Perfect FBS Schedule Theory (2025)

Abstract

A scheduling framework independent of ranking/selection mechanics. It defines constraints (“house rules”) and public fairness metrics, with examples limited to ACC, Big Ten, Big 12, SEC, and Notre Dame. Opponent-strength bins derive from multi-year win–loss results (2014–2023). Travel is quantified via great-circle distance.

Season Calendar (Structure)

• Weeks 1–12: Regular-season games (three byes per team; one game per week).
• Week 13: Rivalry Window A.
• Week 14: Rivalry Window B.
• Week 15: Conference Championship Week (league title games).
• Week 16: Army–Navy / idle.
• Postseason: CFP first round (on-campus), then quarterfinals & semifinals at bowls; championship at a neutral site.

Definitions and Axioms

• Rivalry integrity: high-salience pairings scheduled in late-season windows.
• Difficulty smoothing: season schedules avoid clustering only elites or only strugglers.
• Travel parity: comparable cumulative travel per team.
• Opponent diversity: breadth of opponents across multi-year windows.

1. Rivalries anchor the late season (two windows).
2. Difficulty belongs to all; avoid all-“A” or all-“F” clusters.
3. Distance is shared; limit back-to-back long hauls.
4. No regular-season repeats.
5. Byes spaced reasonably.
6. One protected heritage series per team beyond the primary rivalry.

House Rules

• 12 games; three byes; one game per week.
• Two late-season rivalry windows (Weeks 13–14).
• No regular-season repeats.
• Conference and cross-conference games permitted (e.g., ACC–SEC, SEC–Big 12, Big Ten–Notre Dame).
• Monitor cumulative miles; avoid consecutive long-haul road trips.
• One heritage slot; periodic review.
• Week 15 is reserved for conference championships.

Worked Example — Weekly Slate (Penn State, Big Ten)

Wk 01  Notre Dame (H)             [Independent]
Wk 02  at West Virginia (A)       [Big 12]
Wk 03  BYE
Wk 04  Pittsburgh (H)             [ACC, heritage]
Wk 05  at Rutgers (A)             [Big Ten]
Wk 06  Maryland (H)               [Big Ten]
Wk 07  BYE
Wk 08  at Iowa (A)                [Big Ten]
Wk 09  Wisconsin (H)              [Big Ten]
Wk 10  at Ohio State (A)          [Big Ten]
Wk 11  UCLA (H)                   [Big Ten]
Wk 12  BYE
Wk 13  at USC (A)                 [Big Ten]
Wk 14  Michigan State (H)         [Big Ten, rivalry window]
Wk 15  Big Ten Championship       [if qualified; otherwise idle]
        

Opponents restricted to ACC, Big Ten, Big 12, SEC, and Notre Dame; byes are spaced; no repeats.

Postseason Context (12-Team CFP)

The CFP fields the five highest-ranked conference champions plus seven at-large teams in a 12-team bracket. Seeds 1–4 receive first-round byes; first-round games are on-campus; quarterfinals and semifinals are at bowls, followed by a neutral-site championship. The 2025–26 calendar places first-round games on Dec. 19–20, quarterfinals Dec. 31–Jan. 1, semifinals Jan. 8–9. (Dates subject to host assignments each year.)

Illustrative First Round (Fixed Paths; Real Teams Only)

1 Georgia — bye
2 Ohio State — bye
3 Texas — bye
4 Michigan — bye
5 Alabama vs 12 Louisville         (host: Alabama)
6 Oregon vs 11 Ole Miss            (host: Oregon)
7 Florida State vs 10 Penn State   (host: Florida State)
8 Oklahoma vs 9 Notre Dame         (host: Oklahoma)
        

Advancement follows fixed paths; rematches are permitted when informative.

Rivalry Windows (2025–26 Alignment)

Two windows reduce congestion and preserve placement. Lists include cross-conference pairings as rivalry/heritage/high-grade options. Duplicates of a team across windows indicate alternate placements—not simultaneous games.

Window A (Week 13)

• Alabama–Auburn (SEC)
• Ole Miss–Mississippi State (SEC)
• Georgia–Georgia Tech (SEC–ACC)
• Florida–Florida State (SEC–ACC)
• Clemson–South Carolina (ACC–SEC)
• USC–UCLA (Big Ten)
• Oregon–Washington (Big Ten)
• Iowa–Nebraska (Big Ten)
• Wisconsin–Minnesota (Big Ten)
• Indiana–Purdue (Big Ten)
• Kansas–Kansas State (Big 12)
• BYU–Utah (Big 12)
• Arizona–Arizona State (Big 12)
• Pitt–West Virginia (ACC–Big 12)
• Kentucky–Louisville (SEC–ACC)
• Stanford–Cal (ACC)
• Baylor–TCU (Big 12)
• Oklahoma State–Oklahoma (Big 12–SEC)

Window B (Week 14)

• Michigan–Ohio State (Big Ten)
• Oklahoma–Texas (SEC)
• LSU–Texas A&M (SEC)
• Penn State–Michigan State (Big Ten)
• Illinois–Northwestern (Big Ten)
• Maryland–Rutgers (Big Ten)
• Notre Dame–USC (Independent–Big Ten)
• Georgia–Florida (SEC)
• Missouri–Arkansas (SEC)
• Tennessee–Vanderbilt (SEC)
• South Carolina–Kentucky (SEC)
• Cincinnati–UCF (Big 12)
• Colorado–Utah (Big 12)
• Iowa State–Kansas State (Big 12)
• Duke–North Carolina (ACC)
• North Carolina–NC State (ACC)
• Virginia–Virginia Tech (ACC)
• Miami (Fla.)–Florida (ACC–SEC)

Strength of Schedule: Transparent Bins

Opponents are mapped to bins using 2019–2023 results from the uploaded CSVs: A ≥ .700; B .600–.699; C .500–.599; D .400–.499; F < .400. (Data dictionary consulted; Kaggle 2019 dataset used for schema alignment.)

Worked Example — Georgia Opponent Bins (2019–2023)

Distribution: A=3, B=3, C=3, D=1, F=1 — centered; no extreme clustering.

Worked Example — Penn State Opponent Bins (2019–2023)

Distribution: A=3, B=2, C=5, D=0, F=1 — within target; no extreme clustering.

Travel Parity

Travel is measured as great-circle distance from home campus to away sites. League-level parity can be summarized by the Gini coefficient of team totals (lower is more equal).

Worked Example — Big Ten Cohort (Away-Game Totals)

Gini ≈ 0.337 in this sample, indicating inequality that multi-year rotations should mitigate.

Worked Example — December Ledger (Penn State path)

Total ≈ 4862 miles. Publishing ledgers for all qualifiers makes travel claims auditable.

Rematch Ethics

• Green: prior one-score meeting or materially affected by absences; rematch is informative.
• Yellow: prior multi-score result with significant contextual change (e.g., QB availability, scheme shift).
• Red: prior decisive result without meaningful change; rematch is unlikely to be informative.

Heritage Slot (Non-Rivalry, Protected)

One protected series per team beyond the primary rivalry, reviewed on a fixed cadence. Examples (aligned to 2025–26): Penn State–Pitt (Big Ten–ACC); Missouri–Kansas (SEC–Big 12); SMU–TCU (ACC–Big 12); Notre Dame–Stanford (Ind.–ACC).

Fairness Dashboard (Public Metrics)

1. Rivalry Reliability — proportion of primary rivalries placed in Window A/B.
2. Difficulty Spread — season-level variance of opponent bins (A–F) per team.
3. Travel Parity — league-level Gini of regular-season miles.
4. Opponent Diversity — unique opponents per team over a rolling four-year window.

Worked Example — Team Readout (Penn State)

• Rivalry Reliability: 1.00 (Michigan State in-window).
• Difficulty Spread: centered (A=3, B=2, C=5, F=1).
• Travel: 3552 miles (sample slate) — moderated vs. coastal cross-country burdens.
• Opponent Diversity: 11 unique opponents (single season); multi-year target per league policy.

Operational Steps

1. Place rivalry windows; assign one heritage series per team.
2. Set byes with spacing targets.
3. Fill league slates; avoid back-to-back long hauls.
4. Add cross-conference matchups prudently (ACC–SEC–Big 12–Big Ten–Notre Dame).
5. Audit difficulty via bins; adjust marginal opponents if distributions skew.
6. Publish dashboard and postseason travel ledgers annually.

Evaluation Targets

• Rivalry Reliability ≥ 0.90.
• Travel Gini ≤ 0.10 (regular season).
• Opponent Diversity median ≥ 31 unique opponents over four years (conference-size dependent).
• Difficulty Spread: no team with ≥ 4 “A” opponents; no team with ≤ 1 combined “A/B”.

Conclusion

The framework produces schedules that are transparent, auditable, and compatible with the 12-team postseason. Emphasis on rivalry placement, explainable opponent-strength bins, and measurable travel parity reduces structural variance in evaluations while fitting the 2025–26 conference landscape.

Notes on Data and Computation

Datasets: TBA.