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 · 2020
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
- 238
- 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 · 2020 · full board
| # | Player | Team | Pos | carrys | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | J.K. Dobbins◦ provisional | BAL | RB | 135 | +0.20 | +0.04 | -0.03 – +0.12 |
| 2 | Derrick Henry | TEN | RB | 380 | +0.09 | +0.04 | -0.02 – +0.10 |
| 3 | Gus Edwards◦ provisional | BAL | RB | 144 | +0.12 | +0.02 | -0.06 – +0.10 |
| 4 | Chris Carson◦ provisional | SEA | RB | 141 | +0.12 | +0.02 | -0.06 – +0.10 |
| 5 | Nick Chubb◦ provisional | CLE | RB | 190 | +0.09 | +0.01 | -0.06 – +0.09 |
| 6 | Dalvin Cook | MIN | RB | 315 | +0.05 | +0.01 | -0.05 – +0.08 |
| 7 | Jonathan Taylor◦ provisional | IND | RB | 232 | +0.06 | +0.01 | -0.06 – +0.08 |
| 8 | Aaron Jones◦ provisional | GB | RB | 202 | +0.07 | +0.01 | -0.07 – +0.08 |
| 9 | AJ Dillon◦ provisional | GB | RB | 46 | +0.21 | -0.00 | -0.09 – +0.09 |
| 10 | Alvin Kamara◦ provisional | NO | RB | 187 | +0.05 | -0.00 | -0.08 – +0.07 |
| 11 | Damien Harris◦ provisional | NE | RB | 137 | +0.04 | -0.01 | -0.09 – +0.07 |
| 12 | Antonio Gibson◦ provisional | WAS | RB | 170 | +0.03 | -0.01 | -0.09 – +0.06 |
| 13 | Ronald Jones◦ provisional | TB | RB | 192 | +0.03 | -0.01 | -0.09 – +0.06 |
| 14 | Sony Michel◦ provisional | NE | RB | 79 | +0.07 | -0.02 | -0.10 – +0.07 |
| 15 | Latavius Murray◦ provisional | NO | RB | 146 | +0.02 | -0.02 | -0.10 – +0.06 |
| 16 | Jalen Richard◦ provisional | LV | RB | 22 | +0.25 | -0.02 | -0.11 – +0.08 |
| 17 | Jamaal Williams◦ provisional | GB | RB | 121 | +0.03 | -0.02 | -0.10 – +0.06 |
| 18 | Darrell Henderson◦ provisional | LA | RB | 138 | +0.02 | -0.02 | -0.10 – +0.06 |
| 19 | Rex Burkhead◦ provisional | NE | RB | 67 | +0.06 | -0.02 | -0.11 – +0.07 |
| 20 | Wayne Gallman◦ provisional | NYG | RB | 147 | +0.02 | -0.02 | -0.10 – +0.06 |
| 21 | Christian McCaffrey◦ provisional | CAR | RB | 59 | +0.07 | -0.02 | -0.11 – +0.07 |
| 22 | Kyle Juszczyk◦ provisional | SF | RB | 17 | +0.28 | -0.02 | -0.12 – +0.07 |
| 23 | Devontae Booker◦ provisional | LV | RB | 93 | +0.03 | -0.02 | -0.11 – +0.06 |
| 24 | James Conner◦ provisional | PIT | RB | 169 | +0.01 | -0.02 | -0.10 – +0.05 |
| 25 | Miles Sanders◦ provisional | PHI | RB | 168 | -0.01 | -0.03 | -0.10 – +0.05 |
| 26 | Darrel Williams◦ provisional | KC | RB | 39 | +0.06 | -0.03 | -0.12 – +0.06 |
| 27 | Rodney Smith◦ provisional | CAR | RB | 41 | +0.05 | -0.03 | -0.12 – +0.06 |
| 28 | Carlos Hyde◦ provisional | SEA | RB | 81 | +0.01 | -0.03 | -0.12 – +0.05 |
| 29 | J.J. Taylor◦ provisional | NE | RB | 23 | +0.09 | -0.03 | -0.13 – +0.06 |
| 30 | Ty Johnson◦ provisional | NYJ | RB | 54 | +0.02 | -0.03 | -0.12 – +0.06 |
| 31 | Alex Collins◦ provisional | SEA | RB | 18 | +0.11 | -0.03 | -0.13 – +0.06 |
| 32 | Leonard Fournette◦ provisional | TB | RB | 97 | -0.01 | -0.03 | -0.12 – +0.05 |
| 33 | Alfred Morris◦ provisional | NYG | RB | 55 | +0.00 | -0.04 | -0.12 – +0.05 |
| 34 | David Johnson◦ provisional | HOU | RB | 147 | -0.02 | -0.04 | -0.11 – +0.04 |
| 35 | Kenyan Drake | ARI | RB | 239 | -0.03 | -0.04 | -0.11 – +0.03 |
| 36 | JaMycal Hasty◦ provisional | SF | RB | 39 | +0.00 | -0.04 | -0.13 – +0.05 |
| 37 | Josh Adams◦ provisional | NYJ | RB | 29 | +0.01 | -0.04 | -0.13 – +0.06 |
| 38 | Samaje Perine◦ provisional | CIN | RB | 63 | -0.02 | -0.04 | -0.13 – +0.05 |
| 39 | Tony Pollard◦ provisional | DAL | RB | 101 | -0.03 | -0.04 | -0.12 – +0.04 |
| 40 | Troymaine Pope◦ provisional | LAC | RB | 15 | +0.05 | -0.04 | -0.13 – +0.06 |
| 41 | Royce Freeman◦ provisional | DEN | RB | 35 | -0.01 | -0.04 | -0.13 – +0.05 |
| 42 | David Montgomery | CHI | RB | 248 | -0.04 | -0.04 | -0.11 – +0.03 |
| 43 | Ito Smith◦ provisional | ATL | RB | 63 | -0.03 | -0.04 | -0.13 – +0.05 |
| 44 | Salvon Ahmed◦ provisional | MIA | RB | 75 | -0.04 | -0.04 | -0.13 – +0.04 |
| 45 | Buddy Howell◦ provisional | HOU | RB | 16 | -0.03 | -0.04 | -0.14 – +0.05 |
| 46 | Justin Jackson◦ provisional | LAC | RB | 59 | -0.04 | -0.04 | -0.13 – +0.04 |
| 47 | Kalen Ballage◦ provisional | LAC | RB | 91 | -0.05 | -0.05 | -0.13 – +0.04 |
| 48 | D'Ernest Johnson◦ provisional | CLE | RB | 33 | -0.07 | -0.05 | -0.14 – +0.05 |
| 49 | Ke'Shawn Vaughn◦ provisional | TB | RB | 26 | -0.07 | -0.05 | -0.14 – +0.05 |
| 50 | D'Andre Swift◦ provisional | DET | RB | 114 | -0.05 | -0.05 | -0.13 – +0.03 |
| 51 | Clyde Edwards-Helaire◦ provisional | KC | RB | 181 | -0.05 | -0.05 | -0.12 – +0.03 |
| 52 | Boston Scott◦ provisional | PHI | RB | 80 | -0.06 | -0.05 | -0.13 – +0.04 |
| 53 | James Robinson | JAX | RB | 241 | -0.05 | -0.05 | -0.12 – +0.02 |
| 54 | Peyton Barber◦ provisional | WAS | RB | 95 | -0.06 | -0.05 | -0.13 – +0.04 |
| 55 | Corey Clement◦ provisional | PHI | RB | 21 | -0.12 | -0.05 | -0.15 – +0.04 |
| 56 | D'Onta Foreman◦ provisional | TEN | RB | 22 | -0.12 | -0.05 | -0.15 – +0.04 |
| 57 | Chase Edmonds◦ provisional | ARI | RB | 97 | -0.07 | -0.05 | -0.13 – +0.03 |
| 58 | Zack Moss◦ provisional | BUF | RB | 112 | -0.07 | -0.05 | -0.13 – +0.03 |
| 59 | J.D. McKissic◦ provisional | WAS | RB | 85 | -0.07 | -0.05 | -0.14 – +0.03 |
| 60 | Mark Ingram◦ provisional | BAL | RB | 72 | -0.08 | -0.05 | -0.14 – +0.03 |
| 61 | Jeff Wilson◦ provisional | SF | RB | 126 | -0.07 | -0.05 | -0.13 – +0.03 |
| 62 | Matt Breida◦ provisional | MIA | RB | 59 | -0.09 | -0.05 | -0.14 – +0.04 |
| 63 | Alexander Mattison◦ provisional | MIN | RB | 96 | -0.08 | -0.05 | -0.14 – +0.03 |
| 64 | Dion Lewis◦ provisional | NYG | RB | 29 | -0.13 | -0.05 | -0.15 – +0.04 |
| 65 | Dare Ogunbowale◦ provisional | JAX | RB | 32 | -0.12 | -0.05 | -0.15 – +0.04 |
| 66 | DeeJay Dallas◦ provisional | SEA | RB | 34 | -0.12 | -0.05 | -0.15 – +0.04 |
| 67 | Adrian Peterson◦ provisional | DET | RB | 156 | -0.08 | -0.06 | -0.13 – +0.02 |
| 68 | Anthony McFarland◦ provisional | PIT | RB | 33 | -0.15 | -0.06 | -0.15 – +0.04 |
| 69 | Austin Ekeler◦ provisional | LAC | RB | 116 | -0.09 | -0.06 | -0.14 – +0.02 |
| 70 | Melvin Gordon◦ provisional | DEN | RB | 215 | -0.08 | -0.06 | -0.13 – +0.01 |
| 71 | Raheem Mostert◦ provisional | SF | RB | 104 | -0.10 | -0.06 | -0.14 – +0.02 |
| 72 | Kareem Hunt◦ provisional | CLE | RB | 198 | -0.08 | -0.06 | -0.14 – +0.01 |
| 73 | Jeremy McNichols◦ provisional | TEN | RB | 47 | -0.15 | -0.06 | -0.15 – +0.03 |
| 74 | Devin Singletary◦ provisional | BUF | RB | 156 | -0.09 | -0.06 | -0.14 – +0.01 |
| 75 | James White◦ provisional | NE | RB | 35 | -0.19 | -0.06 | -0.16 – +0.03 |
| 76 | Nyheim Hines◦ provisional | IND | RB | 90 | -0.12 | -0.06 | -0.15 – +0.02 |
| 77 | Jordan Howard◦ provisional | PHI | RB | 35 | -0.20 | -0.06 | -0.16 – +0.03 |
| 78 | Malcolm Brown◦ provisional | LA | RB | 101 | -0.11 | -0.06 | -0.15 – +0.02 |
| 79 | Cordarrelle Patterson◦ provisional | CHI | RB | 64 | -0.14 | -0.06 | -0.15 – +0.02 |
| 80 | Jerick McKinnon◦ provisional | SF | RB | 81 | -0.13 | -0.07 | -0.15 – +0.02 |
| 81 | Devonta Freeman◦ provisional | NYG | RB | 54 | -0.17 | -0.07 | -0.16 – +0.02 |
| 82 | La'Mical Perine◦ provisional | NYJ | RB | 64 | -0.16 | -0.07 | -0.16 – +0.02 |
| 83 | DeAndre Washington◦ provisional | MIA | RB | 31 | -0.25 | -0.07 | -0.16 – +0.03 |
| 84 | Kerryon Johnson◦ provisional | DET | RB | 52 | -0.19 | -0.07 | -0.16 – +0.02 |
| 85 | Todd Gurley◦ provisional | ATL | RB | 195 | -0.10 | -0.07 | -0.14 – +0.00 |
| 86 | Darwin Thompson◦ provisional | KC | RB | 27 | -0.30 | -0.07 | -0.16 – +0.02 |
| 87 | Tevin Coleman◦ provisional | SF | RB | 28 | -0.30 | -0.07 | -0.16 – +0.02 |
| 88 | Saquon Barkley◦ provisional | NYG | RB | 19 | -0.43 | -0.07 | -0.17 – +0.02 |
| 89 | Brian Hill◦ provisional | ATL | RB | 100 | -0.14 | -0.07 | -0.16 – +0.01 |
| 90 | Mike Davis◦ provisional | CAR | RB | 165 | -0.12 | -0.07 | -0.15 – +0.00 |
| 91 | Travis Homer◦ provisional | SEA | RB | 25 | -0.40 | -0.08 | -0.17 – +0.02 |
| 92 | Ezekiel Elliott | DAL | RB | 245 | -0.12 | -0.08 | -0.15 – -0.01 |
| 93 | Le'Veon Bell◦ provisional | KC | RB | 82 | -0.19 | -0.08 | -0.17 – +0.00 |
| 94 | Phillip Lindsay◦ provisional | DEN | RB | 118 | -0.16 | -0.08 | -0.16 – -0.00 |
| 95 | Giovani Bernard◦ provisional | CIN | RB | 124 | -0.16 | -0.09 | -0.17 – -0.00 |
| 96 | Josh Jacobs | LV | RB | 273 | -0.12 | -0.09 | -0.15 – -0.02 |
| 97 | Joe Mixon◦ provisional | CIN | RB | 119 | -0.18 | -0.09 | -0.17 – -0.01 |
| 98 | Myles Gaskin◦ provisional | MIA | RB | 142 | -0.17 | -0.09 | -0.17 – -0.01 |
| 99 | Trayveon Williams◦ provisional | CIN | RB | 26 | -0.56 | -0.09 | -0.19 – -0.00 |
| 100 | Jordan Wilkins◦ provisional | IND | RB | 86 | -0.25 | -0.10 | -0.18 – -0.01 |
| 101 | Cam Akers◦ provisional | LA | RB | 145 | -0.22 | -0.11 | -0.19 – -0.03 |
| 102 | Duke Johnson◦ provisional | HOU | RB | 77 | -0.33 | -0.11 | -0.20 – -0.03 |
| 103 | Benny Snell◦ provisional | PIT | RB | 111 | -0.27 | -0.12 | -0.20 – -0.03 |
| 104 | Joshua Kelley◦ provisional | LAC | RB | 111 | -0.27 | -0.12 | -0.20 – -0.03 |
| 105 | Frank Gore◦ provisional | NYJ | RB | 187 | -0.22 | -0.12 | -0.20 – -0.05 |
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).