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 · 2022
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
- 908
- 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 · 2022 · full board
| # | Player | Team | Pos | attempts | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Geno Smith◦ provisional | SEA | QB | 552 | +5.6 | +2.2 | +0.3 – +4.0 |
| 2 | Patrick Mahomes◦ provisional | KC | QB | 611 | +3.6 | +1.5 | -0.4 – +3.3 |
| 3 | Joe Burrow◦ provisional | CIN | QB | 590 | +2.7 | +1.1 | -0.7 – +3.0 |
| 4 | Jalen Hurts◦ provisional | PHI | QB | 435 | +2.7 | +0.9 | -1.0 – +2.9 |
| 5 | Jacoby Brissett◦ provisional | CLE | QB | 351 | +2.9 | +0.9 | -1.2 – +2.9 |
| 6 | Daniel Jones◦ provisional | NYG | QB | 443 | +2.3 | +0.8 | -1.2 – +2.8 |
| 7 | Sam Darnold◦ provisional | CAR | QB | 119 | +4.9 | +0.6 | -1.6 – +2.9 |
| 8 | Justin Herbert◦ provisional | LAC | QB | 675 | +1.3 | +0.6 | -1.2 – +2.4 |
| 9 | Trevor Lawrence◦ provisional | JAX | QB | 562 | +1.4 | +0.6 | -1.3 – +2.5 |
| 10 | Bailey Zappe◦ provisional | NE | QB | 88 | +5.8 | +0.6 | -1.7 – +2.8 |
| 11 | Kirk Cousins◦ provisional | MIN | QB | 612 | +1.3 | +0.6 | -1.3 – +2.4 |
| 12 | Nick Mullens◦ provisional | MIN | QB | 25 | +15.5 | +0.5 | -1.9 – +2.8 |
| 13 | Tua Tagovailoa◦ provisional | MIA | QB | 387 | +1.4 | +0.5 | -1.5 – +2.5 |
| 14 | Josh Allen◦ provisional | BUF | QB | 544 | +1.0 | +0.4 | -1.5 – +2.3 |
| 15 | Taylor Heinicke◦ provisional | WAS | QB | 243 | +1.7 | +0.4 | -1.7 – +2.5 |
| 16 | Tyler Huntley◦ provisional | BAL | QB | 107 | +3.2 | +0.4 | -1.9 – +2.7 |
| 17 | Jameis Winston◦ provisional | NO | QB | 111 | +2.7 | +0.4 | -1.9 – +2.6 |
| 18 | Mitchell Trubisky◦ provisional | PIT | QB | 177 | +1.6 | +0.3 | -1.9 – +2.5 |
| 19 | Kenny Pickett◦ provisional | PIT | QB | 369 | +0.8 | +0.3 | -1.7 – +2.3 |
| 20 | Tom Brady◦ provisional | TB | QB | 707 | +0.5 | +0.3 | -1.5 – +2.0 |
| 21 | Aaron Rodgers◦ provisional | GB | QB | 520 | +0.5 | +0.2 | -1.7 – +2.1 |
| 22 | Andy Dalton◦ provisional | NO | QB | 364 | +0.6 | +0.2 | -1.8 – +2.2 |
| 23 | Ryan Tannehill◦ provisional | TEN | QB | 317 | +0.5 | +0.2 | -1.9 – +2.2 |
| 24 | Jarrett Stidham◦ provisional | LV | QB | 79 | +1.5 | +0.2 | -2.1 – +2.5 |
| 25 | Teddy Bridgewater◦ provisional | MIA | QB | 75 | +1.6 | +0.2 | -2.1 – +2.5 |
| 26 | David Blough◦ provisional | ARI | QB | 56 | +0.6 | +0.1 | -2.2 – +2.4 |
| 27 | Dak Prescott◦ provisional | DAL | QB | 388 | +0.0 | +0.1 | -1.9 – +2.0 |
| 28 | Matthew Stafford◦ provisional | LA | QB | 296 | -0.0 | +0.0 | -2.0 – +2.1 |
| 29 | Colt McCoy◦ provisional | ARI | QB | 129 | -0.3 | +0.0 | -2.2 – +2.3 |
| 30 | Matt Ryan◦ provisional | IND | QB | 439 | -0.1 | +0.0 | -2.0 – +2.0 |
| 31 | Joshua Dobbs◦ provisional | TEN | QB | 65 | -1.6 | -0.0 | -2.4 – +2.3 |
| 32 | Brock Purdy◦ provisional | SF | QB | 166 | -0.7 | -0.1 | -2.3 – +2.1 |
| 33 | Gardner Minshew◦ provisional | PHI | QB | 70 | -1.8 | -0.1 | -2.4 – +2.2 |
| 34 | Desmond Ridder◦ provisional | ATL | QB | 110 | -1.3 | -0.1 | -2.3 – +2.2 |
| 35 | Trevor Siemian◦ provisional | CHI | QB | 25 | -5.8 | -0.1 | -2.4 – +2.3 |
| 36 | Mac Jones◦ provisional | NE | QB | 424 | -0.4 | -0.1 | -2.1 – +1.9 |
| 37 | Marcus Mariota◦ provisional | ATL | QB | 290 | -0.6 | -0.1 | -2.2 – +2.0 |
| 38 | Lamar Jackson◦ provisional | BAL | QB | 309 | -0.6 | -0.1 | -2.2 – +2.0 |
| 39 | Kyler Murray◦ provisional | ARI | QB | 372 | -0.8 | -0.2 | -2.2 – +1.8 |
| 40 | Jimmy Garoppolo◦ provisional | SF | QB | 306 | -1.0 | -0.2 | -2.3 – +1.8 |
| 41 | Davis Webb◦ provisional | NYG | QB | 38 | -7.0 | -0.2 | -2.6 – +2.1 |
| 42 | Brett Rypien◦ provisional | DEN | QB | 87 | -3.7 | -0.3 | -2.5 – +2.0 |
| 43 | Sam Ehlinger◦ provisional | IND | QB | 99 | -3.5 | -0.3 | -2.6 – +2.0 |
| 44 | Nick Foles◦ provisional | IND | QB | 41 | -8.2 | -0.3 | -2.6 – +2.0 |
| 45 | John Wolford◦ provisional | LA | QB | 61 | -5.7 | -0.3 | -2.6 – +2.0 |
| 46 | Russell Wilson◦ provisional | DEN | QB | 454 | -1.2 | -0.3 | -2.3 – +1.6 |
| 47 | Bryce Perkins◦ provisional | LA | QB | 33 | -11.8 | -0.4 | -2.7 – +2.0 |
| 48 | Deshaun Watson◦ provisional | CLE | QB | 155 | -3.3 | -0.4 | -2.6 – +1.8 |
| 49 | Trey Lance◦ provisional | SF | QB | 29 | -16.5 | -0.5 | -2.8 – +1.9 |
| 50 | Skylar Thompson◦ provisional | MIA | QB | 100 | -5.2 | -0.5 | -2.7 – +1.8 |
| 51 | Malik Willis◦ provisional | TEN | QB | 52 | -10.6 | -0.5 | -2.8 – +1.8 |
| 52 | Jared Goff◦ provisional | DET | QB | 562 | -1.5 | -0.5 | -2.4 – +1.3 |
| 53 | Justin Fields◦ provisional | CHI | QB | 303 | -2.5 | -0.6 | -2.6 – +1.5 |
| 54 | Joe Flacco◦ provisional | NYJ | QB | 182 | -4.1 | -0.6 | -2.8 – +1.5 |
| 55 | Kyle Allen◦ provisional | HOU | QB | 75 | -9.1 | -0.6 | -2.9 – +1.7 |
| 56 | PJ Walker◦ provisional | CAR | QB | 105 | -7.6 | -0.7 | -3.0 – +1.5 |
| 57 | Trace McSorley◦ provisional | ARI | QB | 77 | -10.6 | -0.8 | -3.1 – +1.5 |
| 58 | Carson Wentz◦ provisional | WAS | QB | 270 | -3.8 | -0.8 | -2.9 – +1.3 |
| 59 | Anthony Brown◦ provisional | BAL | QB | 47 | -19.3 | -0.9 | -3.2 – +1.4 |
| 60 | Mike White◦ provisional | NYJ | QB | 169 | -6.2 | -0.9 | -3.1 – +1.3 |
| 61 | Derek Carr◦ provisional | LV | QB | 478 | -2.9 | -0.9 | -2.9 – +1.0 |
| 62 | Cooper Rush◦ provisional | DAL | QB | 157 | -6.8 | -1.0 | -3.2 – +1.2 |
| 63 | Zach Wilson◦ provisional | NYJ | QB | 221 | -5.6 | -1.0 | -3.2 – +1.1 |
| 64 | Davis Mills◦ provisional | HOU | QB | 463 | -3.8 | -1.2 | -3.2 – +0.7 |
| 65 | Baker Mayfield◦ provisional | LA | QB | 322 | -7.0 | -1.8 | -3.8 – +0.3 |
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).