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.
CPOE · 2020
Completion % over expected (accounts for depth & situation).
- Beats raw by
- 17.9%
- lower out-of-sample error
- RMSE raw → shrunk
- 4.9 → 4.0
- odd vs. even weeks
- Split-half reliability
- 0.35
- how repeatable the raw stat is
- Stabilizes at
- 271
- 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.
CPOE · 2020 · full board
| # | Player | Team | Pos | attempts | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Aaron Rodgers | GB | QB | 501 | +7.2 | +5.1 | +2.5 – +7.7 |
| 2 | Russell Wilson | SEA | QB | 532 | +6.8 | +5.0 | +2.4 – +7.5 |
| 3 | Josh Allen | BUF | QB | 548 | +6.6 | +4.8 | +2.3 – +7.3 |
| 4 | Deshaun Watson | HOU | QB | 523 | +6.5 | +4.7 | +2.2 – +7.3 |
| 5 | Kirk Cousins | MIN | QB | 485 | +4.6 | +3.4 | +0.8 – +6.0 |
| 6 | Teddy Bridgewater | CAR | QB | 469 | +4.0 | +3.0 | +0.4 – +5.6 |
| 7 | Gardner Minshew | JAX | QB | 309 | +4.3 | +2.9 | -0.1 – +5.8 |
| 8 | Tom Brady | TB | QB | 590 | +3.6 | +2.8 | +0.4 – +5.3 |
| 9 | Kyle Allen◦ provisional | WAS | QB | 79 | +8.0 | +2.8 | -1.0 – +6.6 |
| 10 | Patrick Mahomes | KC | QB | 570 | +2.8 | +2.3 | -0.1 – +4.8 |
| 11 | Ryan Fitzpatrick◦ provisional | MIA | QB | 264 | +3.4 | +2.3 | -0.8 – +5.4 |
| 12 | Baker Mayfield | CLE | QB | 453 | +2.8 | +2.2 | -0.4 – +4.9 |
| 13 | Ryan Tannehill | TEN | QB | 464 | +2.7 | +2.1 | -0.5 – +4.8 |
| 14 | Derek Carr | LV | QB | 491 | +2.6 | +2.1 | -0.5 – +4.7 |
| 15 | Brett Rypien◦ provisional | DEN | QB | 37 | +8.2 | +2.1 | -2.0 – +6.2 |
| 16 | Kyler Murray | ARI | QB | 528 | +2.2 | +1.9 | -0.6 – +4.4 |
| 17 | Joe Burrow | CIN | QB | 392 | +2.1 | +1.8 | -1.0 – +4.5 |
| 18 | Chad Henne◦ provisional | KC | QB | 37 | +4.4 | +1.6 | -2.4 – +5.7 |
| 19 | Nick Foles | CHI | QB | 299 | +1.7 | +1.5 | -1.5 – +4.5 |
| 20 | Drew Brees | NO | QB | 379 | +1.6 | +1.5 | -1.4 – +4.3 |
| 21 | Matt Ryan | ATL | QB | 603 | +1.2 | +1.2 | -1.2 – +3.7 |
| 22 | Mitchell Trubisky | CHI | QB | 293 | +1.1 | +1.2 | -1.8 – +4.2 |
| 23 | Lamar Jackson | BAL | QB | 363 | +1.0 | +1.1 | -1.7 – +4.0 |
| 24 | Jared Goff | LA | QB | 525 | +0.9 | +1.0 | -1.5 – +3.6 |
| 25 | Chase Daniel◦ provisional | DET | QB | 41 | -1.1 | +0.9 | -3.1 – +5.0 |
| 26 | Philip Rivers | IND | QB | 527 | +0.7 | +0.9 | -1.6 – +3.4 |
| 27 | Jimmy Garoppolo◦ provisional | SF | QB | 138 | +0.2 | +0.9 | -2.6 – +4.4 |
| 28 | Marcus Mariota◦ provisional | LV | QB | 26 | -2.7 | +0.9 | -3.2 – +5.1 |
| 29 | Mason Rudolph◦ provisional | PIT | QB | 42 | -1.3 | +0.9 | -3.1 – +5.0 |
| 30 | Tyrod Taylor◦ provisional | LAC | QB | 29 | -2.5 | +0.9 | -3.2 – +5.0 |
| 31 | Dak Prescott◦ provisional | DAL | QB | 218 | +0.3 | +0.8 | -2.4 – +4.1 |
| 32 | Colt McCoy◦ provisional | NYG | QB | 66 | -1.4 | +0.7 | -3.2 – +4.6 |
| 33 | C.J. Beathard◦ provisional | SF | QB | 97 | -0.9 | +0.7 | -3.1 – +4.4 |
| 34 | Ryan Finley◦ provisional | CIN | QB | 32 | -6.0 | +0.5 | -3.6 – +4.6 |
| 35 | Justin Herbert | LAC | QB | 580 | +0.0 | +0.4 | -2.0 – +2.9 |
| 36 | John Wolford◦ provisional | LA | QB | 37 | -5.8 | +0.4 | -3.7 – +4.5 |
| 37 | Andy Dalton | DAL | QB | 318 | -0.4 | +0.4 | -2.6 – +3.3 |
| 38 | Garrett Gilbert◦ provisional | DAL | QB | 37 | -6.4 | +0.3 | -3.8 – +4.4 |
| 39 | Alex Smith◦ provisional | WAS | QB | 238 | -0.8 | +0.3 | -2.9 – +3.4 |
| 40 | PJ Walker◦ provisional | CAR | QB | 56 | -5.1 | +0.2 | -3.8 – +4.1 |
| 41 | Joe Flacco◦ provisional | NYJ | QB | 124 | -2.3 | +0.1 | -3.5 – +3.7 |
| 42 | Tua Tagovailoa | MIA | QB | 281 | -1.2 | -0.0 | -3.0 – +3.0 |
| 43 | Cam Newton | NE | QB | 355 | -1.0 | -0.0 | -2.9 – +2.8 |
| 44 | Jeff Driskel◦ provisional | DEN | QB | 62 | -5.9 | -0.1 | -4.0 – +3.8 |
| 45 | Ben DiNucci◦ provisional | DAL | QB | 41 | -9.9 | -0.2 | -4.3 – +3.8 |
| 46 | Matthew Stafford | DET | QB | 510 | -1.0 | -0.2 | -2.8 – +2.3 |
| 47 | Jarrett Stidham◦ provisional | NE | QB | 38 | -11.4 | -0.3 | -4.4 – +3.8 |
| 48 | Ben Roethlisberger | PIT | QB | 606 | -1.1 | -0.3 | -2.8 – +2.1 |
| 49 | Brandon Allen◦ provisional | CIN | QB | 139 | -3.6 | -0.4 | -3.9 – +3.1 |
| 50 | Sam Darnold | NYJ | QB | 338 | -1.9 | -0.5 | -3.4 – +2.4 |
| 51 | Mike Glennon◦ provisional | JAX | QB | 171 | -3.7 | -0.7 | -4.1 – +2.7 |
| 52 | Nick Mullens | SF | QB | 319 | -2.6 | -0.8 | -3.8 – +2.1 |
| 53 | Daniel Jones | NYG | QB | 432 | -2.2 | -0.9 | -3.6 – +1.8 |
| 54 | Carson Wentz | PHI | QB | 417 | -3.5 | -1.6 | -4.4 – +1.1 |
| 55 | Dwayne Haskins◦ provisional | WAS | QB | 234 | -5.5 | -1.9 | -5.1 – +1.3 |
| 56 | Jalen Hurts◦ provisional | PHI | QB | 134 | -8.3 | -1.9 | -5.5 – +1.6 |
| 57 | Jake Luton◦ provisional | JAX | QB | 105 | -10.5 | -2.0 | -5.7 – +1.7 |
| 58 | Drew Lock | DEN | QB | 426 | -5.5 | -2.9 | -5.6 – -0.2 |
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).