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 · 2025
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
- 255
- 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 · 2025 · full board
| # | Player | Team | Pos | attempts | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Drake Maye | NE | QB | 472 | +10.8 | +7.2 | +4.6 – +9.9 |
| 2 | Brock Purdy | SF | QB | 272 | +7.2 | +4.1 | +0.9 – +7.2 |
| 3 | Jordan Love | GB | QB | 411 | +5.5 | +3.7 | +0.9 – +6.4 |
| 4 | Sam Darnold | SEA | QB | 451 | +5.2 | +3.6 | +0.9 – +6.3 |
| 5 | Malik Willis◦ provisional | GB | QB | 35 | +22.0 | +3.2 | -1.0 – +7.4 |
| 6 | Tyler Huntley◦ provisional | BAL | QB | 65 | +12.9 | +3.2 | -0.8 – +7.2 |
| 7 | Joe Burrow◦ provisional | CIN | QB | 248 | +4.7 | +2.6 | -0.6 – +5.8 |
| 8 | Josh Allen | BUF | QB | 445 | +3.5 | +2.5 | -0.2 – +5.2 |
| 9 | Jalen Hurts | PHI | QB | 427 | +3.2 | +2.2 | -0.5 – +5.0 |
| 10 | Mac Jones | SF | QB | 278 | +3.7 | +2.2 | -0.9 – +5.3 |
| 11 | Marcus Mariota◦ provisional | WAS | QB | 210 | +3.2 | +1.8 | -1.5 – +5.1 |
| 12 | Dak Prescott | DAL | QB | 584 | +2.2 | +1.7 | -0.8 – +4.2 |
| 13 | Daniel Jones | IND | QB | 373 | +2.3 | +1.6 | -1.2 – +4.5 |
| 14 | Mitchell Trubisky◦ provisional | BUF | QB | 34 | +7.8 | +1.5 | -2.7 – +5.7 |
| 15 | Mason Rudolph◦ provisional | PIT | QB | 50 | +5.8 | +1.5 | -2.6 – +5.6 |
| 16 | Spencer Rattler◦ provisional | NO | QB | 245 | +2.4 | +1.5 | -1.7 – +4.7 |
| 17 | Tua Tagovailoa | MIA | QB | 369 | +2.0 | +1.5 | -1.4 – +4.3 |
| 18 | Jared Goff | DET | QB | 546 | +1.8 | +1.4 | -1.1 – +3.9 |
| 19 | Andy Dalton◦ provisional | CAR | QB | 36 | +6.6 | +1.4 | -2.8 – +5.6 |
| 20 | Matthew Stafford | LA | QB | 580 | +1.6 | +1.3 | -1.2 – +3.8 |
| 21 | Jacoby Brissett | ARI | QB | 457 | +1.6 | +1.3 | -1.4 – +4.0 |
| 22 | Justin Herbert | LAC | QB | 494 | +1.6 | +1.3 | -1.3 – +3.9 |
| 23 | Lamar Jackson | BAL | QB | 290 | +1.8 | +1.2 | -1.8 – +4.3 |
| 24 | Tyler Shough | NO | QB | 315 | +1.6 | +1.2 | -1.8 – +4.2 |
| 25 | Josh Johnson◦ provisional | WAS | QB | 48 | +2.0 | +0.9 | -3.2 – +5.0 |
| 26 | Bryce Young | CAR | QB | 444 | +1.0 | +0.9 | -1.8 – +3.6 |
| 27 | Carson Wentz◦ provisional | MIN | QB | 161 | +1.1 | +0.8 | -2.7 – +4.3 |
| 28 | Tanner McKee◦ provisional | PHI | QB | 37 | +1.4 | +0.8 | -3.4 – +4.9 |
| 29 | Quinn Ewers◦ provisional | MIA | QB | 82 | +1.0 | +0.7 | -3.2 – +4.6 |
| 30 | Geno Smith | LV | QB | 428 | +0.7 | +0.7 | -2.0 – +3.4 |
| 31 | Jake Browning◦ provisional | CIN | QB | 120 | +0.4 | +0.6 | -3.1 – +4.3 |
| 32 | C.J. Stroud | HOU | QB | 401 | +0.4 | +0.5 | -2.3 – +3.3 |
| 33 | Patrick Mahomes | KC | QB | 473 | +0.3 | +0.5 | -2.2 – +3.1 |
| 34 | Aaron Rodgers | PIT | QB | 472 | +0.0 | +0.3 | -2.4 – +2.9 |
| 35 | Cooper Rush◦ provisional | BAL | QB | 51 | -1.9 | +0.2 | -3.9 – +4.3 |
| 36 | Kyler Murray◦ provisional | ARI | QB | 157 | -0.5 | +0.2 | -3.3 – +3.7 |
| 37 | Jaxson Dart | NYG | QB | 329 | -0.2 | +0.2 | -2.8 – +3.1 |
| 38 | Tyrod Taylor◦ provisional | NYJ | QB | 127 | -0.9 | +0.1 | -3.5 – +3.8 |
| 39 | Russell Wilson◦ provisional | NYG | QB | 109 | -1.5 | +0.0 | -3.7 – +3.8 |
| 40 | Jameis Winston◦ provisional | NYG | QB | 63 | -3.1 | -0.1 | -4.1 – +3.9 |
| 41 | Chris Oladokun◦ provisional | KC | QB | 52 | -3.9 | -0.1 | -4.2 – +4.0 |
| 42 | Max Brosmer◦ provisional | MIN | QB | 68 | -3.5 | -0.2 | -4.2 – +3.8 |
| 43 | Riley Leonard◦ provisional | IND | QB | 64 | -3.9 | -0.2 | -4.3 – +3.8 |
| 44 | Kenny Pickett◦ provisional | LV | QB | 44 | -6.5 | -0.4 | -4.5 – +3.7 |
| 45 | Justin Fields◦ provisional | NYJ | QB | 194 | -1.9 | -0.4 | -3.8 – +2.9 |
| 46 | Philip Rivers◦ provisional | IND | QB | 90 | -3.7 | -0.5 | -4.3 – +3.4 |
| 47 | Bo Nix | DEN | QB | 583 | -1.2 | -0.6 | -3.1 – +1.8 |
| 48 | Jayden Daniels◦ provisional | WAS | QB | 174 | -2.7 | -0.7 | -4.2 – +2.7 |
| 49 | Brandon Allen◦ provisional | TEN | QB | 30 | -13.1 | -0.8 | -5.0 – +3.5 |
| 50 | Trey Lance◦ provisional | LAC | QB | 50 | -9.8 | -1.1 | -5.1 – +3.0 |
| 51 | Kirk Cousins | ATL | QB | 255 | -2.8 | -1.1 | -4.2 – +2.1 |
| 52 | Trevor Lawrence | JAX | QB | 544 | -1.9 | -1.1 | -3.6 – +1.5 |
| 53 | Baker Mayfield | TB | QB | 527 | -2.1 | -1.2 | -3.8 – +1.3 |
| 54 | Joe Flacco | CIN | QB | 386 | -2.8 | -1.4 | -4.3 – +1.4 |
| 55 | Michael Penix Jr. | ATL | QB | 264 | -3.6 | -1.5 | -4.7 – +1.6 |
| 56 | Cam Ward | TEN | QB | 499 | -2.9 | -1.7 | -4.3 – +0.9 |
| 57 | Shedeur Sanders◦ provisional | CLE | QB | 195 | -5.0 | -1.8 | -5.2 – +1.6 |
| 58 | Davis Mills◦ provisional | HOU | QB | 152 | -6.6 | -2.1 | -5.6 – +1.5 |
| 59 | Caleb Williams | CHI | QB | 526 | -3.5 | -2.1 | -4.7 – +0.4 |
| 60 | J.J. McCarthy◦ provisional | MIN | QB | 238 | -5.7 | -2.4 | -5.6 – +0.8 |
| 61 | Dillon Gabriel◦ provisional | CLE | QB | 181 | -7.5 | -2.7 | -6.2 – +0.7 |
| 62 | Brady Cook◦ provisional | NYJ | QB | 148 | -10.0 | -3.3 | -6.8 – +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).