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 · 2019
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
- 255
- 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 · 2019 · full board
| # | Player | Team | Pos | attempts | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Russell Wilson | SEA | QB | 493 | +7.0 | +4.7 | +2.0 – +7.3 |
| 2 | Ryan Tannehill | TEN | QB | 278 | +7.7 | +4.1 | +1.0 – +7.3 |
| 3 | Derek Carr | LV | QB | 481 | +5.7 | +3.8 | +1.1 – +6.4 |
| 4 | Drew Brees | NO | QB | 365 | +6.1 | +3.7 | +0.8 – +6.5 |
| 5 | Kirk Cousins | MIN | QB | 421 | +4.4 | +2.8 | +0.1 – +5.6 |
| 6 | Philip Rivers | LAC | QB | 571 | +3.7 | +2.6 | +0.1 – +5.1 |
| 7 | Lamar Jackson | BAL | QB | 386 | +3.8 | +2.4 | -0.5 – +5.2 |
| 8 | Matt Schaub◦ provisional | ATL | QB | 64 | +7.5 | +1.7 | -2.3 – +5.7 |
| 9 | Patrick Mahomes | KC | QB | 470 | +2.5 | +1.7 | -1.0 – +4.3 |
| 10 | Jimmy Garoppolo | SF | QB | 465 | +2.4 | +1.6 | -1.1 – +4.3 |
| 11 | Deshaun Watson | HOU | QB | 483 | +2.0 | +1.4 | -1.3 – +4.0 |
| 12 | Matt Ryan | ATL | QB | 590 | +1.8 | +1.3 | -1.1 – +3.8 |
| 13 | Matthew Stafford | DET | QB | 284 | +2.1 | +1.2 | -1.9 – +4.3 |
| 14 | Devlin Hodges◦ provisional | PIT | QB | 144 | +2.1 | +0.9 | -2.7 – +4.5 |
| 15 | Dak Prescott | DAL | QB | 576 | +1.0 | +0.7 | -1.8 – +3.2 |
| 16 | Sam Darnold | NYJ | QB | 414 | +1.0 | +0.7 | -2.0 – +3.5 |
| 17 | Chase Daniel◦ provisional | CHI | QB | 64 | +2.1 | +0.6 | -3.4 – +4.6 |
| 18 | Nick Foles◦ provisional | JAX | QB | 110 | +1.5 | +0.6 | -3.2 – +4.4 |
| 19 | Jameis Winston | TB | QB | 604 | +0.7 | +0.5 | -1.9 – +3.0 |
| 20 | Aaron Rodgers | GB | QB | 538 | +0.7 | +0.5 | -2.0 – +3.1 |
| 21 | Teddy Bridgewater◦ provisional | NO | QB | 187 | +0.4 | +0.3 | -3.1 – +3.7 |
| 22 | Matt Moore◦ provisional | KC | QB | 88 | -0.6 | +0.0 | -3.8 – +3.9 |
| 23 | Joe Flacco◦ provisional | DEN | QB | 250 | -0.2 | +0.0 | -3.2 – +3.2 |
| 24 | Drew Lock◦ provisional | DEN | QB | 152 | -0.8 | -0.2 | -3.7 – +3.4 |
| 25 | Robert Griffin III◦ provisional | BAL | QB | 37 | -3.2 | -0.2 | -4.4 – +4.0 |
| 26 | Ryan Fitzpatrick | MIA | QB | 493 | -0.5 | -0.3 | -2.9 – +2.3 |
| 27 | Colt McCoy◦ provisional | WAS | QB | 27 | -5.4 | -0.3 | -4.6 – +4.0 |
| 28 | Carson Wentz | PHI | QB | 596 | -0.6 | -0.4 | -2.8 – +2.1 |
| 29 | Case Keenum◦ provisional | WAS | QB | 240 | -1.1 | -0.4 | -3.6 – +2.8 |
| 30 | AJ McCarron◦ provisional | HOU | QB | 33 | -6.2 | -0.5 | -4.7 – +3.7 |
| 31 | Mason Rudolph | PIT | QB | 274 | -1.2 | -0.5 | -3.7 – +2.6 |
| 32 | Kyle Allen | CAR | QB | 463 | -1.0 | -0.5 | -3.2 – +2.1 |
| 33 | Jeff Driskel◦ provisional | DET | QB | 97 | -2.8 | -0.6 | -4.4 – +3.2 |
| 34 | Luke Falk◦ provisional | NYJ | QB | 72 | -4.0 | -0.7 | -4.7 – +3.3 |
| 35 | Eli Manning◦ provisional | NYG | QB | 141 | -2.6 | -0.8 | -4.4 – +2.8 |
| 36 | Josh Allen | BUF | QB | 434 | -1.6 | -0.9 | -3.7 – +1.8 |
| 37 | Kyler Murray | ARI | QB | 517 | -1.5 | -0.9 | -3.5 – +1.6 |
| 38 | Daniel Jones | NYG | QB | 447 | -1.9 | -1.2 | -3.9 – +1.6 |
| 39 | Marcus Mariota◦ provisional | TEN | QB | 148 | -3.6 | -1.2 | -4.7 – +2.4 |
| 40 | Jared Goff | LA | QB | 607 | -1.8 | -1.2 | -3.6 – +1.3 |
| 41 | Will Grier◦ provisional | CAR | QB | 49 | -9.8 | -1.4 | -5.5 – +2.7 |
| 42 | Tom Brady | NE | QB | 580 | -2.1 | -1.4 | -3.9 – +1.1 |
| 43 | Mitchell Trubisky | CHI | QB | 503 | -2.3 | -1.5 | -4.1 – +1.1 |
| 44 | Cam Newton◦ provisional | CAR | QB | 86 | -6.8 | -1.5 | -5.4 – +2.3 |
| 45 | Brian Hoyer◦ provisional | IND | QB | 64 | -8.7 | -1.6 | -5.6 – +2.5 |
| 46 | Ben Roethlisberger◦ provisional | PIT | QB | 62 | -10.2 | -1.8 | -5.8 – +2.2 |
| 47 | Dwayne Haskins◦ provisional | WAS | QB | 196 | -4.7 | -1.9 | -5.3 – +1.5 |
| 48 | Baker Mayfield | CLE | QB | 513 | -3.0 | -1.9 | -4.5 – +0.7 |
| 49 | Jacoby Brissett | IND | QB | 424 | -3.3 | -2.0 | -4.7 – +0.8 |
| 50 | Matt Barkley◦ provisional | BUF | QB | 50 | -13.4 | -2.0 | -6.1 – +2.1 |
| 51 | Andy Dalton | CIN | QB | 504 | -3.3 | -2.1 | -4.7 – +0.5 |
| 52 | Gardner Minshew | JAX | QB | 451 | -3.8 | -2.4 | -5.1 – +0.3 |
| 53 | Brandon Allen◦ provisional | DEN | QB | 77 | -14.3 | -3.1 | -7.1 – +0.8 |
| 54 | Josh Rosen◦ provisional | MIA | QB | 109 | -12.7 | -3.6 | -7.4 – +0.1 |
| 55 | Ryan Finley◦ provisional | CIN | QB | 84 | -16.0 | -3.8 | -7.7 – +0.1 |
| 56 | David Blough◦ provisional | DET | QB | 168 | -13.6 | -5.3 | -8.7 – -1.8 |
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).