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 · 2016
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
- 229
- 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 · 2016 · full board
| # | Player | Team | Pos | attempts | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Matt Ryan | ATL | QB | 527 | +6.9 | +5.0 | +2.3 – +7.7 |
| 2 | Kirk Cousins | WAS | QB | 592 | +5.0 | +3.8 | +1.2 – +6.3 |
| 3 | Ryan Tannehill | MIA | QB | 381 | +5.3 | +3.6 | +0.6 – +6.5 |
| 4 | Sam Bradford | MIN | QB | 549 | +4.5 | +3.4 | +0.7 – +6.0 |
| 5 | Russell Wilson | SEA | QB | 528 | +4.5 | +3.3 | +0.7 – +6.0 |
| 6 | Drew Brees | NO | QB | 661 | +4.2 | +3.3 | +0.8 – +5.7 |
| 7 | Dak Prescott | DAL | QB | 455 | +4.2 | +3.0 | +0.2 – +5.8 |
| 8 | Aaron Rodgers | GB | QB | 604 | +3.5 | +2.7 | +0.2 – +5.3 |
| 9 | Tom Brady | NE | QB | 428 | +3.7 | +2.6 | -0.3 – +5.5 |
| 10 | Cody Kessler◦ provisional | CLE | QB | 191 | +4.7 | +2.5 | -1.1 – +6.1 |
| 11 | Andy Dalton | CIN | QB | 542 | +2.8 | +2.2 | -0.5 – +4.8 |
| 12 | Brian Hoyer◦ provisional | CHI | QB | 194 | +3.4 | +1.9 | -1.7 – +5.5 |
| 13 | Tyrod Taylor | BUF | QB | 422 | +2.2 | +1.7 | -1.2 – +4.5 |
| 14 | Nick Foles◦ provisional | KC | QB | 55 | +5.5 | +1.6 | -2.8 – +5.9 |
| 15 | Ben Roethlisberger | PIT | QB | 504 | +1.9 | +1.5 | -1.2 – +4.2 |
| 16 | Alex Smith | KC | QB | 480 | +1.9 | +1.5 | -1.2 – +4.3 |
| 17 | Jameis Winston | TB | QB | 560 | +1.7 | +1.4 | -1.3 – +4.0 |
| 18 | Derek Anderson◦ provisional | CAR | QB | 53 | +4.4 | +1.3 | -3.0 – +5.7 |
| 19 | Marcus Mariota | TEN | QB | 439 | +1.4 | +1.1 | -1.7 – +4.0 |
| 20 | Jimmy Garoppolo◦ provisional | NE | QB | 63 | +2.7 | +1.1 | -3.2 – +5.4 |
| 21 | Andrew Luck | IND | QB | 533 | +1.2 | +1.0 | -1.6 – +3.7 |
| 22 | Scott Tolzien◦ provisional | IND | QB | 37 | +2.5 | +0.9 | -3.6 – +5.4 |
| 23 | Matt Moore◦ provisional | MIA | QB | 85 | +1.6 | +0.9 | -3.3 – +5.0 |
| 24 | Matt Cassel◦ provisional | TEN | QB | 48 | +0.9 | +0.7 | -3.7 – +5.1 |
| 25 | Landry Jones◦ provisional | PIT | QB | 85 | +0.2 | +0.5 | -3.6 – +4.6 |
| 26 | Carson Palmer | ARI | QB | 589 | +0.4 | +0.5 | -2.1 – +3.0 |
| 27 | Tom Savage◦ provisional | HOU | QB | 73 | -0.5 | +0.4 | -3.9 – +4.6 |
| 28 | Philip Rivers | LAC | QB | 562 | +0.2 | +0.3 | -2.3 – +2.9 |
| 29 | Matthew Stafford | DET | QB | 580 | +0.1 | +0.3 | -2.3 – +2.8 |
| 30 | Derek Carr | LV | QB | 553 | -0.0 | +0.2 | -2.5 – +2.8 |
| 31 | Paxton Lynch◦ provisional | DEN | QB | 82 | -1.2 | +0.1 | -4.0 – +4.3 |
| 32 | Joe Flacco | BAL | QB | 658 | -0.2 | +0.0 | -2.4 – +2.5 |
| 33 | Jacoby Brissett◦ provisional | NE | QB | 55 | -2.8 | -0.0 | -4.4 – +4.3 |
| 34 | Matt Barkley◦ provisional | CHI | QB | 215 | -0.9 | -0.1 | -3.6 – +3.4 |
| 35 | Trevor Siemian | DEN | QB | 472 | -0.5 | -0.1 | -2.9 – +2.6 |
| 36 | Shaun Hill◦ provisional | MIN | QB | 35 | -5.4 | -0.2 | -4.7 – +4.3 |
| 37 | Carson Wentz | PHI | QB | 600 | -0.9 | -0.5 | -3.0 – +2.1 |
| 38 | Jay Cutler◦ provisional | CHI | QB | 134 | -2.4 | -0.5 | -4.3 – +3.4 |
| 39 | Robert Griffin III◦ provisional | CLE | QB | 146 | -2.7 | -0.7 | -4.4 – +3.1 |
| 40 | Eli Manning | NYG | QB | 597 | -1.6 | -1.0 | -3.6 – +1.6 |
| 41 | EJ Manuel◦ provisional | BUF | QB | 26 | -16.5 | -1.1 | -5.7 – +3.5 |
| 42 | Case Keenum | LA | QB | 319 | -3.7 | -1.9 | -5.0 – +1.2 |
| 43 | Bryce Petty◦ provisional | NYJ | QB | 131 | -6.5 | -2.0 | -5.8 – +1.9 |
| 44 | Drew Stanton◦ provisional | ARI | QB | 45 | -15.9 | -2.1 | -6.5 – +2.4 |
| 45 | Josh McCown◦ provisional | CLE | QB | 164 | -6.2 | -2.2 | -5.9 – +1.5 |
| 46 | Brock Osweiler | HOU | QB | 504 | -3.7 | -2.3 | -5.1 – +0.4 |
| 47 | Blaine Gabbert◦ provisional | SF | QB | 159 | -6.7 | -2.4 | -6.1 – +1.4 |
| 48 | Ryan Fitzpatrick | NYJ | QB | 401 | -4.1 | -2.4 | -5.3 – +0.5 |
| 49 | Colin Kaepernick | SF | QB | 327 | -4.7 | -2.5 | -5.6 – +0.6 |
| 50 | Blake Bortles | JAX | QB | 622 | -4.5 | -3.1 | -5.6 – -0.6 |
| 51 | Cam Newton | CAR | QB | 500 | -5.5 | -3.6 | -6.3 – -0.9 |
| 52 | Jared Goff◦ provisional | LA | QB | 202 | -10.9 | -4.8 | -8.3 – -1.3 |
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).