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 · 2021
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
- 200
- 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 · 2021 · full board
| # | Player | Team | Pos | dropbacks | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Aaron Rodgers | GB | QB | 559 | +0.23 | +0.18 | +0.09 – +0.27 |
| 2 | Patrick Mahomes | KC | QB | 688 | +0.20 | +0.17 | +0.08 – +0.25 |
| 3 | Tom Brady | TB | QB | 740 | +0.20 | +0.16 | +0.08 – +0.25 |
| 4 | Jimmy Garoppolo | SF | QB | 469 | +0.20 | +0.15 | +0.05 – +0.25 |
| 5 | Matthew Stafford | LA | QB | 634 | +0.19 | +0.15 | +0.06 – +0.24 |
| 6 | Justin Herbert | LAC | QB | 709 | +0.17 | +0.14 | +0.06 – +0.23 |
| 7 | Dak Prescott | DAL | QB | 631 | +0.17 | +0.14 | +0.05 – +0.23 |
| 8 | Joe Burrow | CIN | QB | 571 | +0.17 | +0.14 | +0.05 – +0.23 |
| 9 | Josh Johnson◦ provisional | BAL | QB | 88 | +0.31 | +0.12 | -0.03 – +0.28 |
| 10 | Kyler Murray | ARI | QB | 514 | +0.13 | +0.10 | +0.01 – +0.20 |
| 11 | Josh Allen | BUF | QB | 675 | +0.12 | +0.10 | +0.01 – +0.19 |
| 12 | Teddy Bridgewater | DEN | QB | 460 | +0.12 | +0.10 | -0.00 – +0.20 |
| 13 | Kirk Cousins | MIN | QB | 587 | +0.12 | +0.10 | +0.01 – +0.19 |
| 14 | Gardner Minshew◦ provisional | PHI | QB | 66 | +0.24 | +0.09 | -0.07 – +0.25 |
| 15 | Mac Jones | NE | QB | 550 | +0.10 | +0.08 | -0.01 – +0.18 |
| 16 | Jameis Winston◦ provisional | NO | QB | 172 | +0.13 | +0.08 | -0.05 – +0.21 |
| 17 | Colt McCoy◦ provisional | ARI | QB | 105 | +0.14 | +0.07 | -0.07 – +0.22 |
| 18 | Trey Lance◦ provisional | SF | QB | 75 | +0.14 | +0.07 | -0.09 – +0.22 |
| 19 | Cooper Rush◦ provisional | DAL | QB | 50 | +0.16 | +0.07 | -0.10 – +0.23 |
| 20 | Joe Flacco◦ provisional | NYJ | QB | 44 | +0.14 | +0.06 | -0.11 – +0.23 |
| 21 | Nick Foles◦ provisional | CHI | QB | 40 | +0.14 | +0.06 | -0.11 – +0.22 |
| 22 | Derek Carr | LV | QB | 666 | +0.06 | +0.05 | -0.04 – +0.14 |
| 23 | Tua Tagovailoa | MIA | QB | 409 | +0.05 | +0.05 | -0.06 – +0.15 |
| 24 | Nick Mullens◦ provisional | CLE | QB | 29 | +0.08 | +0.05 | -0.12 – +0.22 |
| 25 | Lamar Jackson | BAL | QB | 421 | +0.05 | +0.04 | -0.06 – +0.15 |
| 26 | Ryan Tannehill | TEN | QB | 578 | +0.04 | +0.04 | -0.05 – +0.14 |
| 27 | Jalen Hurts | PHI | QB | 459 | +0.04 | +0.04 | -0.06 – +0.14 |
| 28 | Russell Wilson | SEA | QB | 435 | +0.04 | +0.04 | -0.06 – +0.14 |
| 29 | Mike White◦ provisional | NYJ | QB | 137 | +0.01 | +0.03 | -0.11 – +0.17 |
| 30 | Carson Wentz | IND | QB | 552 | +0.02 | +0.03 | -0.07 – +0.12 |
| 31 | Garrett Gilbert◦ provisional | WAS | QB | 33 | -0.08 | +0.02 | -0.15 – +0.19 |
| 32 | Geno Smith◦ provisional | SEA | QB | 107 | -0.02 | +0.02 | -0.13 – +0.17 |
| 33 | Matt Ryan | ATL | QB | 601 | +0.01 | +0.02 | -0.07 – +0.11 |
| 34 | Tim Boyle◦ provisional | DET | QB | 95 | -0.04 | +0.02 | -0.14 – +0.17 |
| 35 | Baker Mayfield | CLE | QB | 462 | -0.01 | +0.01 | -0.10 – +0.11 |
| 36 | Jordan Love◦ provisional | GB | QB | 66 | -0.11 | +0.00 | -0.15 – +0.16 |
| 37 | Case Keenum◦ provisional | CLE | QB | 77 | -0.11 | +0.00 | -0.15 – +0.16 |
| 38 | Mason Rudolph◦ provisional | PIT | QB | 57 | -0.15 | -0.00 | -0.16 – +0.16 |
| 39 | Drew Lock◦ provisional | DEN | QB | 119 | -0.08 | -0.00 | -0.15 – +0.14 |
| 40 | Daniel Jones | NYG | QB | 383 | -0.03 | -0.00 | -0.11 – +0.10 |
| 41 | Trevor Siemian | NO | QB | 201 | -0.05 | -0.01 | -0.13 – +0.12 |
| 42 | Sean Mannion◦ provisional | MIN | QB | 38 | -0.29 | -0.01 | -0.18 – +0.16 |
| 43 | Brandon Allen◦ provisional | CIN | QB | 38 | -0.29 | -0.01 | -0.18 – +0.16 |
| 44 | Tyrod Taylor◦ provisional | HOU | QB | 162 | -0.09 | -0.02 | -0.15 – +0.12 |
| 45 | Jared Goff | DET | QB | 529 | -0.05 | -0.02 | -0.12 – +0.07 |
| 46 | PJ Walker◦ provisional | CAR | QB | 73 | -0.20 | -0.02 | -0.18 – +0.13 |
| 47 | Taylor Heinicke | WAS | QB | 532 | -0.06 | -0.03 | -0.12 – +0.07 |
| 48 | Jacoby Brissett | MIA | QB | 244 | -0.10 | -0.03 | -0.16 – +0.09 |
| 49 | Ben Roethlisberger | PIT | QB | 646 | -0.07 | -0.04 | -0.13 – +0.05 |
| 50 | Andy Dalton | CHI | QB | 256 | -0.12 | -0.05 | -0.17 – +0.07 |
| 51 | Tyler Huntley | BAL | QB | 205 | -0.15 | -0.05 | -0.18 – +0.07 |
| 52 | Davis Mills | HOU | QB | 424 | -0.10 | -0.06 | -0.16 – +0.05 |
| 53 | Trevor Lawrence | JAX | QB | 636 | -0.09 | -0.06 | -0.15 – +0.03 |
| 54 | Cam Newton◦ provisional | CAR | QB | 137 | -0.29 | -0.09 | -0.23 – +0.05 |
| 55 | Ian Book◦ provisional | NO | QB | 28 | -1.06 | -0.09 | -0.27 – +0.08 |
| 56 | Jake Fromm◦ provisional | NYG | QB | 66 | -0.53 | -0.10 | -0.26 – +0.06 |
| 57 | Sam Darnold | CAR | QB | 442 | -0.17 | -0.11 | -0.21 – -0.00 |
| 58 | Justin Fields | CHI | QB | 304 | -0.21 | -0.11 | -0.23 – +0.00 |
| 59 | Zach Wilson | NYJ | QB | 429 | -0.22 | -0.14 | -0.24 – -0.04 |
| 60 | Mike Glennon◦ provisional | NYG | QB | 174 | -0.47 | -0.20 | -0.33 – -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).