2024-12-07 · 11-2 · played title game | 2024-12-21 14 days · 4 wins · 17 total | 2024-12-21 14 days · 4 wins · 17 total |
| 11. Alabama2024-11-30 · 9-3 · no title game | 2024-12-14 14 days · 5 wins · 17 total | 2024-12-21 21 days · 4 wins · 16 total |
| 12. Arizona State2024-12-07 · 11-2 · played title game | 2024-12-21 14 days · 4 wins · 17 total | 2024-12-21 14 days · 4 wins · 17 total |
| 13. Miami2024-11-30 · 10-2 · no title game | 2024-12-14 14 days · 5 wins · 17 total | 2024-12-21 21 days · 4 wins · 16 total |
| 14. Ole Miss2024-11-29 · 9-3 · no title game | 2024-12-14 15 days · 5 wins · 17 total | 2024-12-14 15 days · 5 wins · 17 total |
| 15. South Carolina2024-11-30 · 9-3 · no title game | 2024-12-14 14 days · 5 wins · 17 total | 2024-12-14 14 days · 5 wins · 17 total |
| 16. Clemson2024-12-07 · 10-3 · played title game | 2024-12-21 14 days · 4 wins · 17 total | 2024-12-21 14 days · 4 wins · 17 total |
| 17. BYU2024-11-30 · 10-2 · no title game | 2024-12-14 14 days · 5 wins · 17 total | 2024-12-14 14 days · 5 wins · 17 total |
| 18. Iowa State2024-12-07 · 10-3 · played title game | 2024-12-14 7 days · 5 wins · 18 total | 2024-12-14 7 days · 5 wins · 18 total |
A first-round loss adds one postseason game; reaching the final adds the full listed path. Maximum season burden is 18 games in this field. The downloadable path rows retain all subsequent intervals, and sample traces show dates, pairings and hosts in both formats.
Under the default illustrative profile, expected total team round trips are 24.00 for the proposal and 26.00 for the alternative. Each away or neutral appearance counts as one out-and-back campus trip; a campus host counts zero. The alternative’s two extra neutral games mechanically add two total trips because two campus opening games disappear. Actual itineraries, miles, costs and fan travel are not estimated.
Per-entrant expected games and trips under the default profile
| Entrant | Proposal | Alternative |
|---|---|---|
| 1. Oregon | 2.39 / 0.55 | 3.25 / 1.52 |
| 2. Georgia | 3.02 / 1.41 | 3.04 / 1.42 |
| 3. Texas | 2.02 / 0.81 | 2.78 / 1.69 |
| 4. Penn State | 2.56 / 1.61 | 2.52 / 1.60 |
| 5. Notre Dame | 2.33 / 2.09 | 2.31 / 1.95 |
| 6. Ohio State | 2.13 / 2.03 | 2.11 / 1.95 |
| 7. Tennessee | 2.66 / 1.63 | 1.93 / 1.87 |
| 8. Indiana | 2.45 / 1.44 | 1.76 / 1.73 |
| 9. Boise State | 1.64 / 1.63 | 1.62 / 1.60 |
| 10. SMU | 1.52 / 1.51 | 1.49 / 1.48 |
| 11. Alabama | 1.93 / 0.93 | 1.38 / 1.37 |
| 12. Arizona State | 1.31 / 1.31 | 1.29 / 1.29 |
| 13. Miami | 1.66 / 0.66 | 1.21 / 1.21 |
| 14. Ole Miss | 1.55 / 1.55 | 1.76 / 0.76 |
| 15. South Carolina | 1.39 / 1.39 | 1.65 / 0.65 |
| 16. Clemson | 1.11 / 1.11 | 1.09 / 1.09 |
| 17. BYU | 1.20 / 1.20 | 1.45 / 1.45 |
| 18. Iowa State | 1.15 / 1.15 | 1.37 / 1.37 |
Decision brief
Keep the proposal while testing the tradeoff.
This comparison establishes a valid single-bye alternative and makes its costs visible. It does not establish that long layoffs offset a skipped game. Retain the proposal’s double-bye policy for now; synthetic probabilities alone are insufficient grounds to change it.
- Competition: freeze a separately calibrated predictive-strength model using only selection-date information and evaluate game probabilities on unseen games. Rerun both formats on identical inputs; keep earned seed separate from strength rank.
- Athletes and operations: obtain athlete-led and medical review of training, recovery and travel arrangements; verify campus academic access and the additional two neutral slots. Calendar arithmetic is not feasibility certification.
- Owner decision: reconsider the double bye if credible evidence shows an unacceptable competitive or athlete burden and a feasible alternative preserves enough earned reward. Record what is lost as well as gained before changing policy.
Audience demand, media revenue and coaching effort require separate studies. An underdog’s nonzero simulated chance is not evidence of fan interest or an endorsement of eighteen teams.
Frozen before simulation
Inspect the rules and rerun the experiment.
Run node scripts/audit-bracket-rewards.mjs from the matching source. It verifies SHA-256 hashes before running. The protocol, input field, allocator and simulation source were frozen before results. 720,000 simulated brackets each contain seventeen games and exactly two redraws. Calendar and protection checks, existing historical allocation tests, and the equal-strength analytic cross-check are separate from empirical validation.