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 · 2024
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
- 202
- 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 · 2024 · full board
| # | Player | Team | Pos | attempts | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Joe Burrow | CIN | QB | 628 | +6.8 | +5.4 | +2.9 – +7.8 |
| 2 | Jalen Hurts | PHI | QB | 334 | +7.5 | +5.1 | +2.0 – +8.1 |
| 3 | Geno Smith | SEA | QB | 554 | +5.6 | +4.4 | +1.8 – +7.0 |
| 4 | Jared Goff | DET | QB | 510 | +5.7 | +4.4 | +1.7 – +7.0 |
| 5 | Marcus Mariota◦ provisional | WAS | QB | 42 | +16.6 | +3.7 | -0.8 – +8.2 |
| 6 | Lamar Jackson | BAL | QB | 454 | +4.6 | +3.5 | +0.7 – +6.2 |
| 7 | Russell Wilson | PIT | QB | 306 | +4.5 | +3.1 | -0.0 – +6.2 |
| 8 | Sam Darnold | MIN | QB | 514 | +3.9 | +3.1 | +0.4 – +5.7 |
| 9 | Joe Milton III◦ provisional | NE | QB | 27 | +17.1 | +2.9 | -1.7 – +7.6 |
| 10 | Baker Mayfield | TB | QB | 562 | +3.6 | +2.9 | +0.4 – +5.5 |
| 11 | Tua Tagovailoa | MIA | QB | 388 | +3.8 | +2.8 | -0.1 – +5.8 |
| 12 | Jayden Daniels | WAS | QB | 461 | +3.5 | +2.8 | +0.0 – +5.5 |
| 13 | Derek Carr | NO | QB | 262 | +3.3 | +2.3 | -1.0 – +5.6 |
| 14 | Malik Willis◦ provisional | GB | QB | 53 | +6.9 | +2.3 | -2.2 – +6.7 |
| 15 | Patrick Mahomes | KC | QB | 553 | +2.6 | +2.2 | -0.4 – +4.7 |
| 16 | Drake Maye | NE | QB | 322 | +2.8 | +2.1 | -0.9 – +5.2 |
| 17 | Tyler Huntley◦ provisional | MIA | QB | 124 | +3.1 | +1.8 | -2.1 – +5.7 |
| 18 | Kyler Murray | ARI | QB | 521 | +2.1 | +1.8 | -0.8 – +4.4 |
| 19 | Brock Purdy | SF | QB | 440 | +2.1 | +1.7 | -1.0 – +4.5 |
| 20 | Justin Herbert | LAC | QB | 485 | +1.9 | +1.7 | -1.0 – +4.4 |
| 21 | Tommy DeVito◦ provisional | NYG | QB | 41 | +4.7 | +1.7 | -2.9 – +6.2 |
| 22 | Justin Fields◦ provisional | PIT | QB | 152 | +2.4 | +1.6 | -2.1 – +5.4 |
| 23 | Mitchell Trubisky◦ provisional | BUF | QB | 25 | +5.8 | +1.6 | -3.1 – +6.3 |
| 24 | Daniel Jones | NYG | QB | 317 | +1.5 | +1.3 | -1.8 – +4.4 |
| 25 | Skylar Thompson◦ provisional | MIA | QB | 32 | +2.2 | +1.2 | -3.4 – +5.8 |
| 26 | Joshua Dobbs◦ provisional | SF | QB | 46 | +1.6 | +1.2 | -3.3 – +5.6 |
| 27 | Joe Flacco | IND | QB | 242 | +1.1 | +1.1 | -2.3 – +4.4 |
| 28 | Kirk Cousins | ATL | QB | 437 | +1.0 | +1.0 | -1.8 – +3.8 |
| 29 | Kenny Pickett◦ provisional | PHI | QB | 39 | +0.5 | +1.0 | -3.6 – +5.5 |
| 30 | Josh Allen | BUF | QB | 459 | +0.8 | +0.9 | -1.8 – +3.7 |
| 31 | Tanner McKee◦ provisional | PHI | QB | 45 | -0.0 | +0.9 | -3.6 – +5.3 |
| 32 | Bryce Young | CAR | QB | 359 | +0.7 | +0.8 | -2.2 – +3.8 |
| 33 | Jordan Love | GB | QB | 411 | +0.6 | +0.8 | -2.1 – +3.6 |
| 34 | Gardner Minshew | LV | QB | 281 | +0.5 | +0.7 | -2.5 – +4.0 |
| 35 | Bo Nix | DEN | QB | 546 | +0.6 | +0.7 | -1.9 – +3.3 |
| 36 | Mason Rudolph | TEN | QB | 214 | +0.2 | +0.6 | -2.8 – +4.1 |
| 37 | Jimmy Garoppolo◦ provisional | LA | QB | 40 | -3.1 | +0.4 | -4.2 – +4.9 |
| 38 | Brandon Allen◦ provisional | SF | QB | 27 | -5.0 | +0.3 | -4.3 – +5.0 |
| 39 | Caleb Williams | CHI | QB | 522 | -0.1 | +0.2 | -2.4 – +2.8 |
| 40 | Mac Jones | JAX | QB | 250 | -0.5 | +0.2 | -3.1 – +3.5 |
| 41 | Will Levis | TEN | QB | 292 | -0.4 | +0.2 | -3.0 – +3.4 |
| 42 | Andy Dalton◦ provisional | CAR | QB | 156 | -1.1 | +0.1 | -3.6 – +3.8 |
| 43 | Dak Prescott | DAL | QB | 277 | -0.9 | -0.0 | -3.3 – +3.2 |
| 44 | Trevor Lawrence | JAX | QB | 272 | -1.0 | -0.1 | -3.4 – +3.1 |
| 45 | Desmond Ridder◦ provisional | LV | QB | 78 | -3.2 | -0.1 | -4.3 – +4.1 |
| 46 | Matthew Stafford | LA | QB | 500 | -0.7 | -0.2 | -2.8 – +2.5 |
| 47 | Trey Lance◦ provisional | DAL | QB | 40 | -6.9 | -0.3 | -4.8 – +4.3 |
| 48 | Jameis Winston | CLE | QB | 288 | -1.8 | -0.6 | -3.8 – +2.6 |
| 49 | Deshaun Watson | CLE | QB | 210 | -2.2 | -0.6 | -4.1 – +2.9 |
| 50 | Jacoby Brissett◦ provisional | NE | QB | 150 | -2.9 | -0.6 | -4.4 – +3.1 |
| 51 | Tim Boyle◦ provisional | NYG | QB | 46 | -8.5 | -0.7 | -5.2 – +3.8 |
| 52 | Michael Penix Jr.◦ provisional | ATL | QB | 102 | -4.4 | -0.8 | -4.8 – +3.3 |
| 53 | Bailey Zappe◦ provisional | CLE | QB | 30 | -13.6 | -0.8 | -5.5 – +3.8 |
| 54 | Davis Mills◦ provisional | HOU | QB | 36 | -11.7 | -0.9 | -5.5 – +3.7 |
| 55 | C.J. Stroud | HOU | QB | 509 | -1.7 | -0.9 | -3.6 – +1.7 |
| 56 | Aidan O'Connell | LV | QB | 232 | -3.6 | -1.4 | -4.8 – +2.0 |
| 57 | Aaron Rodgers | NYJ | QB | 568 | -2.6 | -1.6 | -4.2 – +0.9 |
| 58 | Jake Haener◦ provisional | NO | QB | 37 | -17.3 | -1.8 | -6.4 – +2.8 |
| 59 | Drew Lock◦ provisional | NYG | QB | 173 | -6.1 | -2.2 | -5.9 – +1.4 |
| 60 | Dorian Thompson-Robinson◦ provisional | CLE | QB | 106 | -11.7 | -3.3 | -7.4 – +0.7 |
| 61 | Spencer Rattler | NO | QB | 213 | -9.1 | -4.1 | -7.6 – -0.7 |
| 62 | Cooper Rush | DAL | QB | 303 | -8.1 | -4.4 | -7.6 – -1.3 |
| 63 | Anthony Richardson | IND | QB | 249 | -10.9 | -5.5 | -8.9 – -2.2 |
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).