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 · 2023
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
- 304
- 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 · 2023 · full board
| # | Player | Team | Pos | attempts | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Josh Allen | BUF | QB | 545 | +5.0 | +3.4 | +0.9 – +5.8 |
| 2 | Brock Purdy | SF | QB | 427 | +5.4 | +3.3 | +0.7 – +6.0 |
| 3 | Tua Tagovailoa | MIA | QB | 543 | +4.5 | +3.1 | +0.6 – +5.5 |
| 4 | Russell Wilson | DEN | QB | 415 | +4.9 | +3.0 | +0.3 – +5.7 |
| 5 | Dak Prescott | DAL | QB | 581 | +3.9 | +2.7 | +0.3 – +5.1 |
| 6 | Mason Rudolph◦ provisional | PIT | QB | 69 | +12.4 | +2.7 | -1.0 – +6.4 |
| 7 | Jalen Hurts | PHI | QB | 500 | +3.8 | +2.5 | +0.0 – +5.1 |
| 8 | Kirk Cousins◦ provisional | MIN | QB | 302 | +4.3 | +2.4 | -0.5 – +5.3 |
| 9 | Lamar Jackson | BAL | QB | 441 | +3.5 | +2.3 | -0.4 – +4.9 |
| 10 | Nick Mullens◦ provisional | MIN | QB | 143 | +5.7 | +2.1 | -1.2 – +5.5 |
| 11 | Derek Carr | NO | QB | 523 | +3.0 | +2.1 | -0.4 – +4.6 |
| 12 | Jake Browning◦ provisional | CIN | QB | 234 | +3.9 | +2.0 | -1.1 – +5.0 |
| 13 | Patrick Mahomes | KC | QB | 562 | +2.7 | +1.9 | -0.5 – +4.4 |
| 14 | Tyrod Taylor◦ provisional | NYG | QB | 164 | +4.4 | +1.8 | -1.5 – +5.1 |
| 15 | C.J. Beathard◦ provisional | JAX | QB | 52 | +9.8 | +1.8 | -2.0 – +5.6 |
| 16 | Geno Smith | SEA | QB | 472 | +2.4 | +1.7 | -0.9 – +4.2 |
| 17 | Jared Goff | DET | QB | 573 | +1.3 | +1.0 | -1.4 – +3.4 |
| 18 | Jordan Love | GB | QB | 559 | +1.1 | +0.9 | -1.5 – +3.3 |
| 19 | Joe Burrow | CIN | QB | 351 | +1.2 | +0.9 | -1.9 – +3.7 |
| 20 | Trevor Lawrence | JAX | QB | 552 | +0.9 | +0.8 | -1.7 – +3.2 |
| 21 | Ryan Tannehill◦ provisional | TEN | QB | 222 | +1.0 | +0.7 | -2.4 – +3.8 |
| 22 | Justin Fields | CHI | QB | 339 | +0.8 | +0.6 | -2.2 – +3.5 |
| 23 | Daniel Jones◦ provisional | NYG | QB | 153 | +0.3 | +0.4 | -2.9 – +3.8 |
| 24 | Baker Mayfield | TB | QB | 548 | +0.2 | +0.3 | -2.1 – +2.8 |
| 25 | C.J. Stroud | HOU | QB | 476 | +0.2 | +0.3 | -2.2 – +2.9 |
| 26 | Sam Darnold◦ provisional | SF | QB | 44 | -1.4 | +0.2 | -3.6 – +4.1 |
| 27 | Deshaun Watson◦ provisional | CLE | QB | 165 | -0.3 | +0.2 | -3.1 – +3.5 |
| 28 | Will Levis◦ provisional | TEN | QB | 247 | -0.4 | +0.1 | -3.0 – +3.1 |
| 29 | Justin Herbert | LAC | QB | 443 | -0.3 | +0.0 | -2.6 – +2.6 |
| 30 | Case Keenum◦ provisional | HOU | QB | 51 | -2.9 | -0.0 | -3.8 – +3.8 |
| 31 | Sam Howell | WAS | QB | 578 | -0.4 | -0.1 | -2.5 – +2.3 |
| 32 | Mitchell Trubisky◦ provisional | PIT | QB | 104 | -2.2 | -0.2 | -3.8 – +3.3 |
| 33 | Jarrett Stidham◦ provisional | DEN | QB | 62 | -3.7 | -0.2 | -4.0 – +3.5 |
| 34 | Tyler Huntley◦ provisional | BAL | QB | 35 | -7.1 | -0.3 | -4.2 – +3.6 |
| 35 | Jimmy Garoppolo◦ provisional | LV | QB | 165 | -1.9 | -0.4 | -3.7 – +2.9 |
| 36 | Jeff Driskel◦ provisional | CLE | QB | 25 | -11.0 | -0.4 | -4.3 – +3.5 |
| 37 | Tyson Bagent◦ provisional | CHI | QB | 138 | -2.4 | -0.4 | -3.8 – +3.0 |
| 38 | Andy Dalton◦ provisional | CAR | QB | 57 | -5.5 | -0.5 | -4.2 – +3.3 |
| 39 | Desmond Ridder | ATL | QB | 375 | -1.3 | -0.5 | -3.3 – +2.2 |
| 40 | Jameis Winston◦ provisional | NO | QB | 45 | -8.0 | -0.6 | -4.4 – +3.2 |
| 41 | Drew Lock◦ provisional | SEA | QB | 75 | -5.1 | -0.6 | -4.3 – +3.0 |
| 42 | Bryce Young | CAR | QB | 476 | -1.4 | -0.7 | -3.2 – +1.9 |
| 43 | Tim Boyle◦ provisional | NYJ | QB | 74 | -5.6 | -0.7 | -4.4 – +3.0 |
| 44 | Tommy DeVito◦ provisional | NYG | QB | 168 | -2.9 | -0.7 | -4.0 – +2.6 |
| 45 | Kyler Murray◦ provisional | ARI | QB | 262 | -2.3 | -0.8 | -3.8 – +2.2 |
| 46 | Joshua Dobbs | MIN | QB | 398 | -1.8 | -0.8 | -3.5 – +1.9 |
| 47 | Kenny Pickett | PIT | QB | 310 | -2.1 | -0.8 | -3.7 – +2.0 |
| 48 | Joe Flacco◦ provisional | CLE | QB | 197 | -2.9 | -0.8 | -4.0 – +2.4 |
| 49 | Brian Hoyer◦ provisional | LV | QB | 42 | -11.2 | -0.9 | -4.8 – +2.9 |
| 50 | Blaine Gabbert◦ provisional | KC | QB | 34 | -15.4 | -1.1 | -5.0 – +2.8 |
| 51 | Anthony Richardson◦ provisional | IND | QB | 81 | -7.7 | -1.2 | -4.9 – +2.4 |
| 52 | Mac Jones | NE | QB | 339 | -2.9 | -1.3 | -4.1 – +1.5 |
| 53 | Matthew Stafford | LA | QB | 495 | -2.6 | -1.4 | -3.9 – +1.1 |
| 54 | Easton Stick◦ provisional | LAC | QB | 169 | -4.8 | -1.4 | -4.7 – +1.9 |
| 55 | Zach Wilson | NYJ | QB | 343 | -3.1 | -1.4 | -4.2 – +1.4 |
| 56 | Bailey Zappe◦ provisional | NE | QB | 202 | -4.4 | -1.5 | -4.7 – +1.7 |
| 57 | Brett Rypien◦ provisional | LA | QB | 37 | -19.0 | -1.6 | -5.5 – +2.2 |
| 58 | Davis Mills◦ provisional | HOU | QB | 38 | -19.5 | -1.7 | -5.6 – +2.1 |
| 59 | Aidan O'Connell | LV | QB | 322 | -3.9 | -1.8 | -4.6 – +1.1 |
| 60 | Gardner Minshew | IND | QB | 465 | -3.3 | -1.8 | -4.4 – +0.8 |
| 61 | Taylor Heinicke◦ provisional | ATL | QB | 127 | -9.1 | -2.3 | -5.8 – +1.1 |
| 62 | Trevor Siemian◦ provisional | NYJ | QB | 144 | -8.9 | -2.5 | -5.9 – +0.8 |
| 63 | Dorian Thompson-Robinson◦ provisional | CLE | QB | 105 | -11.7 | -2.6 | -6.2 – +0.9 |
| 64 | PJ Walker◦ provisional | CLE | QB | 105 | -13.0 | -3.0 | -6.5 – +0.6 |
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).