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 · 2018
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
- 190
- 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 · 2018 · full board
| # | Player | Team | Pos | attempts | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Russell Wilson | SEA | QB | 400 | +7.5 | +5.3 | +2.4 – +8.3 |
| 2 | Drew Brees | NO | QB | 482 | +6.5 | +4.9 | +2.1 – +7.7 |
| 3 | Carson Wentz | PHI | QB | 396 | +5.1 | +3.7 | +0.8 – +6.7 |
| 4 | Deshaun Watson | HOU | QB | 493 | +4.6 | +3.6 | +0.8 – +6.3 |
| 5 | Patrick Mahomes | KC | QB | 561 | +4.5 | +3.6 | +1.0 – +6.2 |
| 6 | Matt Ryan | ATL | QB | 595 | +4.3 | +3.5 | +1.0 – +6.1 |
| 7 | Ryan Fitzpatrick | TB | QB | 245 | +5.2 | +3.3 | -0.1 – +6.8 |
| 8 | Nick Foles | PHI | QB | 193 | +5.7 | +3.3 | -0.3 – +7.0 |
| 9 | Derek Carr | LV | QB | 529 | +3.8 | +3.0 | +0.4 – +5.7 |
| 10 | Philip Rivers | LAC | QB | 503 | +3.6 | +2.9 | +0.1 – +5.6 |
| 11 | Marcus Mariota | TEN | QB | 321 | +3.4 | +2.5 | -0.7 – +5.7 |
| 12 | Cam Newton | CAR | QB | 454 | +3.0 | +2.4 | -0.4 – +5.2 |
| 13 | Kirk Cousins | MIN | QB | 592 | +2.6 | +2.2 | -0.4 – +4.7 |
| 14 | Chase Daniel◦ provisional | CHI | QB | 76 | +4.2 | +1.8 | -2.6 – +6.2 |
| 15 | Jameis Winston | TB | QB | 373 | +2.2 | +1.8 | -1.3 – +4.8 |
| 16 | Mitchell Trubisky | CHI | QB | 426 | +2.0 | +1.6 | -1.2 – +4.5 |
| 17 | Cody Kessler◦ provisional | JAX | QB | 122 | +2.7 | +1.6 | -2.5 – +5.6 |
| 18 | Ben Roethlisberger | PIT | QB | 663 | +1.7 | +1.5 | -0.9 – +4.0 |
| 19 | Nick Mullens | SF | QB | 261 | +1.9 | +1.5 | -1.9 – +4.9 |
| 20 | Jared Goff | LA | QB | 538 | +1.5 | +1.4 | -1.3 – +4.0 |
| 21 | Matt Barkley◦ provisional | BUF | QB | 25 | +4.7 | +1.3 | -3.6 – +6.2 |
| 22 | Baker Mayfield | CLE | QB | 472 | +1.3 | +1.2 | -1.6 – +4.0 |
| 23 | Dak Prescott | DAL | QB | 516 | +1.1 | +1.0 | -1.6 – +3.7 |
| 24 | Tom Brady | NE | QB | 552 | +1.0 | +1.0 | -1.6 – +3.6 |
| 25 | Kyle Allen◦ provisional | CAR | QB | 31 | +1.3 | +0.9 | -3.9 – +5.7 |
| 26 | Andrew Luck | IND | QB | 629 | +0.8 | +0.9 | -1.6 – +3.4 |
| 27 | Taylor Heinicke◦ provisional | CAR | QB | 55 | +0.4 | +0.8 | -3.8 – +5.3 |
| 28 | Colt McCoy◦ provisional | WAS | QB | 52 | -0.4 | +0.6 | -4.0 – +5.2 |
| 29 | Brock Osweiler◦ provisional | MIA | QB | 165 | +0.3 | +0.6 | -3.2 – +4.4 |
| 30 | Eli Manning | NYG | QB | 567 | +0.5 | +0.6 | -2.0 – +3.2 |
| 31 | Ryan Tannehill | MIA | QB | 267 | -0.9 | -0.2 | -3.5 – +3.2 |
| 32 | Aaron Rodgers | GB | QB | 575 | -0.6 | -0.2 | -2.8 – +2.4 |
| 33 | Derek Anderson◦ provisional | BUF | QB | 69 | -4.8 | -0.6 | -5.1 – +3.8 |
| 34 | Case Keenum | DEN | QB | 562 | -1.3 | -0.7 | -3.3 – +1.9 |
| 35 | Alex Smith | WAS | QB | 315 | -1.7 | -0.7 | -3.9 – +2.4 |
| 36 | Josh Johnson◦ provisional | WAS | QB | 87 | -4.9 | -0.9 | -5.2 – +3.4 |
| 37 | Matthew Stafford | DET | QB | 544 | -2.1 | -1.3 | -4.0 – +1.3 |
| 38 | Joe Flacco | BAL | QB | 369 | -2.6 | -1.4 | -4.5 – +1.6 |
| 39 | Mark Sanchez◦ provisional | WAS | QB | 34 | -14.4 | -1.4 | -6.2 – +3.3 |
| 40 | Sam Bradford◦ provisional | ARI | QB | 80 | -7.3 | -1.5 | -5.9 – +2.8 |
| 41 | Jimmy Garoppolo◦ provisional | SF | QB | 87 | -6.9 | -1.6 | -5.9 – +2.7 |
| 42 | DeShone Kizer◦ provisional | GB | QB | 39 | -13.7 | -1.6 | -6.3 – +3.1 |
| 43 | Andy Dalton | CIN | QB | 357 | -3.0 | -1.7 | -4.7 – +1.4 |
| 44 | Jeff Driskel◦ provisional | CIN | QB | 171 | -4.5 | -1.7 | -5.4 – +2.1 |
| 45 | Blaine Gabbert◦ provisional | TEN | QB | 99 | -8.0 | -2.2 | -6.4 – +2.0 |
| 46 | Lamar Jackson◦ provisional | BAL | QB | 164 | -6.0 | -2.3 | -6.1 – +1.5 |
| 47 | Josh McCown◦ provisional | NYJ | QB | 105 | -9.5 | -2.8 | -7.0 – +1.3 |
| 48 | C.J. Beathard◦ provisional | SF | QB | 167 | -7.1 | -2.9 | -6.6 – +0.9 |
| 49 | Sam Darnold | NYJ | QB | 400 | -4.6 | -2.9 | -5.8 – +0.1 |
| 50 | Tyrod Taylor◦ provisional | CLE | QB | 82 | -12.1 | -3.0 | -7.4 – +1.3 |
| 51 | Nathan Peterman◦ provisional | BUF | QB | 79 | -13.9 | -3.5 | -7.8 – +0.9 |
| 52 | Josh Allen | BUF | QB | 303 | -6.9 | -3.9 | -7.1 – -0.7 |
| 53 | Blake Bortles | JAX | QB | 400 | -6.9 | -4.4 | -7.4 – -1.5 |
| 54 | Josh Rosen | ARI | QB | 371 | -8.2 | -5.2 | -8.2 – -2.1 |
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).