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 % · 2019
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
- 211
- 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 % · 2019 · full board
| # | Player | Team | Pos | attempts | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Drew Brees | NO | QB | 391 | 71.9% | 67.4% | 64.3% – 70.5% |
| 2 | Derek Carr | LV | QB | 543 | 66.5% | 64.4% | 61.6% – 67.3% |
| 3 | Kirk Cousins | MIN | QB | 475 | 64.6% | 62.9% | 59.9% – 66.0% |
| 4 | Jimmy Garoppolo | SF | QB | 516 | 63.8% | 62.4% | 59.5% – 65.4% |
| 5 | Patrick Mahomes | KC | QB | 502 | 63.5% | 62.3% | 59.3% – 65.2% |
| 6 | Matt Schaub◦ provisional | ATL | QB | 72 | 69.4% | 61.8% | 57.0% – 66.5% |
| 7 | Dak Prescott | DAL | QB | 621 | 62.5% | 61.6% | 58.9% – 64.4% |
| 8 | Ryan Tannehill | TEN | QB | 318 | 63.2% | 61.6% | 58.1% – 65.0% |
| 9 | Teddy Bridgewater◦ provisional | NO | QB | 208 | 63.9% | 61.5% | 57.6% – 65.4% |
| 10 | Philip Rivers | LAC | QB | 626 | 62.3% | 61.5% | 58.7% – 64.3% |
| 11 | Lamar Jackson | BAL | QB | 425 | 62.4% | 61.3% | 58.1% – 64.5% |
| 12 | Deshaun Watson | HOU | QB | 540 | 61.7% | 61.0% | 58.0% – 63.9% |
| 13 | Matt Ryan | ATL | QB | 669 | 61.0% | 60.6% | 57.8% – 63.2% |
| 14 | Drew Lock◦ provisional | DEN | QB | 161 | 62.1% | 60.5% | 56.3% – 64.6% |
| 15 | Jared Goff | LA | QB | 650 | 60.6% | 60.3% | 57.5% – 63.0% |
| 16 | Chase Daniel◦ provisional | CHI | QB | 71 | 63.4% | 60.2% | 55.4% – 65.0% |
| 17 | Case Keenum | WAS | QB | 264 | 60.6% | 60.0% | 56.3% – 63.6% |
| 18 | Russell Wilson | SEA | QB | 566 | 60.3% | 60.0% | 57.0% – 62.8% |
| 19 | Matthew Stafford | DET | QB | 310 | 60.3% | 59.9% | 56.3% – 63.4% |
| 20 | Carson Wentz | PHI | QB | 647 | 60.0% | 59.8% | 57.0% – 62.5% |
| 21 | Nick Foles◦ provisional | JAX | QB | 128 | 60.2% | 59.6% | 55.1% – 63.9% |
| 22 | Eli Manning◦ provisional | NYG | QB | 152 | 59.9% | 59.5% | 55.2% – 63.7% |
| 23 | Matt Moore◦ provisional | KC | QB | 99 | 59.6% | 59.3% | 54.7% – 63.9% |
| 24 | Joe Flacco | DEN | QB | 289 | 59.2% | 59.2% | 55.5% – 62.8% |
| 25 | Mason Rudolph | PIT | QB | 299 | 58.9% | 59.0% | 55.4% – 62.5% |
| 26 | Kyler Murray | ARI | QB | 593 | 58.9% | 58.9% | 56.1% – 61.8% |
| 27 | Mitchell Trubisky | CHI | QB | 555 | 58.7% | 58.9% | 55.9% – 61.8% |
| 28 | Colt McCoy◦ provisional | WAS | QB | 33 | 54.5% | 58.6% | 53.3% – 63.7% |
| 29 | Aaron Rodgers | GB | QB | 607 | 58.1% | 58.4% | 55.6% – 61.2% |
| 30 | Tom Brady | NE | QB | 642 | 58.1% | 58.4% | 55.6% – 61.1% |
| 31 | Devlin Hodges◦ provisional | PIT | QB | 175 | 57.1% | 58.3% | 54.1% – 62.4% |
| 32 | Robert Griffin III◦ provisional | BAL | QB | 43 | 53.5% | 58.2% | 53.1% – 63.3% |
| 33 | Ben Roethlisberger◦ provisional | PIT | QB | 64 | 54.7% | 58.1% | 53.2% – 63.0% |
| 34 | Jacoby Brissett | IND | QB | 475 | 57.3% | 57.9% | 54.7% – 60.9% |
| 35 | Sam Darnold | NYJ | QB | 477 | 57.2% | 57.8% | 54.7% – 60.9% |
| 36 | AJ McCarron◦ provisional | HOU | QB | 42 | 50.0% | 57.6% | 52.5% – 62.7% |
| 37 | Ryan Fitzpatrick | MIA | QB | 546 | 57.0% | 57.6% | 54.6% – 60.5% |
| 38 | Matt Barkley◦ provisional | BUF | QB | 53 | 50.9% | 57.5% | 52.5% – 62.5% |
| 39 | Daniel Jones | NYG | QB | 500 | 56.8% | 57.5% | 54.4% – 60.5% |
| 40 | Kyle Allen | CAR | QB | 537 | 56.4% | 57.2% | 54.2% – 60.2% |
| 41 | Cam Newton◦ provisional | CAR | QB | 95 | 52.6% | 57.1% | 52.5% – 61.8% |
| 42 | Luke Falk◦ provisional | NYJ | QB | 90 | 52.2% | 57.1% | 52.4% – 61.8% |
| 43 | Gardner Minshew | JAX | QB | 508 | 56.1% | 57.0% | 54.0% – 60.0% |
| 44 | Jeff Driskel◦ provisional | DET | QB | 117 | 53.0% | 57.0% | 52.4% – 61.4% |
| 45 | Jameis Winston | TB | QB | 676 | 56.2% | 56.9% | 54.2% – 59.6% |
| 46 | Will Grier◦ provisional | CAR | QB | 58 | 48.3% | 56.8% | 51.8% – 61.8% |
| 47 | Brian Hoyer◦ provisional | IND | QB | 71 | 49.3% | 56.7% | 51.8% – 61.5% |
| 48 | Andy Dalton | CIN | QB | 567 | 55.4% | 56.4% | 53.5% – 59.3% |
| 49 | Baker Mayfield | CLE | QB | 577 | 54.9% | 56.1% | 53.2% – 59.0% |
| 50 | Josh Allen | BUF | QB | 501 | 54.1% | 55.6% | 52.5% – 58.7% |
| 51 | Marcus Mariota◦ provisional | TEN | QB | 185 | 51.3% | 55.5% | 51.4% – 59.6% |
| 52 | David Blough◦ provisional | DET | QB | 188 | 50.0% | 54.9% | 50.7% – 58.9% |
| 53 | Dwayne Haskins | WAS | QB | 235 | 50.6% | 54.7% | 50.8% – 58.5% |
| 54 | Josh Rosen◦ provisional | MIA | QB | 125 | 46.4% | 54.4% | 49.9% – 58.9% |
| 55 | Brandon Allen◦ provisional | DEN | QB | 93 | 41.9% | 53.9% | 49.2% – 58.6% |
| 56 | Ryan Finley◦ provisional | CIN | QB | 98 | 41.8% | 53.7% | 49.0% – 58.3% |
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).