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 · 2021
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
- 258
- 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 · 2021 · full board
| # | Player | Team | Pos | attempts | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Joe Burrow | CIN | QB | 506 | +6.6 | +4.5 | +1.9 – +7.1 |
| 2 | Aaron Rodgers | GB | QB | 510 | +5.8 | +3.9 | +1.3 – +6.5 |
| 3 | Kyler Murray | ARI | QB | 461 | +4.2 | +2.8 | +0.1 – +5.5 |
| 4 | Teddy Bridgewater | DEN | QB | 405 | +3.9 | +2.5 | -0.3 – +5.3 |
| 5 | Russell Wilson | SEA | QB | 386 | +3.2 | +2.0 | -0.8 – +4.8 |
| 6 | Patrick Mahomes | KC | QB | 620 | +2.7 | +2.0 | -0.4 – +4.4 |
| 7 | Geno Smith◦ provisional | SEA | QB | 88 | +6.5 | +1.9 | -2.0 – +5.7 |
| 8 | Jimmy Garoppolo | SF | QB | 426 | +2.6 | +1.7 | -1.0 – +4.5 |
| 9 | Dak Prescott | DAL | QB | 586 | +2.3 | +1.7 | -0.8 – +4.2 |
| 10 | Mac Jones | NE | QB | 511 | +2.4 | +1.7 | -0.9 – +4.3 |
| 11 | Ryan Tannehill | TEN | QB | 519 | +2.4 | +1.7 | -0.9 – +4.2 |
| 12 | Derek Carr | LV | QB | 601 | +2.2 | +1.6 | -0.8 – +4.1 |
| 13 | Josh Allen | BUF | QB | 614 | +2.1 | +1.6 | -0.9 – +4.0 |
| 14 | Tom Brady | TB | QB | 704 | +1.7 | +1.3 | -1.0 – +3.6 |
| 15 | Matt Ryan | ATL | QB | 542 | +1.8 | +1.3 | -1.3 – +3.8 |
| 16 | Tua Tagovailoa | MIA | QB | 380 | +1.9 | +1.3 | -1.6 – +4.1 |
| 17 | Colt McCoy◦ provisional | ARI | QB | 98 | +3.5 | +1.2 | -2.6 – +5.0 |
| 18 | Kirk Cousins | MIN | QB | 537 | +1.4 | +1.0 | -1.5 – +3.5 |
| 19 | Joe Flacco◦ provisional | NYJ | QB | 38 | +5.4 | +0.9 | -3.2 – +5.1 |
| 20 | Gardner Minshew◦ provisional | PHI | QB | 57 | +3.2 | +0.8 | -3.2 – +4.8 |
| 21 | Nick Mullens◦ provisional | CLE | QB | 29 | +4.7 | +0.7 | -3.5 – +5.0 |
| 22 | Nick Foles◦ provisional | CHI | QB | 35 | +2.5 | +0.5 | -3.6 – +4.7 |
| 23 | Lamar Jackson | BAL | QB | 371 | +0.7 | +0.5 | -2.3 – +3.4 |
| 24 | Jared Goff | DET | QB | 467 | +0.6 | +0.5 | -2.2 – +3.1 |
| 25 | Josh Johnson◦ provisional | BAL | QB | 82 | +0.6 | +0.4 | -3.5 – +4.2 |
| 26 | Garrett Gilbert◦ provisional | WAS | QB | 30 | +0.8 | +0.3 | -3.9 – +4.5 |
| 27 | Taylor Heinicke | WAS | QB | 480 | +0.3 | +0.3 | -2.3 – +2.9 |
| 28 | Jalen Hurts | PHI | QB | 409 | +0.1 | +0.2 | -2.6 – +2.9 |
| 29 | Case Keenum◦ provisional | CLE | QB | 70 | -0.7 | +0.1 | -3.9 – +4.0 |
| 30 | Matthew Stafford | LA | QB | 596 | -0.1 | +0.0 | -2.4 – +2.5 |
| 31 | Davis Mills | HOU | QB | 378 | -0.2 | -0.0 | -2.9 – +2.8 |
| 32 | Tyler Huntley◦ provisional | BAL | QB | 182 | -1.1 | -0.3 | -3.7 – +3.1 |
| 33 | Cooper Rush◦ provisional | DAL | QB | 47 | -3.5 | -0.3 | -4.4 – +3.8 |
| 34 | Justin Herbert | LAC | QB | 657 | -0.6 | -0.4 | -2.7 – +2.0 |
| 35 | Daniel Jones | NYG | QB | 347 | -0.8 | -0.4 | -3.3 – +2.5 |
| 36 | Sean Mannion◦ provisional | MIN | QB | 34 | -5.4 | -0.4 | -4.6 – +3.8 |
| 37 | Mike White◦ provisional | NYJ | QB | 131 | -2.1 | -0.5 | -4.2 – +3.1 |
| 38 | Trey Lance◦ provisional | SF | QB | 69 | -4.1 | -0.7 | -4.6 – +3.3 |
| 39 | Tim Boyle◦ provisional | DET | QB | 93 | -3.5 | -0.7 | -4.5 – +3.1 |
| 40 | Drew Lock◦ provisional | DEN | QB | 109 | -3.3 | -0.8 | -4.5 – +2.9 |
| 41 | Jordan Love◦ provisional | GB | QB | 60 | -5.5 | -0.8 | -4.8 – +3.2 |
| 42 | Justin Fields | CHI | QB | 261 | -2.0 | -0.8 | -4.0 – +2.3 |
| 43 | Jacoby Brissett◦ provisional | MIA | QB | 217 | -2.2 | -0.9 | -4.1 – +2.4 |
| 44 | Mason Rudolph◦ provisional | PIT | QB | 56 | -6.1 | -0.9 | -4.9 – +3.2 |
| 45 | Jameis Winston◦ provisional | NO | QB | 153 | -3.1 | -1.0 | -4.5 – +2.5 |
| 46 | Tyrod Taylor◦ provisional | HOU | QB | 144 | -3.6 | -1.1 | -4.7 – +2.4 |
| 47 | Carson Wentz | IND | QB | 497 | -2.1 | -1.3 | -3.9 – +1.3 |
| 48 | Baker Mayfield | CLE | QB | 400 | -2.7 | -1.5 | -4.3 – +1.2 |
| 49 | Ben Roethlisberger | PIT | QB | 596 | -2.4 | -1.6 | -4.0 – +0.9 |
| 50 | PJ Walker◦ provisional | CAR | QB | 65 | -9.2 | -1.6 | -5.6 – +2.4 |
| 51 | Brandon Allen◦ provisional | CIN | QB | 33 | -17.4 | -1.7 | -5.9 – +2.5 |
| 52 | Trevor Siemian◦ provisional | NO | QB | 175 | -4.7 | -1.7 | -5.2 – +1.7 |
| 53 | Andy Dalton◦ provisional | CHI | QB | 227 | -4.2 | -1.8 | -5.1 – +1.4 |
| 54 | Mike Glennon◦ provisional | NYG | QB | 154 | -7.9 | -2.8 | -6.3 – +0.8 |
| 55 | Sam Darnold | CAR | QB | 384 | -4.9 | -2.8 | -5.6 – +0.0 |
| 56 | Jake Fromm◦ provisional | NYG | QB | 58 | -18.5 | -3.2 | -7.2 – +0.8 |
| 57 | Trevor Lawrence | JAX | QB | 581 | -4.8 | -3.2 | -5.7 – -0.8 |
| 58 | Cam Newton◦ provisional | CAR | QB | 124 | -12.6 | -3.9 | -7.6 – -0.3 |
| 59 | Zach Wilson | NYJ | QB | 366 | -9.6 | -5.5 | -8.4 – -2.7 |
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).