An open ranking engine your state association can adopt.

open-bethel computes strength ratings, strength of schedule, and per-game contributions for sports teams from a list of head-to-head results. The math is published and peer-reviewed. The implementation is short enough to read in an afternoon. The license is MIT.

What it produces

Strength ratings: Each team gets a single number reflecting how strong its results show it to be, accounting for opponent quality. Derived by maximum likelihood under the Bradley-Terry model with a Bayesian prior so low-data and disconnected graphs stay well-behaved.
Classical RPI: The traditional 25/50/25 blend of win percentage, opponents' win percentage, and opponents' opponents' win percentage. Reported alongside the strength rating for direct comparison with established formulas.
Per-game contributions: For any team, a leave-one-out decomposition of which games raised the rating and which lowered it, sorted by impact. Lets a coach, AD, or journalist answer which win mattered most? with arithmetic, not narrative.
Pairwise diagnostics: For any two teams, the level of indirection between them in the head-to-head graph. Surfaces when a comparison is well-grounded versus when it relies on long inferential chains — a transparency the formula owes to the people it ranks.

Who it's for

State athletic associations, conferences, and tournament directors who want a defensible, reproducible seeding mechanism instead of a proprietary number nobody can audit. Statisticians, athletic directors, coaches, and reporters who need to show their work. Anyone who has to explain a ranking to the people it affects.

Why it exists

Ranking decisions decide who makes the playoffs, who earns a seed, and who is left out. Those decisions deserve to be reproducible by the parties affected. Many of the systems state associations now defer to are proprietary: the formula is not published, the inputs are not released in full, and even administrators applying the numbers cannot always show their work.

open-bethel is the alternative: specified in the open, implemented in the open, free for anyone to run.

The method

The core method is the iterative Bradley-Terry-Ford strength rating with a Bayesian prior, derived in An Optimal Value for the Bradley-Terry Model for Estimating Strength-of-Schedule (Roy Bethel, MITRE Corporation, 2005). The test suite reproduces the paper's Table 2 — converged strengths for all 31 NFL teams after the 1999 regular season — to four decimal places given the same 248-game schedule, so the implementation is verifiable against a published ground truth, not just self-consistent.

The algorithm is dependency-free Python — standard library only. The full essay walking through the math, the failure modes, and the parameter decisions lives in docs/bethel-essence.md.

Examples

Two end-to-end runs. The first reproduces the published reference; the second is a current high-school season.

1999 NFL regular season

Bethel's 2005 paper publishes converged Bradley-Terry-Ford strengths for all 31 NFL teams after the 1999 regular season (Table 2). Running open-bethel on the same 248-game schedule recovers his table to four decimals — every team, every position. The test suite asserts this on every commit.

Rank	Team	W-L	Strength	Bethel '05	RPI
1	Indianapolis	13-3	6.9927	6.9927	.594
2	Jacksonville	14-2	5.0117	5.0117	.553
3	Buffalo	11-5	3.8538	3.8538	.581
4	Tennessee	13-3	3.7348	3.7348	.557
5	Miami	9-7	2.5624	2.5624	.557
6	Tampa Bay	11-5	2.2356	2.2356	.535
7	NY Jets	8-8	2.1129	2.1129	.552
8	St. Louis	13-3	2.0762	2.0762	.519
⋮	23 teams omitted; full results in tests/test_bethel_nfl_1999.py
29	San Francisco	4-12	0.1591	0.1591	.415
30	New Orleans	3-13	0.1062	0.1062	.399
31	Cleveland	2-14	0.0830	0.0830	.410

Strengths normalized so the geometric mean over real teams is 1. Bethel '05 is the published reference value from Table 2; Strength is what open-bethel computes today. RPI is the classical 25/50/25 blend, shown for comparison.

FHSAA Class 2A Region 1 District 3 — baseball, 2026

The five schools in northeast Florida's Class 2A District 3: Bishop Snyder, Bolles, Episcopal, Providence, and Trinity Christian. The run uses the full Florida high-school baseball graph for the 2026 season — 7,085 games across 951 teams — so strength-of-schedule chains extend through every opponent and every opponent's opponents statewide. The table below shows the five district members; the rightmost column is each team's rank against all 951 Florida programs.

Rank	Team	W-L	Strength	RPI	State rk
1	Trinity Christian	20-7	18.8315	.659	19
2	Bishop Snyder	19-6	14.2762	.621	30
3	Bolles	18-7	9.7697	.611	54
4	Episcopal	17-10	5.0386	.567	107
5	Providence	13-12	4.9520	.578	113

Run with the default Bayesian prior (prior_games=1); converged in 588 iterations. The district order tracks what happened on the field: Trinity Christian beat Bishop Snyder 11-10 in the district final on 2026-04-17, and the two are the closest pair in the table. See the essay for why a small Bayesian prior matters when graphs include thinly-connected teams.

Use

Install:

pip install open-bethel

Library:

from open_bethel import bethel_strengths, classical_rpi, load_games

teams, games = load_games("games.csv")
strengths, iters, converged = bethel_strengths(teams, games)

Or from the command line:

open-bethel-rank      games.csv  team-a  team-b
open-bethel-validate  games.csv  2026-04-01
open-bethel-diagnose  games.csv

The CSV expects one row per game with columns date, home_team, away_team, home_score, away_score. Team identifiers are free-form. Tied games are dropped — the model is undefined for ties.

Adopt

open-bethel is MIT licensed and dependency-free. There is nothing to license, nothing to procure, no per-school fee. A state association, conference, or tournament director can run it on its own infrastructure with no commercial relationship and no recurring cost. Source, issues, and discussion live at github.com/Londonberry/open-bethel.