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.
Completion % · 2018
Completions per pass attempt. Depth-of-target confound: a checkdown offense completes more. Pair with CPOE.
- Beats raw by
- 15.6%
- lower out-of-sample error
- RMSE raw → shrunk
- 5.2% → 4.4%
- odd vs. even weeks
- Split-half reliability
- 0.42
- how repeatable the raw stat is
- Stabilizes at
- 147
- 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.
Completion % · 2018 · full board
| # | Player | Team | Pos | attempts | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Drew Brees | NO | QB | 508 | 71.7% | 69.0% | 66.0% – 71.9% |
| 2 | Nick Foles | PHI | QB | 205 | 68.8% | 65.0% | 60.8% – 69.2% |
| 3 | Kirk Cousins | MIN | QB | 651 | 65.3% | 64.3% | 61.5% – 67.0% |
| 4 | Andrew Luck | IND | QB | 660 | 65.1% | 64.2% | 61.4% – 66.9% |
| 5 | Matt Ryan | ATL | QB | 656 | 64.3% | 63.5% | 60.7% – 66.3% |
| 6 | Ben Roethlisberger | PIT | QB | 704 | 64.2% | 63.4% | 60.7% – 66.1% |
| 7 | Carson Wentz | PHI | QB | 433 | 64.4% | 63.3% | 59.9% – 66.5% |
| 8 | Philip Rivers | LAC | QB | 547 | 63.4% | 62.7% | 59.6% – 65.7% |
| 9 | Cam Newton | CAR | QB | 504 | 63.5% | 62.7% | 59.5% – 65.8% |
| 10 | Tom Brady | NE | QB | 592 | 63.3% | 62.6% | 59.7% – 65.5% |
| 11 | Patrick Mahomes | KC | QB | 607 | 63.1% | 62.5% | 59.5% – 65.3% |
| 12 | Derek Carr | LV | QB | 605 | 63.0% | 62.4% | 59.4% – 65.2% |
| 13 | Mitchell Trubisky | CHI | QB | 462 | 62.5% | 61.9% | 58.6% – 65.1% |
| 14 | Ryan Fitzpatrick | TB | QB | 261 | 62.8% | 61.7% | 57.8% – 65.7% |
| 15 | Matthew Stafford | DET | QB | 598 | 61.4% | 61.1% | 58.1% – 64.0% |
| 16 | Dak Prescott | DAL | QB | 583 | 61.1% | 60.8% | 57.8% – 63.8% |
| 17 | Jared Goff | LA | QB | 597 | 61.0% | 60.7% | 57.8% – 63.7% |
| 18 | Marcus Mariota | TEN | QB | 374 | 61.0% | 60.6% | 57.1% – 64.1% |
| 19 | Kyle Allen◦ provisional | CAR | QB | 31 | 64.5% | 60.6% | 54.5% – 66.5% |
| 20 | Deshaun Watson | HOU | QB | 568 | 60.7% | 60.5% | 57.5% – 63.5% |
| 21 | Chase Daniel◦ provisional | CHI | QB | 86 | 61.6% | 60.5% | 55.2% – 65.7% |
| 22 | Eli Manning | NYG | QB | 628 | 60.5% | 60.4% | 57.5% – 63.2% |
| 23 | Nick Mullens | SF | QB | 292 | 60.3% | 60.1% | 56.3% – 63.9% |
| 24 | Baker Mayfield | CLE | QB | 518 | 59.9% | 59.8% | 56.7% – 62.9% |
| 25 | Jameis Winston | TB | QB | 408 | 59.8% | 59.8% | 56.4% – 63.2% |
| 26 | Taylor Heinicke◦ provisional | CAR | QB | 59 | 59.3% | 59.7% | 54.0% – 65.2% |
| 27 | Matt Barkley◦ provisional | BUF | QB | 26 | 57.7% | 59.5% | 53.3% – 65.5% |
| 28 | Teddy Bridgewater◦ provisional | NO | QB | 25 | 56.0% | 59.2% | 53.0% – 65.3% |
| 29 | Sam Bradford◦ provisional | ARI | QB | 87 | 57.5% | 58.9% | 53.6% – 64.2% |
| 30 | Case Keenum | DEN | QB | 622 | 58.7% | 58.9% | 56.0% – 61.8% |
| 31 | Colt McCoy◦ provisional | WAS | QB | 60 | 56.7% | 58.9% | 53.2% – 64.5% |
| 32 | Blaine Gabbert◦ provisional | TEN | QB | 106 | 57.6% | 58.9% | 53.7% – 63.9% |
| 33 | Alex Smith | WAS | QB | 351 | 58.4% | 58.8% | 55.2% – 62.4% |
| 34 | Joe Flacco | BAL | QB | 397 | 58.4% | 58.8% | 55.3% – 62.3% |
| 35 | Andy Dalton | CIN | QB | 387 | 58.4% | 58.8% | 55.3% – 62.3% |
| 36 | Russell Wilson | SEA | QB | 479 | 58.5% | 58.8% | 55.5% – 62.0% |
| 37 | Brock Osweiler | MIA | QB | 196 | 57.6% | 58.6% | 54.2% – 62.9% |
| 38 | Derek Anderson◦ provisional | BUF | QB | 75 | 56.0% | 58.5% | 53.0% – 63.9% |
| 39 | Ryan Tannehill | MIA | QB | 309 | 57.0% | 57.9% | 54.0% – 61.7% |
| 40 | Aaron Rodgers | GB | QB | 649 | 57.3% | 57.8% | 54.9% – 60.6% |
| 41 | Cody Kessler | JAX | QB | 153 | 55.6% | 57.6% | 52.9% – 62.3% |
| 42 | Blake Bortles | JAX | QB | 436 | 55.7% | 56.8% | 53.4% – 60.1% |
| 43 | Mark Sanchez◦ provisional | WAS | QB | 42 | 45.2% | 56.6% | 50.6% – 62.4% |
| 44 | C.J. Beathard | SF | QB | 189 | 54.0% | 56.5% | 52.0% – 60.9% |
| 45 | Jeff Driskel | CIN | QB | 195 | 53.8% | 56.4% | 52.0% – 60.8% |
| 46 | Jimmy Garoppolo◦ provisional | SF | QB | 103 | 51.5% | 56.4% | 51.2% – 61.5% |
| 47 | Josh Johnson◦ provisional | WAS | QB | 102 | 51.0% | 56.2% | 51.0% – 61.3% |
| 48 | Lamar Jackson | BAL | QB | 186 | 53.2% | 56.1% | 51.6% – 60.6% |
| 49 | Josh McCown◦ provisional | NYJ | QB | 117 | 51.3% | 56.0% | 51.0% – 61.0% |
| 50 | DeShone Kizer◦ provisional | GB | QB | 46 | 43.5% | 55.9% | 50.0% – 61.7% |
| 51 | Nathan Peterman◦ provisional | BUF | QB | 89 | 49.4% | 55.9% | 50.5% – 61.2% |
| 52 | Sam Darnold | NYJ | QB | 445 | 53.7% | 55.2% | 51.8% – 58.6% |
| 53 | Tyrod Taylor◦ provisional | CLE | QB | 98 | 42.9% | 53.0% | 47.8% – 58.2% |
| 54 | Josh Rosen | ARI | QB | 439 | 49.4% | 52.0% | 48.6% – 55.4% |
| 55 | Josh Allen | BUF | QB | 348 | 48.3% | 51.7% | 48.0% – 55.4% |
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).