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 % · 2016
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
- 148
- 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 % · 2016 · full board
| # | Player | Team | Pos | attempts | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Drew Brees | NO | QB | 702 | 67.1% | 65.6% | 62.9% – 68.3% |
| 2 | Sam Bradford | MIN | QB | 590 | 67.0% | 65.3% | 62.4% – 68.2% |
| 3 | Matt Ryan | ATL | QB | 575 | 64.9% | 63.6% | 60.7% – 66.5% |
| 4 | Tom Brady | NE | QB | 449 | 64.8% | 63.3% | 60.0% – 66.5% |
| 5 | Kirk Cousins | WAS | QB | 631 | 64.3% | 63.3% | 60.4% – 66.1% |
| 6 | Brian Hoyer | CHI | QB | 204 | 65.7% | 62.8% | 58.5% – 67.0% |
| 7 | Dak Prescott | DAL | QB | 486 | 64.0% | 62.8% | 59.6% – 65.9% |
| 8 | Alex Smith | KC | QB | 519 | 63.2% | 62.2% | 59.1% – 65.3% |
| 9 | Aaron Rodgers | GB | QB | 647 | 62.0% | 61.4% | 58.5% – 64.2% |
| 10 | Ryan Tannehill | MIA | QB | 420 | 62.1% | 61.3% | 57.9% – 64.6% |
| 11 | Joe Flacco | BAL | QB | 710 | 61.4% | 61.0% | 58.2% – 63.7% |
| 12 | Derek Anderson◦ provisional | CAR | QB | 54 | 66.7% | 60.9% | 55.2% – 66.4% |
| 13 | Matthew Stafford | DET | QB | 633 | 61.3% | 60.8% | 57.9% – 63.7% |
| 14 | Derek Carr | LV | QB | 582 | 61.3% | 60.8% | 57.8% – 63.8% |
| 15 | Ben Roethlisberger | PIT | QB | 535 | 61.3% | 60.8% | 57.7% – 63.8% |
| 16 | Jimmy Garoppolo◦ provisional | NE | QB | 66 | 65.1% | 60.7% | 55.2% – 66.1% |
| 17 | Eli Manning | NYG | QB | 619 | 60.9% | 60.5% | 57.6% – 63.4% |
| 18 | Matt Moore◦ provisional | MIA | QB | 88 | 62.5% | 60.2% | 54.9% – 65.3% |
| 19 | Andy Dalton | CIN | QB | 604 | 60.3% | 60.0% | 57.0% – 62.9% |
| 20 | Russell Wilson | SEA | QB | 589 | 59.9% | 59.7% | 56.7% – 62.6% |
| 21 | Nick Foles◦ provisional | KC | QB | 59 | 61.0% | 59.4% | 53.7% – 65.0% |
| 22 | Carson Wentz | PHI | QB | 643 | 58.9% | 58.9% | 56.0% – 61.8% |
| 23 | Tom Savage◦ provisional | HOU | QB | 78 | 59.0% | 58.8% | 53.4% – 64.2% |
| 24 | Landry Jones◦ provisional | PIT | QB | 90 | 58.9% | 58.8% | 53.5% – 64.0% |
| 25 | Andrew Luck | IND | QB | 589 | 58.7% | 58.7% | 55.8% – 61.7% |
| 26 | Cody Kessler | CLE | QB | 218 | 58.7% | 58.7% | 54.5% – 62.9% |
| 27 | Scott Tolzien◦ provisional | IND | QB | 40 | 57.5% | 58.5% | 52.5% – 64.3% |
| 28 | Matt Barkley | CHI | QB | 222 | 58.1% | 58.4% | 54.1% – 62.5% |
| 29 | Marcus Mariota | TEN | QB | 478 | 57.7% | 58.0% | 54.7% – 61.2% |
| 30 | Jacoby Brissett◦ provisional | NE | QB | 61 | 55.7% | 57.9% | 52.2% – 63.4% |
| 31 | Charlie Whitehurst◦ provisional | CLE | QB | 27 | 51.8% | 57.7% | 51.5% – 63.8% |
| 32 | Shaun Hill◦ provisional | MIN | QB | 36 | 52.8% | 57.6% | 51.5% – 63.5% |
| 33 | Case Keenum | LA | QB | 345 | 56.8% | 57.4% | 53.7% – 61.0% |
| 34 | Kevin Hogan◦ provisional | CLE | QB | 28 | 50.0% | 57.4% | 51.2% – 63.4% |
| 35 | Matt Cassel◦ provisional | TEN | QB | 56 | 53.6% | 57.3% | 51.6% – 63.0% |
| 36 | Jameis Winston | TB | QB | 607 | 56.8% | 57.2% | 54.2% – 60.2% |
| 37 | Carson Palmer | ARI | QB | 641 | 56.8% | 57.1% | 54.3% – 60.0% |
| 38 | Philip Rivers | LAC | QB | 616 | 56.7% | 57.1% | 54.1% – 60.0% |
| 39 | Tyrod Taylor | BUF | QB | 479 | 56.2% | 56.8% | 53.5% – 60.0% |
| 40 | Paxton Lynch◦ provisional | DEN | QB | 92 | 53.3% | 56.6% | 51.4% – 61.9% |
| 41 | Brock Osweiler | HOU | QB | 537 | 56.0% | 56.6% | 53.5% – 59.7% |
| 42 | Trevor Siemian | DEN | QB | 518 | 55.8% | 56.5% | 53.3% – 59.6% |
| 43 | Blake Bortles | JAX | QB | 660 | 55.8% | 56.3% | 53.4% – 59.2% |
| 44 | Blaine Gabbert | SF | QB | 171 | 53.2% | 55.8% | 51.2% – 60.3% |
| 45 | Jay Cutler | CHI | QB | 154 | 52.6% | 55.6% | 50.9% – 60.3% |
| 46 | Ryan Fitzpatrick | NYJ | QB | 422 | 54.0% | 55.3% | 51.8% – 58.7% |
| 47 | Bryce Petty◦ provisional | NYJ | QB | 146 | 51.4% | 55.1% | 50.3% – 59.8% |
| 48 | EJ Manuel◦ provisional | BUF | QB | 30 | 36.7% | 55.0% | 48.9% – 61.1% |
| 49 | Colin Kaepernick | SF | QB | 367 | 53.4% | 54.9% | 51.3% – 58.5% |
| 50 | Robert Griffin III | CLE | QB | 169 | 51.5% | 54.9% | 50.3% – 59.5% |
| 51 | Drew Stanton◦ provisional | ARI | QB | 49 | 38.8% | 53.8% | 47.9% – 59.6% |
| 52 | Josh McCown | CLE | QB | 184 | 48.9% | 53.3% | 48.8% – 57.8% |
| 53 | Jared Goff | LA | QB | 231 | 48.5% | 52.5% | 48.3% – 56.7% |
| 54 | Cam Newton | CAR | QB | 550 | 49.1% | 51.1% | 48.0% – 54.3% |
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).