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 rush · 2022
Mean EPA per carry. Blocking & scheme are large, un-controlled inputs.
- Beats raw by
- 21.1%
- lower out-of-sample error
- RMSE raw → shrunk
- 0.16 → 0.13
- odd vs. even weeks
- Split-half reliability
- 0.17
- how repeatable the raw stat is
- Stabilizes at
- 385
- carrys 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 rush · 2022 · full board
| # | Player | Team | Pos | carrys | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Nick Chubb◦ provisional | CLE | RB | 303 | +0.05 | -0.01 | -0.06 – +0.05 |
| 2 | Miles Sanders◦ provisional | PHI | RB | 260 | +0.05 | -0.01 | -0.07 – +0.05 |
| 3 | Breece Hall◦ provisional | NYJ | RB | 80 | +0.17 | -0.01 | -0.08 – +0.06 |
| 4 | Aaron Jones◦ provisional | GB | RB | 213 | +0.06 | -0.01 | -0.07 – +0.05 |
| 5 | Rashaad Penny◦ provisional | SEA | RB | 57 | +0.23 | -0.01 | -0.08 – +0.06 |
| 6 | Tyler Allgeier◦ provisional | ATL | RB | 211 | +0.05 | -0.01 | -0.07 – +0.05 |
| 7 | Jeff Wilson◦ provisional | MIA | RB | 176 | +0.04 | -0.02 | -0.08 – +0.05 |
| 8 | J.K. Dobbins◦ provisional | BAL | RB | 92 | +0.10 | -0.02 | -0.09 – +0.05 |
| 9 | Elijah Mitchell◦ provisional | SF | RB | 45 | +0.22 | -0.02 | -0.09 – +0.05 |
| 10 | Jaylen Warren◦ provisional | PIT | RB | 77 | +0.11 | -0.02 | -0.09 – +0.05 |
| 11 | Kenneth Gainwell◦ provisional | PHI | RB | 53 | +0.15 | -0.02 | -0.10 – +0.05 |
| 12 | Tony Pollard◦ provisional | DAL | RB | 193 | +0.02 | -0.02 | -0.09 – +0.04 |
| 13 | D'Andre Swift◦ provisional | DET | RB | 100 | +0.07 | -0.02 | -0.09 – +0.05 |
| 14 | D'Onta Foreman◦ provisional | CAR | RB | 204 | +0.02 | -0.02 | -0.09 – +0.04 |
| 15 | James Cook◦ provisional | BUF | RB | 89 | +0.07 | -0.02 | -0.09 – +0.05 |
| 16 | Christian McCaffrey◦ provisional | SF | RB | 246 | +0.01 | -0.03 | -0.09 – +0.04 |
| 17 | Josh Jacobs◦ provisional | LV | RB | 341 | -0.00 | -0.03 | -0.08 – +0.03 |
| 18 | AJ Dillon◦ provisional | GB | RB | 186 | +0.01 | -0.03 | -0.09 – +0.04 |
| 19 | Caleb Huntley◦ provisional | ATL | RB | 76 | +0.05 | -0.03 | -0.10 – +0.04 |
| 20 | Khalil Herbert◦ provisional | CHI | RB | 129 | +0.01 | -0.03 | -0.10 – +0.03 |
| 21 | Raheem Mostert◦ provisional | MIA | RB | 181 | -0.01 | -0.03 | -0.10 – +0.03 |
| 22 | Benny Snell◦ provisional | PIT | RB | 20 | +0.22 | -0.03 | -0.11 – +0.04 |
| 23 | Chuba Hubbard◦ provisional | CAR | RB | 95 | +0.02 | -0.03 | -0.10 – +0.04 |
| 24 | Joshua Kelley◦ provisional | LAC | RB | 69 | +0.04 | -0.03 | -0.11 – +0.04 |
| 25 | Darrel Williams◦ provisional | ARI | RB | 21 | +0.20 | -0.03 | -0.11 – +0.04 |
| 26 | Cordarrelle Patterson◦ provisional | ATL | RB | 144 | -0.00 | -0.03 | -0.10 – +0.03 |
| 27 | Austin Ekeler◦ provisional | LAC | RB | 204 | -0.01 | -0.03 | -0.10 – +0.03 |
| 28 | Clyde Edwards-Helaire◦ provisional | KC | RB | 71 | +0.03 | -0.03 | -0.11 – +0.04 |
| 29 | Jordan Mason◦ provisional | SF | RB | 43 | +0.07 | -0.03 | -0.11 – +0.04 |
| 30 | DeeJay Dallas◦ provisional | SEA | RB | 35 | +0.09 | -0.04 | -0.11 – +0.04 |
| 31 | James Conner◦ provisional | ARI | RB | 183 | -0.01 | -0.04 | -0.10 – +0.03 |
| 32 | Darrell Henderson◦ provisional | LA | RB | 70 | +0.02 | -0.04 | -0.11 – +0.04 |
| 33 | Gus Edwards◦ provisional | BAL | RB | 87 | -0.00 | -0.04 | -0.11 – +0.03 |
| 34 | Alexander Mattison◦ provisional | MIN | RB | 74 | +0.01 | -0.04 | -0.11 – +0.03 |
| 35 | Isiah Pacheco◦ provisional | KC | RB | 170 | -0.02 | -0.04 | -0.10 – +0.03 |
| 36 | Matt Breida◦ provisional | NYG | RB | 54 | +0.01 | -0.04 | -0.11 – +0.03 |
| 37 | Eno Benjamin◦ provisional | NO | RB | 78 | -0.01 | -0.04 | -0.11 – +0.03 |
| 38 | Raheem Blackshear◦ provisional | CAR | RB | 23 | +0.06 | -0.04 | -0.12 – +0.04 |
| 39 | Latavius Murray◦ provisional | DEN | RB | 172 | -0.03 | -0.04 | -0.11 – +0.02 |
| 40 | Brian Robinson◦ provisional | WAS | RB | 205 | -0.03 | -0.04 | -0.10 – +0.02 |
| 41 | Ronald Jones◦ provisional | KC | RB | 17 | +0.07 | -0.04 | -0.12 – +0.03 |
| 42 | Dontrell Hilliard◦ provisional | TEN | RB | 22 | +0.03 | -0.04 | -0.12 – +0.03 |
| 43 | Avery Williams◦ provisional | ATL | RB | 22 | +0.01 | -0.04 | -0.12 – +0.03 |
| 44 | Travis Etienne◦ provisional | JAX | RB | 221 | -0.04 | -0.04 | -0.11 – +0.02 |
| 45 | Damien Harris◦ provisional | NE | RB | 106 | -0.04 | -0.04 | -0.11 – +0.03 |
| 46 | Samaje Perine◦ provisional | CIN | RB | 96 | -0.04 | -0.05 | -0.11 – +0.02 |
| 47 | Malcolm Brown◦ provisional | LA | RB | 18 | -0.03 | -0.05 | -0.12 – +0.03 |
| 48 | Rhamondre Stevenson◦ provisional | NE | RB | 210 | -0.05 | -0.05 | -0.11 – +0.02 |
| 49 | Boston Scott◦ provisional | PHI | RB | 54 | -0.05 | -0.05 | -0.12 – +0.03 |
| 50 | Corey Clement◦ provisional | ARI | RB | 15 | -0.05 | -0.05 | -0.12 – +0.03 |
| 51 | Marlon Mack◦ provisional | DEN | RB | 16 | -0.06 | -0.05 | -0.12 – +0.03 |
| 52 | Jaret Patterson◦ provisional | WAS | RB | 17 | -0.06 | -0.05 | -0.12 – +0.03 |
| 53 | Ezekiel Elliott◦ provisional | DAL | RB | 231 | -0.05 | -0.05 | -0.11 – +0.01 |
| 54 | Zamir White◦ provisional | LV | RB | 17 | -0.09 | -0.05 | -0.12 – +0.03 |
| 55 | Justice Hill◦ provisional | BAL | RB | 49 | -0.07 | -0.05 | -0.12 – +0.02 |
| 56 | Phillip Lindsay◦ provisional | IND | RB | 16 | -0.11 | -0.05 | -0.12 – +0.03 |
| 57 | Sony Michel◦ provisional | LAC | RB | 36 | -0.08 | -0.05 | -0.12 – +0.03 |
| 58 | Saquon Barkley◦ provisional | NYG | RB | 295 | -0.05 | -0.05 | -0.11 – +0.01 |
| 59 | Kevin Harris◦ provisional | NE | RB | 18 | -0.11 | -0.05 | -0.12 – +0.03 |
| 60 | Joe Mixon◦ provisional | CIN | RB | 210 | -0.06 | -0.05 | -0.11 – +0.01 |
| 61 | Hassan Haskins◦ provisional | TEN | RB | 25 | -0.10 | -0.05 | -0.12 – +0.03 |
| 62 | Travis Homer◦ provisional | SEA | RB | 19 | -0.13 | -0.05 | -0.13 – +0.03 |
| 63 | Malik Davis◦ provisional | DAL | RB | 38 | -0.09 | -0.05 | -0.12 – +0.02 |
| 64 | Ke'Shawn Vaughn◦ provisional | TB | RB | 17 | -0.18 | -0.05 | -0.13 – +0.02 |
| 65 | Mike Boone◦ provisional | DEN | RB | 24 | -0.15 | -0.05 | -0.13 – +0.02 |
| 66 | Kyren Williams◦ provisional | LA | RB | 35 | -0.12 | -0.05 | -0.13 – +0.02 |
| 67 | Ty Johnson◦ provisional | NYJ | RB | 30 | -0.14 | -0.05 | -0.13 – +0.02 |
| 68 | Kenneth Walker III◦ provisional | SEA | RB | 228 | -0.07 | -0.05 | -0.11 – +0.01 |
| 69 | Gary Brightwell◦ provisional | NYG | RB | 31 | -0.14 | -0.05 | -0.13 – +0.02 |
| 70 | J.D. McKissic◦ provisional | WAS | RB | 22 | -0.18 | -0.05 | -0.13 – +0.02 |
| 71 | Craig Reynolds◦ provisional | DET | RB | 23 | -0.18 | -0.05 | -0.13 – +0.02 |
| 72 | Cam Akers◦ provisional | LA | RB | 188 | -0.07 | -0.05 | -0.12 – +0.01 |
| 73 | Derrick Henry◦ provisional | TEN | RB | 349 | -0.06 | -0.05 | -0.11 – +0.00 |
| 74 | Javonte Williams◦ provisional | DEN | RB | 47 | -0.13 | -0.06 | -0.13 – +0.02 |
| 75 | David Montgomery◦ provisional | CHI | RB | 201 | -0.08 | -0.06 | -0.12 – +0.01 |
| 76 | JaMycal Hasty◦ provisional | JAX | RB | 46 | -0.15 | -0.06 | -0.13 – +0.02 |
| 77 | Kareem Hunt◦ provisional | CLE | RB | 123 | -0.09 | -0.06 | -0.13 – +0.01 |
| 78 | Dare Ogunbowale◦ provisional | HOU | RB | 43 | -0.17 | -0.06 | -0.13 – +0.02 |
| 79 | Zack Moss◦ provisional | IND | RB | 93 | -0.11 | -0.06 | -0.13 – +0.01 |
| 80 | Brandon Bolden◦ provisional | LV | RB | 17 | -0.37 | -0.06 | -0.14 – +0.02 |
| 81 | Rex Burkhead◦ provisional | HOU | RB | 26 | -0.26 | -0.06 | -0.14 – +0.02 |
| 82 | Jonathan Williams◦ provisional | WAS | RB | 37 | -0.21 | -0.06 | -0.13 – +0.01 |
| 83 | Jerick McKinnon◦ provisional | KC | RB | 72 | -0.14 | -0.06 | -0.13 – +0.01 |
| 84 | Kenyan Drake◦ provisional | BAL | RB | 109 | -0.11 | -0.06 | -0.13 – +0.01 |
| 85 | Devin Singletary◦ provisional | BUF | RB | 177 | -0.09 | -0.06 | -0.13 – +0.00 |
| 86 | Isaiah Spiller◦ provisional | LAC | RB | 18 | -0.40 | -0.06 | -0.14 – +0.01 |
| 87 | Antonio Gibson◦ provisional | WAS | RB | 149 | -0.11 | -0.06 | -0.13 – +0.00 |
| 88 | Trestan Ebner◦ provisional | CHI | RB | 24 | -0.35 | -0.06 | -0.14 – +0.01 |
| 89 | Mark Ingram◦ provisional | NO | RB | 64 | -0.17 | -0.06 | -0.14 – +0.01 |
| 90 | James Robinson◦ provisional | NYJ | RB | 110 | -0.13 | -0.07 | -0.13 – +0.00 |
| 91 | Keaontay Ingram◦ provisional | ARI | RB | 27 | -0.34 | -0.07 | -0.14 – +0.01 |
| 92 | Jamaal Williams◦ provisional | DET | RB | 263 | -0.10 | -0.07 | -0.13 – -0.01 |
| 93 | Justin Jackson◦ provisional | DET | RB | 43 | -0.25 | -0.07 | -0.14 – +0.01 |
| 94 | Bam Knight◦ provisional | NYJ | RB | 85 | -0.16 | -0.07 | -0.14 – +0.00 |
| 95 | Rachaad White◦ provisional | TB | RB | 130 | -0.14 | -0.07 | -0.14 – -0.00 |
| 96 | Najee Harris◦ provisional | PIT | RB | 272 | -0.11 | -0.07 | -0.13 – -0.01 |
| 97 | Deon Jackson◦ provisional | IND | RB | 68 | -0.23 | -0.07 | -0.15 – -0.00 |
| 98 | Chase Edmonds◦ provisional | DEN | RB | 68 | -0.23 | -0.07 | -0.15 – -0.00 |
| 99 | Tyrion Davis-Price◦ provisional | SF | RB | 34 | -0.40 | -0.07 | -0.15 – -0.00 |
| 100 | Dameon Pierce◦ provisional | HOU | RB | 220 | -0.13 | -0.08 | -0.14 – -0.01 |
| 101 | Nyheim Hines◦ provisional | BUF | RB | 24 | -0.55 | -0.08 | -0.15 – -0.00 |
| 102 | Royce Freeman◦ provisional | HOU | RB | 41 | -0.38 | -0.08 | -0.15 – -0.00 |
| 103 | Michael Carter◦ provisional | NYJ | RB | 114 | -0.19 | -0.08 | -0.15 – -0.01 |
| 104 | Jonathan Taylor◦ provisional | IND | RB | 192 | -0.15 | -0.08 | -0.14 – -0.02 |
| 105 | Leonard Fournette◦ provisional | TB | RB | 189 | -0.20 | -0.10 | -0.16 – -0.03 |
| 106 | Alvin Kamara◦ provisional | NO | RB | 223 | -0.18 | -0.10 | -0.16 – -0.03 |
| 107 | Melvin Gordon◦ provisional | DEN | RB | 90 | -0.33 | -0.10 | -0.17 – -0.03 |
| 108 | Dalvin Cook◦ provisional | MIN | RB | 264 | -0.18 | -0.10 | -0.16 – -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).