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 · 2017
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
- 190
- 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 · 2017 · full board
| # | Player | Team | Pos | dropbacks | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Tom Brady | NE | QB | 618 | +0.23 | +0.18 | +0.09 – +0.27 |
| 2 | Jimmy Garoppolo◦ provisional | SF | QB | 184 | +0.31 | +0.16 | +0.03 – +0.30 |
| 3 | Philip Rivers | LAC | QB | 592 | +0.20 | +0.15 | +0.06 – +0.25 |
| 4 | Carson Wentz | PHI | QB | 473 | +0.21 | +0.15 | +0.05 – +0.25 |
| 5 | Drew Brees | NO | QB | 553 | +0.19 | +0.15 | +0.05 – +0.24 |
| 6 | Jared Goff | LA | QB | 500 | +0.19 | +0.15 | +0.05 – +0.24 |
| 7 | Alex Smith | KC | QB | 540 | +0.17 | +0.13 | +0.03 – +0.22 |
| 8 | Ben Roethlisberger | PIT | QB | 582 | +0.15 | +0.12 | +0.02 – +0.21 |
| 9 | Matt Ryan | ATL | QB | 550 | +0.13 | +0.10 | +0.01 – +0.20 |
| 10 | Case Keenum | MIN | QB | 504 | +0.12 | +0.09 | -0.01 – +0.19 |
| 11 | Jameis Winston | TB | QB | 474 | +0.10 | +0.08 | -0.02 – +0.18 |
| 12 | Deshaun Watson | HOU | QB | 224 | +0.11 | +0.07 | -0.06 – +0.20 |
| 13 | Sam Bradford◦ provisional | MIN | QB | 48 | +0.27 | +0.07 | -0.10 – +0.23 |
| 14 | Aaron Rodgers | GB | QB | 261 | +0.08 | +0.06 | -0.07 – +0.18 |
| 15 | Matthew Stafford | DET | QB | 615 | +0.06 | +0.05 | -0.04 – +0.14 |
| 16 | Patrick Mahomes◦ provisional | KC | QB | 37 | +0.21 | +0.05 | -0.12 – +0.22 |
| 17 | Blake Bortles | JAX | QB | 550 | +0.06 | +0.05 | -0.05 – +0.14 |
| 18 | Derek Carr | LV | QB | 537 | +0.05 | +0.04 | -0.06 – +0.14 |
| 19 | Russell Wilson | SEA | QB | 597 | +0.04 | +0.04 | -0.05 – +0.13 |
| 20 | Ryan Fitzpatrick◦ provisional | TB | QB | 172 | +0.04 | +0.03 | -0.11 – +0.16 |
| 21 | Josh McCown | NYJ | QB | 432 | +0.03 | +0.03 | -0.08 – +0.13 |
| 22 | Kirk Cousins | WAS | QB | 581 | +0.03 | +0.03 | -0.07 – +0.12 |
| 23 | Tyrod Taylor | BUF | QB | 466 | +0.01 | +0.01 | -0.09 – +0.11 |
| 24 | David Fales◦ provisional | MIA | QB | 45 | -0.05 | +0.00 | -0.16 – +0.17 |
| 25 | EJ Manuel◦ provisional | LV | QB | 47 | -0.07 | -0.00 | -0.17 – +0.17 |
| 26 | Cam Newton | CAR | QB | 527 | -0.01 | -0.00 | -0.10 – +0.09 |
| 27 | Carson Palmer | ARI | QB | 290 | -0.01 | -0.00 | -0.12 – +0.12 |
| 28 | Landry Jones◦ provisional | PIT | QB | 31 | -0.12 | -0.00 | -0.18 – +0.17 |
| 29 | Marcus Mariota | TEN | QB | 479 | -0.02 | -0.01 | -0.11 – +0.09 |
| 30 | Geno Smith◦ provisional | NYG | QB | 39 | -0.26 | -0.03 | -0.20 – +0.14 |
| 31 | Jay Cutler | MIA | QB | 449 | -0.05 | -0.03 | -0.13 – +0.07 |
| 32 | Nate Sudfeld◦ provisional | PHI | QB | 26 | -0.43 | -0.04 | -0.21 – +0.14 |
| 33 | Andy Dalton | CIN | QB | 534 | -0.06 | -0.04 | -0.13 – +0.06 |
| 34 | Dak Prescott | DAL | QB | 523 | -0.06 | -0.04 | -0.14 – +0.06 |
| 35 | Kevin Hogan◦ provisional | CLE | QB | 81 | -0.18 | -0.04 | -0.20 – +0.11 |
| 36 | Nick Foles◦ provisional | PHI | QB | 106 | -0.16 | -0.05 | -0.20 – +0.10 |
| 37 | Brock Osweiler◦ provisional | DEN | QB | 182 | -0.11 | -0.05 | -0.18 – +0.09 |
| 38 | Drew Stanton◦ provisional | ARI | QB | 166 | -0.13 | -0.05 | -0.19 – +0.08 |
| 39 | Matt Moore◦ provisional | MIA | QB | 138 | -0.15 | -0.06 | -0.20 – +0.09 |
| 40 | Cody Kessler◦ provisional | CLE | QB | 29 | -0.53 | -0.06 | -0.23 – +0.12 |
| 41 | Sean Mannion◦ provisional | LA | QB | 40 | -0.40 | -0.06 | -0.23 – +0.11 |
| 42 | Jacoby Brissett | IND | QB | 519 | -0.09 | -0.06 | -0.16 – +0.04 |
| 43 | Joe Flacco | BAL | QB | 574 | -0.09 | -0.06 | -0.16 – +0.03 |
| 44 | Brian Hoyer | NE | QB | 228 | -0.14 | -0.07 | -0.19 – +0.06 |
| 45 | Paxton Lynch◦ provisional | DEN | QB | 54 | -0.36 | -0.07 | -0.23 – +0.10 |
| 46 | Mike Glennon◦ provisional | CHI | QB | 148 | -0.18 | -0.07 | -0.21 – +0.07 |
| 47 | Eli Manning | NYG | QB | 607 | -0.10 | -0.08 | -0.17 – +0.02 |
| 48 | Mitchell Trubisky | CHI | QB | 361 | -0.12 | -0.08 | -0.18 – +0.03 |
| 49 | Trevor Siemian | DEN | QB | 384 | -0.13 | -0.08 | -0.19 – +0.03 |
| 50 | T.J. Yates◦ provisional | HOU | QB | 111 | -0.26 | -0.09 | -0.23 – +0.06 |
| 51 | C.J. Beathard | SF | QB | 242 | -0.17 | -0.09 | -0.21 – +0.04 |
| 52 | Tom Savage | HOU | QB | 243 | -0.20 | -0.10 | -0.23 – +0.02 |
| 53 | Bryce Petty◦ provisional | NYJ | QB | 121 | -0.30 | -0.11 | -0.25 – +0.04 |
| 54 | Nathan Peterman◦ provisional | BUF | QB | 48 | -0.61 | -0.11 | -0.28 – +0.06 |
| 55 | Blaine Gabbert | ARI | QB | 194 | -0.28 | -0.13 | -0.26 – -0.00 |
| 56 | Brett Hundley | GB | QB | 346 | -0.22 | -0.13 | -0.25 – -0.02 |
| 57 | Matt Cassel◦ provisional | TEN | QB | 50 | -0.76 | -0.15 | -0.31 – +0.02 |
| 58 | DeShone Kizer | CLE | QB | 513 | -0.22 | -0.15 | -0.25 – -0.06 |
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).