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 · 2021
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
- 393
- 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 · 2021 · full board
| # | Player | Team | Pos | carrys | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Jonathan Taylor◦ provisional | IND | RB | 332 | +0.10 | +0.02 | -0.04 – +0.07 |
| 2 | Tony Pollard◦ provisional | DAL | RB | 130 | +0.10 | -0.02 | -0.08 – +0.05 |
| 3 | Nick Chubb◦ provisional | CLE | RB | 228 | +0.05 | -0.02 | -0.08 – +0.04 |
| 4 | Chase Edmonds◦ provisional | ARI | RB | 116 | +0.10 | -0.02 | -0.09 – +0.04 |
| 5 | Rashaad Penny◦ provisional | SEA | RB | 119 | +0.09 | -0.02 | -0.09 – +0.04 |
| 6 | Leonard Fournette◦ provisional | TB | RB | 180 | +0.05 | -0.03 | -0.09 – +0.04 |
| 7 | AJ Dillon◦ provisional | GB | RB | 187 | +0.03 | -0.03 | -0.09 – +0.03 |
| 8 | Dontrell Hilliard◦ provisional | TEN | RB | 56 | +0.16 | -0.03 | -0.10 – +0.04 |
| 9 | Travis Homer◦ provisional | SEA | RB | 21 | +0.46 | -0.03 | -0.10 – +0.04 |
| 10 | Damien Harris◦ provisional | NE | RB | 202 | +0.02 | -0.03 | -0.09 – +0.03 |
| 11 | Darrel Williams◦ provisional | KC | RB | 144 | +0.03 | -0.03 | -0.10 – +0.03 |
| 12 | D'Ernest Johnson◦ provisional | CLE | RB | 100 | +0.06 | -0.03 | -0.10 – +0.03 |
| 13 | Kareem Hunt◦ provisional | CLE | RB | 79 | +0.08 | -0.03 | -0.10 – +0.03 |
| 14 | Aaron Jones◦ provisional | GB | RB | 171 | +0.01 | -0.04 | -0.10 – +0.02 |
| 15 | Jonathan Williams◦ provisional | WAS | RB | 17 | +0.43 | -0.04 | -0.11 – +0.03 |
| 16 | Rhamondre Stevenson◦ provisional | NE | RB | 133 | +0.02 | -0.04 | -0.10 – +0.02 |
| 17 | Austin Ekeler◦ provisional | LAC | RB | 208 | -0.00 | -0.04 | -0.10 – +0.02 |
| 18 | Miles Sanders◦ provisional | PHI | RB | 138 | +0.01 | -0.04 | -0.10 – +0.02 |
| 19 | Boston Scott◦ provisional | PHI | RB | 87 | +0.04 | -0.04 | -0.11 – +0.03 |
| 20 | Nyheim Hines◦ provisional | IND | RB | 56 | +0.07 | -0.04 | -0.11 – +0.03 |
| 21 | Christian McCaffrey◦ provisional | CAR | RB | 99 | +0.02 | -0.04 | -0.11 – +0.02 |
| 22 | Kenneth Gainwell◦ provisional | PHI | RB | 69 | +0.04 | -0.04 | -0.11 – +0.02 |
| 23 | James Conner◦ provisional | ARI | RB | 202 | -0.02 | -0.04 | -0.11 – +0.02 |
| 24 | Darrell Henderson◦ provisional | LA | RB | 149 | -0.01 | -0.05 | -0.11 – +0.02 |
| 25 | J.D. McKissic◦ provisional | WAS | RB | 49 | +0.06 | -0.05 | -0.12 – +0.03 |
| 26 | Derrick Henry◦ provisional | TEN | RB | 220 | -0.02 | -0.05 | -0.11 – +0.01 |
| 27 | Devin Singletary◦ provisional | BUF | RB | 188 | -0.02 | -0.05 | -0.11 – +0.02 |
| 28 | Jamaal Williams◦ provisional | DET | RB | 153 | -0.02 | -0.05 | -0.11 – +0.02 |
| 29 | Jermar Jefferson◦ provisional | DET | RB | 15 | +0.21 | -0.05 | -0.12 – +0.02 |
| 30 | Jordan Howard◦ provisional | PHI | RB | 86 | -0.01 | -0.05 | -0.12 – +0.02 |
| 31 | Devonta Freeman◦ provisional | BAL | RB | 133 | -0.02 | -0.05 | -0.11 – +0.01 |
| 32 | DeeJay Dallas◦ provisional | SEA | RB | 33 | +0.06 | -0.05 | -0.12 – +0.02 |
| 33 | JaMycal Hasty◦ provisional | SF | RB | 16 | +0.17 | -0.05 | -0.12 – +0.02 |
| 34 | Justin Jackson◦ provisional | LAC | RB | 69 | +0.00 | -0.05 | -0.12 – +0.02 |
| 35 | Dalvin Cook◦ provisional | MIN | RB | 251 | -0.04 | -0.05 | -0.11 – +0.01 |
| 36 | Derrick Gore◦ provisional | KC | RB | 51 | +0.01 | -0.05 | -0.12 – +0.02 |
| 37 | Ryquell Armstead◦ provisional | JAX | RB | 15 | +0.11 | -0.05 | -0.13 – +0.02 |
| 38 | Khalil Herbert◦ provisional | CHI | RB | 103 | -0.03 | -0.05 | -0.12 – +0.01 |
| 39 | Duke Johnson◦ provisional | MIA | RB | 71 | -0.02 | -0.05 | -0.12 – +0.02 |
| 40 | Elijhaa Penny◦ provisional | NYG | RB | 25 | +0.02 | -0.05 | -0.13 – +0.02 |
| 41 | Michael Carter◦ provisional | NYJ | RB | 148 | -0.04 | -0.05 | -0.12 – +0.01 |
| 42 | Ronald Jones◦ provisional | TB | RB | 101 | -0.04 | -0.05 | -0.12 – +0.01 |
| 43 | Chris Evans◦ provisional | CIN | RB | 17 | +0.04 | -0.05 | -0.13 – +0.02 |
| 44 | Patrick Taylor◦ provisional | GB | RB | 23 | +0.01 | -0.05 | -0.13 – +0.02 |
| 45 | Rex Burkhead◦ provisional | HOU | RB | 122 | -0.04 | -0.05 | -0.12 – +0.01 |
| 46 | Brandon Bolden◦ provisional | NE | RB | 45 | -0.02 | -0.06 | -0.13 – +0.02 |
| 47 | Chris Carson◦ provisional | SEA | RB | 54 | -0.03 | -0.06 | -0.13 – +0.01 |
| 48 | Ty'Son Williams◦ provisional | BAL | RB | 35 | -0.02 | -0.06 | -0.13 – +0.02 |
| 49 | Damien Williams◦ provisional | CHI | RB | 40 | -0.03 | -0.06 | -0.13 – +0.01 |
| 50 | Trayveon Williams◦ provisional | CIN | RB | 15 | -0.01 | -0.06 | -0.13 – +0.02 |
| 51 | Trey Sermon◦ provisional | SF | RB | 41 | -0.04 | -0.06 | -0.13 – +0.01 |
| 52 | Latavius Murray◦ provisional | BAL | RB | 119 | -0.06 | -0.06 | -0.12 – +0.01 |
| 53 | Austin Walter◦ provisional | NYJ | RB | 26 | -0.06 | -0.06 | -0.13 – +0.01 |
| 54 | Jaret Patterson◦ provisional | WAS | RB | 68 | -0.07 | -0.06 | -0.13 – +0.01 |
| 55 | Najee Harris◦ provisional | PIT | RB | 307 | -0.06 | -0.06 | -0.12 – -0.00 |
| 56 | Tevin Coleman◦ provisional | NYJ | RB | 84 | -0.07 | -0.06 | -0.13 – +0.01 |
| 57 | Ke'Shawn Vaughn◦ provisional | TB | RB | 36 | -0.09 | -0.06 | -0.13 – +0.01 |
| 58 | James Robinson◦ provisional | JAX | RB | 164 | -0.07 | -0.06 | -0.12 – +0.00 |
| 59 | Ezekiel Elliott◦ provisional | DAL | RB | 240 | -0.07 | -0.06 | -0.12 – -0.00 |
| 60 | Clyde Edwards-Helaire◦ provisional | KC | RB | 119 | -0.07 | -0.06 | -0.13 – +0.00 |
| 61 | Elijah Mitchell◦ provisional | SF | RB | 207 | -0.07 | -0.06 | -0.12 – -0.00 |
| 62 | Corey Clement◦ provisional | DAL | RB | 33 | -0.15 | -0.07 | -0.14 – +0.01 |
| 63 | Wayne Gallman◦ provisional | MIN | RB | 28 | -0.17 | -0.07 | -0.14 – +0.01 |
| 64 | Samaje Perine◦ provisional | CIN | RB | 55 | -0.12 | -0.07 | -0.14 – +0.00 |
| 65 | Zack Moss◦ provisional | BUF | RB | 96 | -0.10 | -0.07 | -0.13 – -0.00 |
| 66 | Devontae Booker◦ provisional | NYG | RB | 145 | -0.09 | -0.07 | -0.13 – -0.00 |
| 67 | Qadree Ollison◦ provisional | ATL | RB | 21 | -0.22 | -0.07 | -0.14 – +0.01 |
| 68 | Godwin Igwebuike◦ provisional | DET | RB | 18 | -0.25 | -0.07 | -0.14 – +0.01 |
| 69 | Javonte Williams◦ provisional | DEN | RB | 203 | -0.09 | -0.07 | -0.13 – -0.01 |
| 70 | Eno Benjamin◦ provisional | ARI | RB | 34 | -0.18 | -0.07 | -0.14 – +0.00 |
| 71 | J.J. Taylor◦ provisional | NE | RB | 19 | -0.27 | -0.07 | -0.14 – +0.00 |
| 72 | Marlon Mack◦ provisional | IND | RB | 28 | -0.21 | -0.07 | -0.14 – +0.00 |
| 73 | Craig Reynolds◦ provisional | DET | RB | 55 | -0.14 | -0.07 | -0.14 – +0.00 |
| 74 | Le'Veon Bell◦ provisional | TB | RB | 40 | -0.17 | -0.07 | -0.14 – +0.00 |
| 75 | D'Onta Foreman◦ provisional | TEN | RB | 133 | -0.10 | -0.07 | -0.13 – -0.01 |
| 76 | Alex Collins◦ provisional | SEA | RB | 108 | -0.11 | -0.07 | -0.14 – -0.00 |
| 77 | Jeff Wilson◦ provisional | SF | RB | 79 | -0.13 | -0.07 | -0.14 – -0.00 |
| 78 | Melvin Gordon◦ provisional | DEN | RB | 203 | -0.09 | -0.07 | -0.13 – -0.01 |
| 79 | Kenyan Drake◦ provisional | LV | RB | 63 | -0.14 | -0.07 | -0.14 – -0.00 |
| 80 | Cordarrelle Patterson◦ provisional | ATL | RB | 153 | -0.10 | -0.07 | -0.13 – -0.01 |
| 81 | Joe Mixon◦ provisional | CIN | RB | 294 | -0.09 | -0.07 | -0.13 – -0.01 |
| 82 | David Montgomery◦ provisional | CHI | RB | 225 | -0.10 | -0.07 | -0.13 – -0.01 |
| 83 | Antonio Gibson◦ provisional | WAS | RB | 259 | -0.09 | -0.07 | -0.13 – -0.01 |
| 84 | Royce Freeman◦ provisional | HOU | RB | 56 | -0.17 | -0.07 | -0.14 – -0.00 |
| 85 | Jeremy McNichols◦ provisional | TEN | RB | 41 | -0.21 | -0.07 | -0.14 – -0.00 |
| 86 | Sony Michel◦ provisional | LA | RB | 208 | -0.10 | -0.07 | -0.13 – -0.01 |
| 87 | Peyton Barber◦ provisional | LV | RB | 55 | -0.18 | -0.07 | -0.14 – -0.00 |
| 88 | Malcolm Brown◦ provisional | MIA | RB | 33 | -0.26 | -0.07 | -0.15 – -0.00 |
| 89 | Matt Breida◦ provisional | BUF | RB | 26 | -0.33 | -0.08 | -0.15 – -0.00 |
| 90 | Ty Johnson◦ provisional | NYJ | RB | 61 | -0.18 | -0.08 | -0.14 – -0.01 |
| 91 | Dare Ogunbowale◦ provisional | JAX | RB | 44 | -0.23 | -0.08 | -0.15 – -0.01 |
| 92 | Adrian Peterson◦ provisional | SEA | RB | 38 | -0.26 | -0.08 | -0.15 – -0.01 |
| 93 | Ameer Abdullah◦ provisional | CAR | RB | 51 | -0.22 | -0.08 | -0.15 – -0.01 |
| 94 | Mike Davis◦ provisional | ATL | RB | 138 | -0.13 | -0.08 | -0.14 – -0.01 |
| 95 | Larry Rountree III◦ provisional | LAC | RB | 36 | -0.28 | -0.08 | -0.15 – -0.01 |
| 96 | Saquon Barkley◦ provisional | NYG | RB | 162 | -0.13 | -0.08 | -0.14 – -0.02 |
| 97 | Salvon Ahmed◦ provisional | MIA | RB | 54 | -0.22 | -0.08 | -0.15 – -0.01 |
| 98 | Benny Snell◦ provisional | PIT | RB | 36 | -0.31 | -0.08 | -0.15 – -0.01 |
| 99 | Chuba Hubbard◦ provisional | CAR | RB | 172 | -0.14 | -0.08 | -0.15 – -0.02 |
| 100 | Joshua Kelley◦ provisional | LAC | RB | 33 | -0.46 | -0.09 | -0.16 – -0.02 |
| 101 | Josh Jacobs◦ provisional | LV | RB | 217 | -0.15 | -0.09 | -0.15 – -0.03 |
| 102 | Myles Gaskin◦ provisional | MIA | RB | 173 | -0.17 | -0.09 | -0.15 – -0.03 |
| 103 | D'Andre Swift◦ provisional | DET | RB | 151 | -0.18 | -0.09 | -0.16 – -0.03 |
| 104 | Alexander Mattison◦ provisional | MIN | RB | 135 | -0.19 | -0.09 | -0.16 – -0.03 |
| 105 | Tony Jones◦ provisional | NO | RB | 54 | -0.35 | -0.09 | -0.16 – -0.02 |
| 106 | Phillip Lindsay◦ provisional | MIA | RB | 88 | -0.26 | -0.10 | -0.16 – -0.03 |
| 107 | David Johnson◦ provisional | HOU | RB | 67 | -0.32 | -0.10 | -0.17 – -0.03 |
| 108 | Mark Ingram◦ provisional | NO | RB | 160 | -0.20 | -0.10 | -0.16 – -0.04 |
| 109 | Alvin Kamara◦ provisional | NO | RB | 241 | -0.17 | -0.10 | -0.16 – -0.04 |
| 110 | Carlos Hyde◦ provisional | JAX | RB | 72 | -0.35 | -0.10 | -0.17 – -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).