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 % · 2017
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
- 158
- 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 % · 2017 · full board
| # | Player | Team | Pos | attempts | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Drew Brees | NO | QB | 556 | 69.4% | 66.7% | 63.8% – 69.6% |
| 2 | Case Keenum | MIN | QB | 504 | 64.5% | 62.8% | 59.7% – 65.8% |
| 3 | Alex Smith | KC | QB | 541 | 63.0% | 61.7% | 58.7% – 64.7% |
| 4 | Tom Brady | NE | QB | 618 | 62.3% | 61.3% | 58.4% – 64.1% |
| 5 | Jimmy Garoppolo | SF | QB | 186 | 64.5% | 61.2% | 56.9% – 65.5% |
| 6 | Matt Ryan | ATL | QB | 553 | 61.8% | 60.8% | 57.8% – 63.8% |
| 7 | Ben Roethlisberger | PIT | QB | 586 | 61.6% | 60.7% | 57.7% – 63.6% |
| 8 | Joe Flacco | BAL | QB | 577 | 61.0% | 60.2% | 57.2% – 63.2% |
| 9 | Josh McCown | NYJ | QB | 437 | 61.1% | 60.1% | 56.8% – 63.4% |
| 10 | Landry Jones◦ provisional | PIT | QB | 31 | 74.2% | 60.1% | 54.2% – 65.9% |
| 11 | Mike Glennon◦ provisional | CHI | QB | 148 | 62.8% | 60.0% | 55.4% – 64.5% |
| 12 | Philip Rivers | LAC | QB | 594 | 60.6% | 59.9% | 57.0% – 62.8% |
| 13 | Matthew Stafford | DET | QB | 615 | 60.3% | 59.7% | 56.8% – 62.6% |
| 14 | Nate Sudfeld◦ provisional | PHI | QB | 26 | 73.1% | 59.6% | 53.5% – 65.4% |
| 15 | Derek Carr | LV | QB | 537 | 60.2% | 59.5% | 56.4% – 62.5% |
| 16 | Sam Bradford◦ provisional | MIN | QB | 48 | 66.7% | 59.5% | 53.8% – 65.0% |
| 17 | Kirk Cousins | WAS | QB | 581 | 59.7% | 59.2% | 56.2% – 62.2% |
| 18 | David Fales◦ provisional | MIA | QB | 45 | 64.4% | 58.9% | 53.2% – 64.5% |
| 19 | Jay Cutler | MIA | QB | 449 | 59.2% | 58.7% | 55.4% – 62.0% |
| 20 | Jameis Winston | TB | QB | 477 | 59.1% | 58.7% | 55.5% – 61.9% |
| 21 | Jared Goff | LA | QB | 502 | 59.0% | 58.6% | 55.4% – 61.7% |
| 22 | Dak Prescott | DAL | QB | 525 | 58.7% | 58.4% | 55.2% – 61.4% |
| 23 | Marcus Mariota | TEN | QB | 480 | 58.5% | 58.2% | 55.0% – 61.4% |
| 24 | Aaron Rodgers | GB | QB | 262 | 58.8% | 58.2% | 54.3% – 62.2% |
| 25 | Eli Manning | NYG | QB | 607 | 58.0% | 57.9% | 54.9% – 60.8% |
| 26 | Patrick Mahomes◦ provisional | KC | QB | 37 | 59.5% | 57.7% | 51.9% – 63.5% |
| 27 | Blake Bortles | JAX | QB | 551 | 57.2% | 57.2% | 54.1% – 60.3% |
| 28 | Kevin Hogan◦ provisional | CLE | QB | 81 | 56.8% | 57.1% | 51.9% – 62.4% |
| 29 | Paxton Lynch◦ provisional | DEN | QB | 54 | 55.6% | 56.9% | 51.3% – 62.4% |
| 30 | Sean Mannion◦ provisional | LA | QB | 40 | 55.0% | 56.9% | 51.0% – 62.6% |
| 31 | Carson Palmer | ARI | QB | 290 | 56.5% | 56.8% | 53.0% – 60.7% |
| 32 | Matt Moore◦ provisional | MIA | QB | 139 | 56.1% | 56.8% | 52.0% – 61.5% |
| 33 | Tyrod Taylor | BUF | QB | 466 | 56.4% | 56.7% | 53.4% – 59.9% |
| 34 | Geno Smith◦ provisional | NYG | QB | 39 | 53.8% | 56.6% | 50.8% – 62.4% |
| 35 | Russell Wilson | SEA | QB | 601 | 56.4% | 56.6% | 53.6% – 59.5% |
| 36 | Ryan Fitzpatrick | TB | QB | 172 | 55.8% | 56.5% | 52.0% – 61.0% |
| 37 | Deshaun Watson | HOU | QB | 226 | 55.8% | 56.4% | 52.2% – 60.5% |
| 38 | Carson Wentz | PHI | QB | 473 | 56.0% | 56.4% | 53.1% – 59.6% |
| 39 | Brett Hundley | GB | QB | 346 | 55.5% | 56.1% | 52.4% – 59.7% |
| 40 | Andy Dalton | CIN | QB | 535 | 55.5% | 55.9% | 52.8% – 59.0% |
| 41 | Nick Foles◦ provisional | PHI | QB | 106 | 53.8% | 55.9% | 50.9% – 60.9% |
| 42 | EJ Manuel◦ provisional | LV | QB | 47 | 51.1% | 55.9% | 50.2% – 61.6% |
| 43 | Matt Cassel◦ provisional | TEN | QB | 50 | 50.0% | 55.6% | 49.9% – 61.2% |
| 44 | Cam Newton | CAR | QB | 529 | 55.0% | 55.5% | 52.4% – 58.7% |
| 45 | Brian Hoyer | NE | QB | 228 | 53.9% | 55.3% | 51.2% – 59.5% |
| 46 | Mitchell Trubisky | CHI | QB | 362 | 54.1% | 55.1% | 51.5% – 58.7% |
| 47 | Nathan Peterman◦ provisional | BUF | QB | 49 | 46.9% | 54.9% | 49.2% – 60.5% |
| 48 | Trevor Siemian | DEN | QB | 384 | 53.6% | 54.7% | 51.2% – 58.2% |
| 49 | Brock Osweiler | DEN | QB | 184 | 52.2% | 54.6% | 50.1% – 59.0% |
| 50 | Cody Kessler◦ provisional | CLE | QB | 29 | 37.9% | 54.3% | 48.3% – 60.3% |
| 51 | Jacoby Brissett | IND | QB | 522 | 52.9% | 53.9% | 50.8% – 57.0% |
| 52 | Tom Savage | HOU | QB | 244 | 51.2% | 53.6% | 49.5% – 57.7% |
| 53 | C.J. Beathard | SF | QB | 243 | 50.6% | 53.3% | 49.2% – 57.4% |
| 54 | Blaine Gabbert | ARI | QB | 195 | 48.7% | 52.6% | 48.2% – 56.9% |
| 55 | Drew Stanton | ARI | QB | 166 | 47.6% | 52.3% | 47.8% – 56.9% |
| 56 | Bryce Petty◦ provisional | NYJ | QB | 121 | 45.5% | 52.2% | 47.3% – 57.1% |
| 57 | DeShone Kizer | CLE | QB | 514 | 49.6% | 51.4% | 48.3% – 54.6% |
| 58 | T.J. Yates◦ provisional | HOU | QB | 111 | 42.3% | 51.1% | 46.1% – 56.1% |
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).