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 · 2023
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
- 143
- 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 · 2023 · full board
| # | Player | Team | Pos | carrys | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | De'Von Achane◦ provisional | MIA | RB | 103 | +0.32 | +0.09 | -0.00 – +0.18 |
| 2 | Kyren Williams | LA | RB | 229 | +0.10 | +0.03 | -0.04 – +0.11 |
| 3 | Keaton Mitchell◦ provisional | BAL | RB | 47 | +0.37 | +0.03 | -0.07 – +0.14 |
| 4 | Raheem Mostert | MIA | RB | 209 | +0.08 | +0.02 | -0.06 – +0.10 |
| 5 | Christian McCaffrey | SF | RB | 272 | +0.05 | +0.01 | -0.06 – +0.08 |
| 6 | James Conner | ARI | RB | 210 | +0.06 | +0.00 | -0.08 – +0.08 |
| 7 | David Montgomery | DET | RB | 220 | +0.05 | +0.00 | -0.08 – +0.08 |
| 8 | Jaleel McLaughlin◦ provisional | DEN | RB | 76 | +0.08 | -0.02 | -0.12 – +0.07 |
| 9 | D'Andre Swift | PHI | RB | 229 | +0.01 | -0.03 | -0.10 – +0.05 |
| 10 | Jordan Mason◦ provisional | SF | RB | 40 | +0.14 | -0.03 | -0.14 – +0.08 |
| 11 | Aaron Jones◦ provisional | GB | RB | 142 | +0.02 | -0.03 | -0.12 – +0.06 |
| 12 | Derrick Henry | TEN | RB | 280 | -0.01 | -0.03 | -0.10 – +0.04 |
| 13 | Alvin Kamara | NO | RB | 182 | -0.01 | -0.04 | -0.12 – +0.04 |
| 14 | Nick Chubb◦ provisional | CLE | RB | 28 | +0.15 | -0.04 | -0.15 – +0.07 |
| 15 | Ty Chandler◦ provisional | MIN | RB | 102 | +0.01 | -0.04 | -0.14 – +0.05 |
| 16 | Isiah Pacheco | KC | RB | 206 | -0.02 | -0.05 | -0.12 – +0.03 |
| 17 | Justice Hill◦ provisional | BAL | RB | 84 | +0.01 | -0.05 | -0.14 – +0.05 |
| 18 | Khalil Herbert◦ provisional | CHI | RB | 133 | -0.01 | -0.05 | -0.14 – +0.04 |
| 19 | Michael Carter◦ provisional | ARI | RB | 30 | +0.10 | -0.05 | -0.16 – +0.06 |
| 20 | James Cook | BUF | RB | 237 | -0.03 | -0.05 | -0.12 – +0.03 |
| 21 | Tyjae Spears◦ provisional | TEN | RB | 100 | -0.01 | -0.05 | -0.14 – +0.04 |
| 22 | Jahmyr Gibbs | DET | RB | 182 | -0.03 | -0.05 | -0.13 – +0.03 |
| 23 | Jaylen Warren | PIT | RB | 149 | -0.03 | -0.05 | -0.14 – +0.03 |
| 24 | Ameer Abdullah◦ provisional | LV | RB | 15 | +0.17 | -0.06 | -0.17 – +0.06 |
| 25 | Damien Harris◦ provisional | BUF | RB | 23 | +0.09 | -0.06 | -0.17 – +0.06 |
| 26 | Tony Jones◦ provisional | ARI | RB | 26 | +0.06 | -0.06 | -0.17 – +0.06 |
| 27 | Kenneth Walker III | SEA | RB | 219 | -0.04 | -0.06 | -0.13 – +0.02 |
| 28 | Kareem Hunt◦ provisional | CLE | RB | 135 | -0.04 | -0.06 | -0.15 – +0.03 |
| 29 | Darrynton Evans◦ provisional | MIA | RB | 32 | +0.02 | -0.06 | -0.17 – +0.05 |
| 30 | D'Onta Foreman◦ provisional | CHI | RB | 109 | -0.04 | -0.06 | -0.15 – +0.03 |
| 31 | Latavius Murray◦ provisional | BUF | RB | 79 | -0.03 | -0.06 | -0.16 – +0.04 |
| 32 | Jeff Wilson◦ provisional | MIA | RB | 41 | -0.02 | -0.07 | -0.17 – +0.04 |
| 33 | Gus Edwards | BAL | RB | 199 | -0.06 | -0.07 | -0.15 – +0.01 |
| 34 | Jonathan Taylor | IND | RB | 169 | -0.06 | -0.07 | -0.15 – +0.01 |
| 35 | Jerick McKinnon◦ provisional | KC | RB | 21 | -0.00 | -0.07 | -0.18 – +0.05 |
| 36 | Ty Johnson◦ provisional | BUF | RB | 30 | -0.02 | -0.07 | -0.18 – +0.04 |
| 37 | Trey Sermon◦ provisional | IND | RB | 35 | -0.03 | -0.07 | -0.18 – +0.04 |
| 38 | Salvon Ahmed◦ provisional | MIA | RB | 22 | -0.01 | -0.07 | -0.18 – +0.04 |
| 39 | Tony Pollard | DAL | RB | 253 | -0.07 | -0.07 | -0.14 – +0.00 |
| 40 | Rico Dowdle◦ provisional | DAL | RB | 89 | -0.06 | -0.07 | -0.17 – +0.03 |
| 41 | Joe Mixon | CIN | RB | 257 | -0.07 | -0.07 | -0.15 – +0.00 |
| 42 | Zach Charbonnet◦ provisional | SEA | RB | 108 | -0.07 | -0.07 | -0.17 – +0.02 |
| 43 | Chris Rodriguez Jr.◦ provisional | WAS | RB | 51 | -0.07 | -0.08 | -0.18 – +0.03 |
| 44 | Devin Singletary | HOU | RB | 216 | -0.08 | -0.08 | -0.16 – -0.00 |
| 45 | Zack Moss | IND | RB | 183 | -0.08 | -0.08 | -0.16 – +0.00 |
| 46 | Kendre Miller◦ provisional | NO | RB | 41 | -0.08 | -0.08 | -0.19 – +0.03 |
| 47 | Cam Akers◦ provisional | MIN | RB | 60 | -0.08 | -0.08 | -0.18 – +0.02 |
| 48 | Roschon Johnson◦ provisional | CHI | RB | 81 | -0.08 | -0.08 | -0.18 – +0.02 |
| 49 | Rhamondre Stevenson | NE | RB | 156 | -0.08 | -0.08 | -0.17 – +0.00 |
| 50 | Royce Freeman◦ provisional | LA | RB | 77 | -0.08 | -0.08 | -0.18 – +0.02 |
| 51 | Emari Demercado◦ provisional | ARI | RB | 58 | -0.09 | -0.08 | -0.19 – +0.02 |
| 52 | La'Mical Perine◦ provisional | KC | RB | 22 | -0.11 | -0.08 | -0.20 – +0.03 |
| 53 | Patrick Taylor◦ provisional | GB | RB | 32 | -0.10 | -0.08 | -0.19 – +0.03 |
| 54 | Trayveon Williams◦ provisional | CIN | RB | 15 | -0.14 | -0.08 | -0.20 – +0.03 |
| 55 | Kevin Harris◦ provisional | NE | RB | 16 | -0.14 | -0.09 | -0.20 – +0.03 |
| 56 | Craig Reynolds◦ provisional | DET | RB | 41 | -0.11 | -0.09 | -0.19 – +0.02 |
| 57 | Chuba Hubbard | CAR | RB | 238 | -0.09 | -0.09 | -0.16 – -0.01 |
| 58 | Israel Abanikanda◦ provisional | NYJ | RB | 22 | -0.13 | -0.09 | -0.20 – +0.03 |
| 59 | Antonio Gibson◦ provisional | WAS | RB | 65 | -0.10 | -0.09 | -0.19 – +0.02 |
| 60 | Breece Hall | NYJ | RB | 224 | -0.09 | -0.09 | -0.16 – -0.01 |
| 61 | Boston Scott◦ provisional | PHI | RB | 20 | -0.16 | -0.09 | -0.20 – +0.03 |
| 62 | Ronnie Rivers◦ provisional | LA | RB | 32 | -0.14 | -0.09 | -0.20 – +0.02 |
| 63 | Chris Brooks◦ provisional | MIA | RB | 19 | -0.18 | -0.09 | -0.21 – +0.02 |
| 64 | Chase Edmonds◦ provisional | TB | RB | 49 | -0.13 | -0.09 | -0.20 – +0.01 |
| 65 | Najee Harris | PIT | RB | 256 | -0.10 | -0.09 | -0.17 – -0.02 |
| 66 | Raheem Blackshear◦ provisional | CAR | RB | 15 | -0.23 | -0.09 | -0.21 – +0.02 |
| 67 | Cordarrelle Patterson◦ provisional | ATL | RB | 50 | -0.16 | -0.10 | -0.21 – +0.01 |
| 68 | Kenneth Gainwell◦ provisional | PHI | RB | 85 | -0.14 | -0.10 | -0.20 – -0.00 |
| 69 | Brian Robinson | WAS | RB | 179 | -0.12 | -0.10 | -0.18 – -0.02 |
| 70 | Tyler Allgeier | ATL | RB | 187 | -0.12 | -0.10 | -0.18 – -0.02 |
| 71 | Elijah Mitchell◦ provisional | SF | RB | 75 | -0.15 | -0.10 | -0.20 – -0.00 |
| 72 | Samaje Perine◦ provisional | DEN | RB | 53 | -0.18 | -0.11 | -0.21 – -0.00 |
| 73 | Bijan Robinson | ATL | RB | 214 | -0.12 | -0.11 | -0.18 – -0.03 |
| 74 | Travis Etienne | JAX | RB | 269 | -0.12 | -0.11 | -0.18 – -0.03 |
| 75 | Pierre Strong◦ provisional | CLE | RB | 64 | -0.17 | -0.11 | -0.21 – -0.00 |
| 76 | AJ Dillon | GB | RB | 178 | -0.13 | -0.11 | -0.19 – -0.03 |
| 77 | Chase Brown◦ provisional | CIN | RB | 44 | -0.20 | -0.11 | -0.22 – -0.00 |
| 78 | Melvin Gordon◦ provisional | BAL | RB | 26 | -0.27 | -0.11 | -0.22 – +0.00 |
| 79 | Sean Tucker◦ provisional | TB | RB | 15 | -0.41 | -0.11 | -0.23 – +0.01 |
| 80 | Zamir White◦ provisional | LV | RB | 104 | -0.17 | -0.12 | -0.21 – -0.02 |
| 81 | Ezekiel Elliott | NE | RB | 184 | -0.15 | -0.12 | -0.20 – -0.04 |
| 82 | Eric Gray◦ provisional | NYG | RB | 17 | -0.46 | -0.12 | -0.24 – -0.00 |
| 83 | Darrell Henderson◦ provisional | LA | RB | 46 | -0.26 | -0.12 | -0.23 – -0.02 |
| 84 | Tank Bigsby◦ provisional | JAX | RB | 50 | -0.25 | -0.12 | -0.23 – -0.02 |
| 85 | Clyde Edwards-Helaire◦ provisional | KC | RB | 70 | -0.21 | -0.12 | -0.22 – -0.02 |
| 86 | Matt Breida◦ provisional | NYG | RB | 55 | -0.25 | -0.13 | -0.23 – -0.02 |
| 87 | Keaontay Ingram◦ provisional | ARI | RB | 35 | -0.32 | -0.13 | -0.24 – -0.02 |
| 88 | Alexander Mattison | MIN | RB | 180 | -0.18 | -0.13 | -0.21 – -0.05 |
| 89 | D'Ernest Johnson◦ provisional | JAX | RB | 41 | -0.32 | -0.13 | -0.24 – -0.03 |
| 90 | Ke'Shawn Vaughn◦ provisional | TB | RB | 24 | -0.46 | -0.13 | -0.25 – -0.02 |
| 91 | Javonte Williams | DEN | RB | 219 | -0.17 | -0.14 | -0.21 – -0.06 |
| 92 | Rachaad White | TB | RB | 272 | -0.17 | -0.14 | -0.21 – -0.06 |
| 93 | Jerome Ford | CLE | RB | 206 | -0.18 | -0.14 | -0.21 – -0.06 |
| 94 | Isaiah Spiller◦ provisional | LAC | RB | 37 | -0.39 | -0.14 | -0.25 – -0.03 |
| 95 | Deuce Vaughn◦ provisional | DAL | RB | 23 | -0.56 | -0.15 | -0.26 – -0.03 |
| 96 | Josh Jacobs | LV | RB | 233 | -0.19 | -0.15 | -0.22 – -0.07 |
| 97 | Joshua Kelley◦ provisional | LAC | RB | 107 | -0.24 | -0.15 | -0.24 – -0.06 |
| 98 | Jamaal Williams◦ provisional | NO | RB | 106 | -0.25 | -0.15 | -0.24 – -0.06 |
| 99 | Miles Sanders◦ provisional | CAR | RB | 129 | -0.24 | -0.15 | -0.24 – -0.06 |
| 100 | Saquon Barkley | NYG | RB | 248 | -0.20 | -0.15 | -0.23 – -0.08 |
| 101 | Austin Ekeler | LAC | RB | 179 | -0.23 | -0.16 | -0.24 – -0.08 |
| 102 | Dalvin Cook◦ provisional | NYJ | RB | 67 | -0.37 | -0.17 | -0.27 – -0.07 |
| 103 | Dameon Pierce | HOU | RB | 145 | -0.28 | -0.18 | -0.27 – -0.09 |
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).