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.
EPA per dropback · 2016
Mean QB EPA per dropback.
- Beats raw by
- 14.9%
- lower out-of-sample error
- RMSE raw → shrunk
- 0.17 → 0.14
- odd vs. even weeks
- Split-half reliability
- 0.47
- how repeatable the raw stat is
- Stabilizes at
- 222
- dropbacks 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.
EPA per dropback · 2016 · full board
| # | Player | Team | Pos | dropbacks | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Tom Brady | NE | QB | 448 | +0.33 | +0.24 | +0.14 – +0.34 |
| 2 | Matt Ryan | ATL | QB | 575 | +0.30 | +0.23 | +0.14 – +0.32 |
| 3 | Dak Prescott | DAL | QB | 484 | +0.25 | +0.19 | +0.10 – +0.29 |
| 4 | Aaron Rodgers | GB | QB | 645 | +0.20 | +0.17 | +0.08 – +0.25 |
| 5 | Kirk Cousins | WAS | QB | 628 | +0.18 | +0.15 | +0.06 – +0.24 |
| 6 | Jimmy Garoppolo◦ provisional | NE | QB | 66 | +0.42 | +0.14 | -0.00 – +0.29 |
| 7 | Matt Moore◦ provisional | MIA | QB | 87 | +0.34 | +0.14 | -0.00 – +0.29 |
| 8 | Drew Brees | NO | QB | 695 | +0.16 | +0.14 | +0.05 – +0.22 |
| 9 | Ben Roethlisberger | PIT | QB | 532 | +0.16 | +0.13 | +0.04 – +0.22 |
| 10 | Derek Carr | LV | QB | 580 | +0.14 | +0.12 | +0.03 – +0.21 |
| 11 | Brian Hoyer◦ provisional | CHI | QB | 202 | +0.17 | +0.12 | -0.01 – +0.24 |
| 12 | Matthew Stafford | DET | QB | 630 | +0.12 | +0.10 | +0.02 – +0.19 |
| 13 | Marcus Mariota | TEN | QB | 475 | +0.12 | +0.10 | +0.01 – +0.20 |
| 14 | Andy Dalton | CIN | QB | 602 | +0.11 | +0.10 | +0.01 – +0.18 |
| 15 | Andrew Luck | IND | QB | 586 | +0.10 | +0.09 | +0.00 – +0.18 |
| 16 | Jameis Winston | TB | QB | 607 | +0.09 | +0.08 | -0.01 – +0.17 |
| 17 | Cody Kessler◦ provisional | CLE | QB | 217 | +0.10 | +0.08 | -0.04 – +0.20 |
| 18 | Russell Wilson | SEA | QB | 587 | +0.09 | +0.08 | -0.01 – +0.17 |
| 19 | Alex Smith | KC | QB | 518 | +0.09 | +0.08 | -0.01 – +0.17 |
| 20 | Shaun Hill◦ provisional | MIN | QB | 36 | +0.17 | +0.08 | -0.08 – +0.24 |
| 21 | Philip Rivers | LAC | QB | 615 | +0.08 | +0.08 | -0.01 – +0.16 |
| 22 | Tyrod Taylor | BUF | QB | 478 | +0.07 | +0.07 | -0.03 – +0.16 |
| 23 | Landry Jones◦ provisional | PIT | QB | 89 | +0.06 | +0.06 | -0.08 – +0.21 |
| 24 | Charlie Whitehurst◦ provisional | CLE | QB | 27 | +0.06 | +0.06 | -0.10 – +0.22 |
| 25 | Sam Bradford | MIN | QB | 590 | +0.06 | +0.06 | -0.03 – +0.15 |
| 26 | Carson Palmer | ARI | QB | 639 | +0.05 | +0.06 | -0.03 – +0.14 |
| 27 | Derek Anderson◦ provisional | CAR | QB | 54 | -0.03 | +0.05 | -0.11 – +0.20 |
| 28 | Trevor Siemian | DEN | QB | 518 | +0.03 | +0.04 | -0.05 – +0.14 |
| 29 | Ryan Tannehill | MIA | QB | 418 | +0.03 | +0.04 | -0.06 – +0.14 |
| 30 | EJ Manuel◦ provisional | BUF | QB | 30 | -0.19 | +0.03 | -0.13 – +0.19 |
| 31 | Paxton Lynch◦ provisional | DEN | QB | 91 | -0.05 | +0.03 | -0.11 – +0.17 |
| 32 | Matt Barkley◦ provisional | CHI | QB | 222 | -0.01 | +0.03 | -0.09 – +0.15 |
| 33 | Nick Foles◦ provisional | KC | QB | 59 | -0.11 | +0.03 | -0.12 – +0.18 |
| 34 | Kevin Hogan◦ provisional | CLE | QB | 28 | -0.27 | +0.03 | -0.13 – +0.19 |
| 35 | Carson Wentz | PHI | QB | 641 | +0.01 | +0.03 | -0.06 – +0.11 |
| 36 | Scott Tolzien◦ provisional | IND | QB | 40 | -0.21 | +0.02 | -0.13 – +0.18 |
| 37 | Jacoby Brissett◦ provisional | NE | QB | 61 | -0.15 | +0.02 | -0.13 – +0.17 |
| 38 | Matt Cassel◦ provisional | TEN | QB | 54 | -0.19 | +0.01 | -0.14 – +0.17 |
| 39 | Eli Manning | NYG | QB | 619 | -0.01 | +0.01 | -0.08 – +0.10 |
| 40 | Tom Savage◦ provisional | HOU | QB | 78 | -0.14 | +0.01 | -0.14 – +0.16 |
| 41 | Colin Kaepernick | SF | QB | 366 | -0.02 | +0.01 | -0.10 – +0.11 |
| 42 | Drew Stanton◦ provisional | ARI | QB | 48 | -0.27 | +0.00 | -0.15 – +0.16 |
| 43 | Ryan Fitzpatrick | NYJ | QB | 422 | -0.04 | -0.01 | -0.11 – +0.09 |
| 44 | Joe Flacco | BAL | QB | 703 | -0.03 | -0.01 | -0.09 – +0.07 |
| 45 | Cam Newton | CAR | QB | 547 | -0.05 | -0.01 | -0.11 – +0.08 |
| 46 | Robert Griffin III◦ provisional | CLE | QB | 169 | -0.13 | -0.02 | -0.15 – +0.11 |
| 47 | Josh McCown◦ provisional | CLE | QB | 183 | -0.14 | -0.03 | -0.15 – +0.10 |
| 48 | Jay Cutler◦ provisional | CHI | QB | 154 | -0.17 | -0.03 | -0.16 – +0.10 |
| 49 | Case Keenum | LA | QB | 345 | -0.10 | -0.04 | -0.14 – +0.07 |
| 50 | Blake Bortles | JAX | QB | 660 | -0.07 | -0.04 | -0.12 – +0.05 |
| 51 | Brock Osweiler | HOU | QB | 534 | -0.09 | -0.04 | -0.13 – +0.05 |
| 52 | Blaine Gabbert◦ provisional | SF | QB | 171 | -0.19 | -0.05 | -0.18 – +0.08 |
| 53 | Bryce Petty◦ provisional | NYJ | QB | 146 | -0.24 | -0.06 | -0.19 – +0.07 |
| 54 | Jared Goff | LA | QB | 230 | -0.38 | -0.16 | -0.28 – -0.04 |
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).