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 · 2020
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 · 2020 · full board
| # | Player | Team | Pos | dropbacks | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Aaron Rodgers | GB | QB | 543 | +0.34 | +0.28 | +0.18 – +0.37 |
| 2 | Patrick Mahomes | KC | QB | 612 | +0.30 | +0.25 | +0.16 – +0.34 |
| 3 | Josh Allen | BUF | QB | 599 | +0.28 | +0.24 | +0.14 – +0.33 |
| 4 | Ryan Tannehill | TEN | QB | 507 | +0.25 | +0.21 | +0.11 – +0.30 |
| 5 | Deshaun Watson | HOU | QB | 595 | +0.22 | +0.19 | +0.10 – +0.28 |
| 6 | Tom Brady | TB | QB | 629 | +0.21 | +0.18 | +0.09 – +0.27 |
| 7 | Philip Rivers | IND | QB | 561 | +0.19 | +0.16 | +0.07 – +0.26 |
| 8 | Baker Mayfield | CLE | QB | 508 | +0.18 | +0.15 | +0.06 – +0.25 |
| 9 | Kirk Cousins | MIN | QB | 559 | +0.17 | +0.15 | +0.06 – +0.24 |
| 10 | Drew Brees | NO | QB | 402 | +0.17 | +0.15 | +0.04 – +0.25 |
| 11 | Ryan Fitzpatrick | MIA | QB | 282 | +0.17 | +0.14 | +0.02 – +0.26 |
| 12 | Chad Henne◦ provisional | KC | QB | 40 | +0.35 | +0.14 | -0.03 – +0.30 |
| 13 | Justin Herbert | LAC | QB | 626 | +0.14 | +0.13 | +0.04 – +0.22 |
| 14 | Lamar Jackson | BAL | QB | 403 | +0.14 | +0.13 | +0.02 – +0.23 |
| 15 | Jimmy Garoppolo◦ provisional | SF | QB | 151 | +0.16 | +0.12 | -0.02 – +0.26 |
| 16 | Russell Wilson | SEA | QB | 606 | +0.13 | +0.12 | +0.03 – +0.21 |
| 17 | Marcus Mariota◦ provisional | LV | QB | 27 | +0.31 | +0.12 | -0.06 – +0.29 |
| 18 | Dak Prescott | DAL | QB | 233 | +0.14 | +0.12 | -0.01 – +0.24 |
| 19 | Mason Rudolph◦ provisional | PIT | QB | 45 | +0.21 | +0.11 | -0.05 – +0.28 |
| 20 | Derek Carr | LV | QB | 540 | +0.11 | +0.11 | +0.01 – +0.20 |
| 21 | Joe Burrow | CIN | QB | 433 | +0.11 | +0.11 | +0.00 – +0.21 |
| 22 | Matt Ryan | ATL | QB | 669 | +0.10 | +0.10 | +0.01 – +0.19 |
| 23 | Matthew Stafford | DET | QB | 563 | +0.10 | +0.10 | +0.00 – +0.19 |
| 24 | Mitchell Trubisky | CHI | QB | 316 | +0.09 | +0.09 | -0.02 – +0.20 |
| 25 | Ben Roethlisberger | PIT | QB | 625 | +0.09 | +0.09 | -0.00 – +0.18 |
| 26 | C.J. Beathard◦ provisional | SF | QB | 113 | +0.08 | +0.09 | -0.06 – +0.23 |
| 27 | Kyle Allen◦ provisional | WAS | QB | 96 | +0.06 | +0.08 | -0.07 – +0.23 |
| 28 | Tyrod Taylor◦ provisional | LAC | QB | 32 | -0.01 | +0.08 | -0.10 – +0.25 |
| 29 | Teddy Bridgewater | CAR | QB | 523 | +0.06 | +0.07 | -0.03 – +0.17 |
| 30 | Brett Rypien◦ provisional | DEN | QB | 41 | -0.04 | +0.07 | -0.10 – +0.23 |
| 31 | Gardner Minshew | JAX | QB | 357 | +0.05 | +0.06 | -0.04 – +0.17 |
| 32 | Kyler Murray | ARI | QB | 579 | +0.05 | +0.06 | -0.03 – +0.16 |
| 33 | John Wolford◦ provisional | LA | QB | 40 | -0.08 | +0.06 | -0.11 – +0.23 |
| 34 | Jared Goff | LA | QB | 574 | +0.04 | +0.06 | -0.04 – +0.15 |
| 35 | Garrett Gilbert◦ provisional | DAL | QB | 39 | -0.13 | +0.05 | -0.12 – +0.22 |
| 36 | Nick Mullens | SF | QB | 347 | +0.01 | +0.04 | -0.07 – +0.15 |
| 37 | Brian Hoyer◦ provisional | NE | QB | 26 | -0.36 | +0.04 | -0.14 – +0.21 |
| 38 | Jalen Hurts◦ provisional | PHI | QB | 161 | -0.03 | +0.03 | -0.10 – +0.17 |
| 39 | Colt McCoy◦ provisional | NYG | QB | 72 | -0.12 | +0.03 | -0.13 – +0.19 |
| 40 | Joe Flacco◦ provisional | NYJ | QB | 141 | -0.07 | +0.02 | -0.12 – +0.16 |
| 41 | Cam Newton | NE | QB | 398 | -0.01 | +0.02 | -0.08 – +0.13 |
| 42 | Brandon Allen◦ provisional | CIN | QB | 149 | -0.06 | +0.02 | -0.12 – +0.16 |
| 43 | Jeff Driskel◦ provisional | DEN | QB | 76 | -0.18 | +0.01 | -0.14 – +0.17 |
| 44 | Andy Dalton | DAL | QB | 357 | -0.03 | +0.01 | -0.10 – +0.12 |
| 45 | Chase Daniel◦ provisional | DET | QB | 45 | -0.33 | +0.01 | -0.16 – +0.18 |
| 46 | Tua Tagovailoa | MIA | QB | 310 | -0.05 | +0.00 | -0.11 – +0.12 |
| 47 | Mike Glennon◦ provisional | JAX | QB | 189 | -0.10 | -0.01 | -0.14 – +0.13 |
| 48 | Jarrett Stidham◦ provisional | NE | QB | 48 | -0.40 | -0.01 | -0.17 – +0.16 |
| 49 | Daniel Jones | NYG | QB | 494 | -0.05 | -0.01 | -0.11 – +0.09 |
| 50 | PJ Walker◦ provisional | CAR | QB | 60 | -0.37 | -0.02 | -0.18 – +0.14 |
| 51 | Drew Lock | DEN | QB | 464 | -0.08 | -0.03 | -0.13 – +0.07 |
| 52 | Ryan Finley◦ provisional | CIN | QB | 41 | -0.59 | -0.03 | -0.20 – +0.14 |
| 53 | Nick Foles | CHI | QB | 330 | -0.10 | -0.03 | -0.15 – +0.08 |
| 54 | Alex Smith | WAS | QB | 274 | -0.12 | -0.03 | -0.15 – +0.09 |
| 55 | Ben DiNucci◦ provisional | DAL | QB | 49 | -0.56 | -0.04 | -0.21 – +0.12 |
| 56 | Dwayne Haskins | WAS | QB | 262 | -0.15 | -0.05 | -0.17 – +0.07 |
| 57 | Jake Luton◦ provisional | JAX | QB | 118 | -0.31 | -0.06 | -0.21 – +0.08 |
| 58 | Carson Wentz | PHI | QB | 492 | -0.17 | -0.10 | -0.19 – +0.00 |
| 59 | Sam Darnold | NYJ | QB | 398 | -0.20 | -0.10 | -0.21 – +0.00 |
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).