Original model research · 2026
Which teams are actually connected by the schedule?
An audit of the completed-game network shows where cross-division comparisons have game evidence and where the common scale depends on model assumptions.
The 668 teams with a completed result form 3 separate schedule components. The largest contains 646 teams and 3239 games; 14 additional teams have no usable completed result.
173 games connect different known divisions. They contribute 3% of total model edge weight after recency and classification adjustments. 646 active teams have a path to at least one FBS team. A path establishes shared result evidence, not precise strength estimates.
- Active schedule components
- 3 Connected sets using completed games only; unplayed teams are counted separately.
- Cross-division games
- 173 0 games have at least one unknown classification and are excluded from this count.
- Teams with a path to FBS
- 646/668 Any direct or indirect path through actual completed games, including FBS teams themselves.
A shared formula needs shared evidence
Treat a team as a node and a completed matchup as an undirected link. If A played B and B played C, there is a path from A to C, even if they never met. A connected component is a set with no game path to any team outside it. Repeated meetings add observations but not new unique links.
A rating difference inside a component can be informed by those paths. Between separate components, every game equation is unchanged if we shift all ratings in one component by the same amount. No score tells the model how high that entire group should sit relative to another disconnected group.
Mathematical uniqueness is not a common-strength measurement
The published ridge penalty of 1.2 makes the numerical solution unique by pulling each team's rating toward zero. It can therefore assign a number to every disconnected group. It does not create an empirical bridge between them. The resulting cross-group ordering reflects the anchor and other model assumptions, not observed head-to-head strength.
Even a connected graph can be weakly linked. A small number of cross-division games can influence many comparisons, and the model deliberately downweights them. The pair table shows direct game counts and their effective weight. A zero means no direct games in this snapshot; an indirect path may still exist through another division.
What to do with that uncertainty
Use within-division and well-connected comparisons first. For a cross-division claim, inspect the component table and the actual team schedules. A team can have many games while its entire network has little evidence connecting it to another part of the country.
These counts describe the available schedule, not a statistical confidence level. We do not convert connection counts into invented error bars. Reporting a single rating to one decimal place should not imply that the scale between all four divisions is known to that precision.
Results from this snapshot
| Example team | Teams | Games | FBS | FCS | D-II | D-III | Unknown |
|---|---|---|---|---|---|---|---|
| Auburn | 646 | 3239 | 138 | 128 | 148 | 232 | 0 |
| Southeastern Oklahoma State | 12 | 65 | 0 | 0 | 12 | 0 | 0 |
| Amherst | 10 | 43 | 0 | 0 | 0 | 10 | 0 |
| Division pair | Completed games | Effective weight |
|---|---|---|
| FBS / FCS | 123 | 51.84 |
| FBS / Division II | 0 | 0.00 |
| FBS / Division III | 0 | 0.00 |
| FCS / Division II | 45 | 18.85 |
| FCS / Division III | 2 | 0.46 |
| Division II / Division III | 3 | 1.29 |
Inspect the team evidence
- Auburn: Its completed-game component contains 646 teams and 3239 games, including FBS teams.
- Southeastern Oklahoma State: Its completed-game component contains 12 teams and 65 games, with no path to an FBS team.
- Amherst: Its completed-game component contains 10 teams and 43 games, with no path to an FBS team.
Team profiles show the current publication. Their ratings can change after the snapshot used for this study.
Reproduce the study
- Build an undirected adjacency set from every usable completed game. Traverse it to identify active components. Count unplayed teams separately instead of treating zero-game ratings as evidence of average strength.
- Count unique opponent pairs once for connectivity, but count repeated games separately as observations. Component division counts use current team metadata.
- Use buildEdges with DEFAULT_CONFIG to total actual game weights. Group cross-division observations using game classifications with team classifications as the fallback. Flag unknown classifications rather than inferring that they are FBS for this audit.
The calculation uses 3,347 completed games and 668 active teams. 14 teams have no usable completed result.
Game results and team metadata come from College Football Data. CFB Power Board calculates the ratings, comparisons, tables, and commentary. The project source contains the research and rating functions named above. The model documentation explains the formula. Download the current source teams, source games, and published ratings and game logs. Filter source games to usable completed results for the study's season before running the methods above. These files are current snapshots, not a permanent historical archive.
Model settings used in this study
- homeFieldAdvantage
- 2.5
- marginCap
- 28
- winBonus
- 2.5
- ridge
- 1.2
- recencyDecay
- 0.97
- recencyFloor
- 0.6
- crossDivisionPenalty
- 0.55
- maxIterations
- 500
- tolerance
- 0.000001
- relaxation
- 1.5
Analysis specification 2026-11-07.1 · content revision v1-3c9aa827. The season and reporting periods identify the data studied; they are not publication or human-review dates.
Limitations
- Connectivity is conditional on this dataset. Missing or misclassified source games can change the graph; this is not a claim of complete NCAA schedule coverage.
- One path is enough to establish connectivity, but not enough to establish a reliable comparison. Counts do not measure path quality, bridge fragility, or a rating's standard error.
- A common ridge anchor supplies mathematical uniqueness to disconnected components. It does not identify their empirical relative strength, even when the displayed numbers share units.
Found an incorrect score, calculation, or explanation? Send the page URL and supporting evidence. Publishing standards describe review and corrections.