NFL · Empirical Bayes
True-Talent Leaderboards
A raw single-season rate is a noisy guess at a player’s real ability, and the noise is worst for the smallest samples — so a naïve leaderboard is topped by whoever got lucky in the fewest tries. This one shrinks every rate toward its position-group prior by how much the sample can be trusted, and shows a 90% credible interval instead of a point. Toggle raw vs. shrunk to watch the flukes fall back to the pack.
CPOE · 2017
Completion % over expected (accounts for depth & situation).
- Beats raw by
- 17.9%
- lower out-of-sample error
- RMSE raw → shrunk
- 4.9 → 4.0
- odd vs. even weeks
- Split-half reliability
- 0.35
- how repeatable the raw stat is
- Stabilizes at
- 230
- attempts to trust the number
Each row is a player: the solid dot is the shrunk estimate, the hollow dot the raw rate, joined by the red pull of regression; the grey bar is the 90% credible interval. A hollow shrunk dot means the sample is below the stabilization line — the number is mostly the position prior. Switch to Raw rank and watch the small-sample names climb.
CPOE · 2017 · full board
| # | Player | Team | Pos | attempts | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Josh McCown | NYJ | QB | 386 | +5.5 | +3.4 | +0.5 – +6.4 |
| 2 | Alex Smith | KC | QB | 491 | +5.0 | +3.4 | +0.6 – +6.1 |
| 3 | Drew Brees | NO | QB | 529 | +4.7 | +3.2 | +0.6 – +5.9 |
| 4 | Jameis Winston | TB | QB | 435 | +4.9 | +3.2 | +0.3 – +6.0 |
| 5 | Russell Wilson | SEA | QB | 524 | +4.6 | +3.2 | +0.5 – +5.9 |
| 6 | Tom Brady | NE | QB | 578 | +3.7 | +2.6 | +0.1 – +5.2 |
| 7 | Jimmy Garoppolo◦ provisional | SF | QB | 176 | +6.0 | +2.6 | -1.1 – +6.2 |
| 8 | Case Keenum | MIN | QB | 475 | +3.6 | +2.4 | -0.4 – +5.1 |
| 9 | Ben Roethlisberger | PIT | QB | 556 | +2.9 | +2.0 | -0.6 – +4.7 |
| 10 | Matt Ryan | ATL | QB | 516 | +3.0 | +2.0 | -0.7 – +4.7 |
| 11 | Sam Bradford◦ provisional | MIN | QB | 43 | +10.9 | +1.6 | -2.8 – +6.1 |
| 12 | Landry Jones◦ provisional | PIT | QB | 28 | +15.3 | +1.6 | -3.0 – +6.1 |
| 13 | Deshaun Watson◦ provisional | HOU | QB | 202 | +2.3 | +1.0 | -2.5 – +4.5 |
| 14 | Tyrod Taylor | BUF | QB | 414 | +1.3 | +0.8 | -2.1 – +3.7 |
| 15 | Philip Rivers | LAC | QB | 565 | +1.0 | +0.7 | -1.9 – +3.3 |
| 16 | Mike Glennon◦ provisional | CHI | QB | 139 | +1.7 | +0.6 | -3.2 – +4.4 |
| 17 | Kirk Cousins | WAS | QB | 534 | +0.8 | +0.6 | -2.1 – +3.2 |
| 18 | Paxton Lynch◦ provisional | DEN | QB | 45 | +3.8 | +0.6 | -3.9 – +5.0 |
| 19 | Marcus Mariota | TEN | QB | 443 | +0.7 | +0.4 | -2.4 – +3.3 |
| 20 | Matthew Stafford | DET | QB | 560 | +0.6 | +0.4 | -2.2 – +3.0 |
| 21 | Aaron Rodgers | GB | QB | 234 | +0.8 | +0.4 | -3.0 – +3.8 |
| 22 | David Fales◦ provisional | MIA | QB | 42 | +2.8 | +0.4 | -4.1 – +4.8 |
| 23 | Patrick Mahomes◦ provisional | KC | QB | 34 | +3.1 | +0.3 | -4.2 – +4.8 |
| 24 | Carson Wentz | PHI | QB | 436 | +0.4 | +0.2 | -2.6 – +3.1 |
| 25 | Kevin Hogan◦ provisional | CLE | QB | 74 | +0.4 | +0.0 | -4.2 – +4.2 |
| 26 | Carson Palmer | ARI | QB | 266 | -0.0 | -0.1 | -3.4 – +3.2 |
| 27 | Matt Moore◦ provisional | MIA | QB | 123 | -0.1 | -0.1 | -4.0 – +3.8 |
| 28 | Dak Prescott | DAL | QB | 482 | -0.2 | -0.2 | -2.9 – +2.6 |
| 29 | Derek Carr | LV | QB | 510 | -0.3 | -0.2 | -2.9 – +2.5 |
| 30 | Jay Cutler | MIA | QB | 420 | -0.4 | -0.3 | -3.2 – +2.6 |
| 31 | Matt Cassel◦ provisional | TEN | QB | 41 | -1.4 | -0.3 | -4.7 – +4.2 |
| 32 | EJ Manuel◦ provisional | LV | QB | 42 | -2.8 | -0.5 | -4.9 – +3.9 |
| 33 | Jared Goff | LA | QB | 469 | -0.9 | -0.6 | -3.4 – +2.1 |
| 34 | Ryan Fitzpatrick◦ provisional | TB | QB | 161 | -1.6 | -0.7 | -4.4 – +3.0 |
| 35 | Geno Smith◦ provisional | NYG | QB | 35 | -5.8 | -0.8 | -5.4 – +3.7 |
| 36 | Joe Flacco | BAL | QB | 543 | -1.2 | -0.9 | -3.5 – +1.8 |
| 37 | Trevor Siemian | DEN | QB | 340 | -1.5 | -0.9 | -4.0 – +2.1 |
| 38 | Sean Mannion◦ provisional | LA | QB | 37 | -6.6 | -1.0 | -5.5 – +3.5 |
| 39 | Nick Foles◦ provisional | PHI | QB | 98 | -3.2 | -1.0 | -5.1 – +3.0 |
| 40 | Andy Dalton | CIN | QB | 474 | -1.7 | -1.2 | -3.9 – +1.6 |
| 41 | Cam Newton | CAR | QB | 483 | -2.3 | -1.6 | -4.3 – +1.1 |
| 42 | Brett Hundley | GB | QB | 312 | -3.0 | -1.8 | -4.9 – +1.4 |
| 43 | Nathan Peterman◦ provisional | BUF | QB | 47 | -11.0 | -1.9 | -6.3 – +2.5 |
| 44 | Blake Bortles | JAX | QB | 513 | -2.9 | -2.0 | -4.7 – +0.7 |
| 45 | Tom Savage◦ provisional | HOU | QB | 220 | -4.2 | -2.1 | -5.5 – +1.4 |
| 46 | Eli Manning | NYG | QB | 567 | -3.6 | -2.6 | -5.2 – -0.0 |
| 47 | Brock Osweiler◦ provisional | DEN | QB | 166 | -6.2 | -2.6 | -6.3 – +1.0 |
| 48 | Jacoby Brissett | IND | QB | 454 | -4.5 | -3.0 | -5.8 – -0.2 |
| 49 | Brian Hoyer◦ provisional | NE | QB | 208 | -6.3 | -3.0 | -6.5 – +0.5 |
| 50 | T.J. Yates◦ provisional | HOU | QB | 93 | -10.4 | -3.0 | -7.1 – +1.0 |
| 51 | Blaine Gabbert◦ provisional | ARI | QB | 169 | -7.4 | -3.2 | -6.9 – +0.5 |
| 52 | Mitchell Trubisky | CHI | QB | 326 | -5.4 | -3.2 | -6.3 – -0.1 |
| 53 | Drew Stanton◦ provisional | ARI | QB | 156 | -8.3 | -3.4 | -7.1 – +0.3 |
| 54 | C.J. Beathard◦ provisional | SF | QB | 221 | -7.1 | -3.5 | -7.0 – -0.1 |
| 55 | DeShone Kizer | CLE | QB | 470 | -6.3 | -4.3 | -7.1 – -1.5 |
| 56 | Bryce Petty◦ provisional | NYJ | QB | 109 | -14.4 | -4.7 | -8.7 – -0.7 |
How the shrinkage works
Two estimators
Rate stats (completion %, success rate, catch rate) use a beta-binomial model: a Beta(α, β) prior fit by marginal likelihood over each position group, then a Beta posterior per player. Per-play averages (EPA, CPOE, yards) use a normal-normal model with DerSimonian–Laird between-player variance. Both pull each player toward their group by exactly how thin their sample is.
Does it help? & the fine print
The trust panel’s numbers come from a leakage-free odd/even-week holdout: fit on odd weeks, predict even-week raw. Shrinkage lowers out-of-sample error for every stat. Priors are fit per season and per position (WR and TE separately), so a TE’s baseline isn’t a skill. Regular season only, 2016–2025. Rushing and receiving efficiency are heavily scheme-driven — read the wide bands as the honesty they are.
Source: nflverse play-by-play. Counted and computed deterministically — never modeled by a language model. Built by build_nfl_leaderboards.py (byte-reproducible).