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 % · 2020
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
- 223
- 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 % · 2020 · full board
| # | Player | Team | Pos | attempts | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Aaron Rodgers | GB | QB | 546 | 68.1% | 66.1% | 63.2% – 68.9% |
| 2 | Drew Brees | NO | QB | 404 | 68.1% | 65.6% | 62.4% – 68.7% |
| 3 | Josh Allen | BUF | QB | 599 | 66.1% | 64.7% | 62.0% – 67.5% |
| 4 | Philip Rivers | IND | QB | 564 | 65.4% | 64.2% | 61.4% – 67.0% |
| 5 | Teddy Bridgewater | CAR | QB | 525 | 64.8% | 63.7% | 60.8% – 66.5% |
| 6 | Jared Goff | LA | QB | 576 | 64.2% | 63.3% | 60.5% – 66.1% |
| 7 | Deshaun Watson | HOU | QB | 597 | 64.0% | 63.2% | 60.4% – 65.9% |
| 8 | Derek Carr | LV | QB | 544 | 64.0% | 63.1% | 60.2% – 66.0% |
| 9 | Ben Roethlisberger | PIT | QB | 625 | 63.8% | 63.1% | 60.4% – 65.8% |
| 10 | Kyler Murray | ARI | QB | 587 | 63.9% | 63.1% | 60.3% – 65.9% |
| 11 | Ryan Fitzpatrick | MIA | QB | 283 | 64.7% | 63.1% | 59.5% – 66.6% |
| 12 | Patrick Mahomes | KC | QB | 613 | 63.6% | 62.9% | 60.2% – 65.7% |
| 13 | Dak Prescott | DAL | QB | 234 | 64.5% | 62.8% | 59.1% – 66.5% |
| 14 | Tom Brady | TB | QB | 633 | 63.3% | 62.7% | 60.0% – 65.5% |
| 15 | Russell Wilson | SEA | QB | 607 | 63.3% | 62.7% | 59.9% – 65.4% |
| 16 | Chad Henne◦ provisional | KC | QB | 40 | 70.0% | 62.4% | 57.5% – 67.3% |
| 17 | Justin Herbert | LAC | QB | 630 | 62.9% | 62.4% | 59.7% – 65.1% |
| 18 | Mitchell Trubisky | CHI | QB | 316 | 63.0% | 62.2% | 58.7% – 65.6% |
| 19 | Kirk Cousins | MIN | QB | 562 | 62.1% | 61.8% | 58.9% – 64.6% |
| 20 | Brett Rypien◦ provisional | DEN | QB | 41 | 65.8% | 61.8% | 56.9% – 66.7% |
| 21 | Ryan Tannehill | TEN | QB | 507 | 62.1% | 61.8% | 58.8% – 64.7% |
| 22 | Jimmy Garoppolo◦ provisional | SF | QB | 151 | 62.3% | 61.5% | 57.4% – 65.6% |
| 23 | Kyle Allen◦ provisional | WAS | QB | 96 | 62.5% | 61.5% | 57.0% – 65.9% |
| 24 | Chase Daniel◦ provisional | DET | QB | 46 | 63.0% | 61.4% | 56.5% – 66.2% |
| 25 | Alex Smith | WAS | QB | 274 | 61.3% | 61.2% | 57.6% – 64.8% |
| 26 | Nick Foles | CHI | QB | 331 | 61.0% | 61.0% | 57.6% – 64.4% |
| 27 | Marcus Mariota◦ provisional | LV | QB | 28 | 60.7% | 61.0% | 55.9% – 66.0% |
| 28 | Nick Mullens | SF | QB | 347 | 60.8% | 60.9% | 57.5% – 64.2% |
| 29 | Matt Ryan | ATL | QB | 670 | 60.8% | 60.8% | 58.1% – 63.5% |
| 30 | Brandon Allen◦ provisional | CIN | QB | 149 | 60.4% | 60.8% | 56.6% – 64.9% |
| 31 | Joe Burrow | CIN | QB | 436 | 60.6% | 60.7% | 57.6% – 63.8% |
| 32 | Andy Dalton | DAL | QB | 357 | 60.5% | 60.7% | 57.4% – 64.0% |
| 33 | Brian Hoyer◦ provisional | NE | QB | 26 | 57.7% | 60.7% | 55.6% – 65.7% |
| 34 | Cam Newton | NE | QB | 400 | 60.5% | 60.7% | 57.5% – 63.9% |
| 35 | Gardner Minshew | JAX | QB | 358 | 60.3% | 60.6% | 57.3% – 63.9% |
| 36 | John Wolford◦ provisional | LA | QB | 40 | 55.0% | 60.2% | 55.1% – 65.0% |
| 37 | Mason Rudolph◦ provisional | PIT | QB | 45 | 55.6% | 60.1% | 55.2% – 65.0% |
| 38 | Lamar Jackson | BAL | QB | 406 | 59.6% | 60.1% | 56.9% – 63.3% |
| 39 | Tua Tagovailoa | MIA | QB | 313 | 59.4% | 60.1% | 56.6% – 63.6% |
| 40 | C.J. Beathard◦ provisional | SF | QB | 114 | 57.9% | 60.0% | 55.6% – 64.3% |
| 41 | Baker Mayfield | CLE | QB | 513 | 59.5% | 59.9% | 57.0% – 62.9% |
| 42 | Matthew Stafford | DET | QB | 570 | 59.5% | 59.9% | 57.0% – 62.8% |
| 43 | Garrett Gilbert◦ provisional | DAL | QB | 40 | 52.5% | 59.8% | 54.8% – 64.7% |
| 44 | Colt McCoy◦ provisional | NYG | QB | 72 | 55.6% | 59.7% | 55.0% – 64.4% |
| 45 | Mike Glennon◦ provisional | JAX | QB | 191 | 58.1% | 59.7% | 55.7% – 63.6% |
| 46 | Tyrod Taylor◦ provisional | LAC | QB | 32 | 50.0% | 59.7% | 54.6% – 64.7% |
| 47 | PJ Walker◦ provisional | CAR | QB | 60 | 53.3% | 59.4% | 54.6% – 64.2% |
| 48 | Dwayne Haskins | WAS | QB | 262 | 56.5% | 58.6% | 54.9% – 62.3% |
| 49 | Jarrett Stidham◦ provisional | NE | QB | 48 | 45.8% | 58.4% | 53.4% – 63.2% |
| 50 | Ben DiNucci◦ provisional | DAL | QB | 50 | 46.0% | 58.3% | 53.4% – 63.2% |
| 51 | Ryan Finley◦ provisional | CIN | QB | 41 | 41.5% | 58.0% | 53.0% – 63.0% |
| 52 | Daniel Jones | NYG | QB | 496 | 56.5% | 57.9% | 54.9% – 60.9% |
| 53 | Joe Flacco◦ provisional | NYJ | QB | 141 | 52.5% | 57.8% | 53.5% – 62.0% |
| 54 | Jake Luton◦ provisional | JAX | QB | 118 | 50.8% | 57.5% | 53.1% – 61.9% |
| 55 | Jeff Driskel◦ provisional | DEN | QB | 76 | 46.1% | 57.3% | 52.5% – 61.9% |
| 56 | Drew Lock | DEN | QB | 466 | 54.5% | 56.6% | 53.5% – 59.7% |
| 57 | Sam Darnold | NYJ | QB | 401 | 54.1% | 56.6% | 53.3% – 59.9% |
| 58 | Jalen Hurts◦ provisional | PHI | QB | 162 | 47.5% | 55.4% | 51.2% – 59.5% |
| 59 | Carson Wentz | PHI | QB | 493 | 50.9% | 54.1% | 51.0% – 57.1% |
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).