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 · 2019
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
- 274
- 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 · 2019 · full board
| # | Player | Team | Pos | dropbacks | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Lamar Jackson | BAL | QB | 423 | +0.34 | +0.23 | +0.13 – +0.33 |
| 2 | Patrick Mahomes | KC | QB | 502 | +0.28 | +0.20 | +0.11 – +0.29 |
| 3 | Drew Brees | NO | QB | 386 | +0.24 | +0.17 | +0.06 – +0.27 |
| 4 | Dak Prescott | DAL | QB | 620 | +0.20 | +0.16 | +0.07 – +0.24 |
| 5 | Matthew Stafford | DET | QB | 308 | +0.22 | +0.15 | +0.04 – +0.25 |
| 6 | Derek Carr | LV | QB | 541 | +0.18 | +0.14 | +0.05 – +0.23 |
| 7 | Kirk Cousins | MIN | QB | 475 | +0.18 | +0.14 | +0.04 – +0.23 |
| 8 | Ryan Tannehill | TEN | QB | 315 | +0.20 | +0.13 | +0.03 – +0.24 |
| 9 | Russell Wilson | SEA | QB | 563 | +0.16 | +0.12 | +0.03 – +0.21 |
| 10 | Jimmy Garoppolo | SF | QB | 514 | +0.16 | +0.12 | +0.03 – +0.22 |
| 11 | Matt Schaub◦ provisional | ATL | QB | 70 | +0.38 | +0.12 | -0.02 – +0.26 |
| 12 | Deshaun Watson | HOU | QB | 538 | +0.14 | +0.11 | +0.02 – +0.21 |
| 13 | Philip Rivers | LAC | QB | 623 | +0.11 | +0.09 | +0.01 – +0.18 |
| 14 | Aaron Rodgers | GB | QB | 606 | +0.10 | +0.09 | -0.00 – +0.17 |
| 15 | Jared Goff | LA | QB | 649 | +0.09 | +0.08 | -0.00 – +0.17 |
| 16 | Teddy Bridgewater◦ provisional | NO | QB | 208 | +0.12 | +0.08 | -0.04 – +0.20 |
| 17 | Drew Lock◦ provisional | DEN | QB | 161 | +0.09 | +0.07 | -0.06 – +0.19 |
| 18 | Carson Wentz | PHI | QB | 646 | +0.07 | +0.06 | -0.02 – +0.15 |
| 19 | Jameis Winston | TB | QB | 674 | +0.07 | +0.06 | -0.02 – +0.15 |
| 20 | Matt Moore◦ provisional | KC | QB | 98 | +0.07 | +0.06 | -0.07 – +0.20 |
| 21 | Chase Daniel◦ provisional | CHI | QB | 71 | +0.07 | +0.06 | -0.08 – +0.20 |
| 22 | Tom Brady | NE | QB | 642 | +0.05 | +0.05 | -0.03 – +0.14 |
| 23 | Robert Griffin III◦ provisional | BAL | QB | 43 | -0.01 | +0.05 | -0.10 – +0.20 |
| 24 | Ryan Fitzpatrick | MIA | QB | 543 | +0.04 | +0.05 | -0.04 – +0.14 |
| 25 | Jacoby Brissett | IND | QB | 472 | +0.03 | +0.04 | -0.06 – +0.13 |
| 26 | Matt Ryan | ATL | QB | 668 | +0.03 | +0.04 | -0.05 – +0.12 |
| 27 | Kyler Murray | ARI | QB | 589 | +0.01 | +0.03 | -0.06 – +0.11 |
| 28 | AJ McCarron◦ provisional | HOU | QB | 42 | -0.20 | +0.02 | -0.12 – +0.17 |
| 29 | Cam Newton◦ provisional | CAR | QB | 94 | -0.08 | +0.02 | -0.11 – +0.16 |
| 30 | Eli Manning◦ provisional | NYG | QB | 152 | -0.05 | +0.02 | -0.11 – +0.15 |
| 31 | Case Keenum◦ provisional | WAS | QB | 262 | -0.02 | +0.02 | -0.09 – +0.13 |
| 32 | Marcus Mariota◦ provisional | TEN | QB | 183 | -0.04 | +0.02 | -0.10 – +0.14 |
| 33 | Matt Barkley◦ provisional | BUF | QB | 52 | -0.18 | +0.02 | -0.13 – +0.16 |
| 34 | Jeff Driskel◦ provisional | DET | QB | 115 | -0.08 | +0.02 | -0.12 – +0.15 |
| 35 | Ben Roethlisberger◦ provisional | PIT | QB | 64 | -0.21 | +0.01 | -0.13 – +0.15 |
| 36 | Baker Mayfield | CLE | QB | 575 | -0.02 | +0.01 | -0.08 – +0.10 |
| 37 | Josh Allen | BUF | QB | 498 | -0.02 | +0.01 | -0.09 – +0.10 |
| 38 | Gardner Minshew | JAX | QB | 507 | -0.02 | +0.00 | -0.09 – +0.10 |
| 39 | Sam Darnold | NYJ | QB | 475 | -0.03 | +0.00 | -0.09 – +0.10 |
| 40 | Andy Dalton | CIN | QB | 560 | -0.03 | +0.00 | -0.09 – +0.09 |
| 41 | Nick Foles◦ provisional | JAX | QB | 128 | -0.13 | -0.00 | -0.13 – +0.13 |
| 42 | Mason Rudolph | PIT | QB | 299 | -0.06 | -0.00 | -0.11 – +0.10 |
| 43 | Joe Flacco | DEN | QB | 288 | -0.08 | -0.01 | -0.12 – +0.10 |
| 44 | Devlin Hodges◦ provisional | PIT | QB | 175 | -0.13 | -0.01 | -0.14 – +0.11 |
| 45 | Brandon Allen◦ provisional | DEN | QB | 93 | -0.23 | -0.02 | -0.15 – +0.12 |
| 46 | Kyle Allen | CAR | QB | 536 | -0.06 | -0.02 | -0.11 – +0.07 |
| 47 | Colt McCoy◦ provisional | WAS | QB | 33 | -0.67 | -0.02 | -0.17 – +0.13 |
| 48 | Mitchell Trubisky | CHI | QB | 552 | -0.06 | -0.02 | -0.11 – +0.07 |
| 49 | Daniel Jones | NYG | QB | 500 | -0.08 | -0.03 | -0.13 – +0.06 |
| 50 | Brian Hoyer◦ provisional | IND | QB | 71 | -0.38 | -0.03 | -0.17 – +0.11 |
| 51 | Will Grier◦ provisional | CAR | QB | 58 | -0.49 | -0.04 | -0.18 – +0.11 |
| 52 | David Blough◦ provisional | DET | QB | 188 | -0.23 | -0.06 | -0.18 – +0.06 |
| 53 | Dwayne Haskins◦ provisional | WAS | QB | 234 | -0.22 | -0.07 | -0.19 – +0.05 |
| 54 | Josh Rosen◦ provisional | MIA | QB | 125 | -0.40 | -0.08 | -0.21 – +0.05 |
| 55 | Ryan Finley◦ provisional | CIN | QB | 98 | -0.54 | -0.10 | -0.23 – +0.04 |
| 56 | Luke Falk◦ provisional | NYJ | QB | 90 | -0.62 | -0.11 | -0.25 – +0.03 |
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).