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 · 2018
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
- 194
- 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 · 2018 · full board
| # | Player | Team | Pos | carrys | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Todd Gurley | LA | RB | 260 | +0.08 | +0.02 | -0.05 – +0.09 |
| 2 | Alvin Kamara | NO | RB | 197 | +0.08 | +0.01 | -0.07 – +0.08 |
| 3 | Melvin Gordon◦ provisional | LAC | RB | 176 | +0.07 | -0.00 | -0.08 – +0.08 |
| 4 | Gus Edwards◦ provisional | BAL | RB | 139 | +0.09 | -0.00 | -0.08 – +0.08 |
| 5 | C.J. Anderson◦ provisional | LA | RB | 67 | +0.18 | -0.00 | -0.10 – +0.09 |
| 6 | Derrick Henry | TEN | RB | 215 | +0.05 | -0.01 | -0.08 – +0.07 |
| 7 | Marlon Mack | IND | RB | 197 | +0.04 | -0.01 | -0.09 – +0.06 |
| 8 | Christian McCaffrey | CAR | RB | 219 | +0.03 | -0.01 | -0.09 – +0.06 |
| 9 | Austin Ekeler◦ provisional | LAC | RB | 106 | +0.08 | -0.02 | -0.10 – +0.07 |
| 10 | Aaron Jones◦ provisional | GB | RB | 133 | +0.05 | -0.02 | -0.10 – +0.06 |
| 11 | Phillip Lindsay◦ provisional | DEN | RB | 193 | +0.03 | -0.02 | -0.10 – +0.06 |
| 12 | Zach Zenner◦ provisional | DET | RB | 55 | +0.11 | -0.03 | -0.12 – +0.07 |
| 13 | Nick Chubb◦ provisional | CLE | RB | 192 | +0.01 | -0.03 | -0.11 – +0.05 |
| 14 | Matt Breida◦ provisional | SF | RB | 153 | +0.02 | -0.03 | -0.11 – +0.05 |
| 15 | Chris Carson | SEA | RB | 247 | -0.00 | -0.03 | -0.10 – +0.04 |
| 16 | Kareem Hunt◦ provisional | KC | RB | 181 | +0.01 | -0.03 | -0.11 – +0.05 |
| 17 | Cordarrelle Patterson◦ provisional | NE | RB | 42 | +0.13 | -0.03 | -0.13 – +0.07 |
| 18 | Jordan Wilkins◦ provisional | IND | RB | 60 | +0.08 | -0.03 | -0.13 – +0.06 |
| 19 | Wendell Smallwood◦ provisional | PHI | RB | 88 | +0.04 | -0.03 | -0.12 – +0.06 |
| 20 | Mike Davis◦ provisional | SEA | RB | 112 | +0.02 | -0.04 | -0.12 – +0.05 |
| 21 | Sony Michel | NE | RB | 209 | -0.01 | -0.04 | -0.11 – +0.03 |
| 22 | Kapri Bibbs◦ provisional | GB | RB | 21 | +0.20 | -0.04 | -0.14 – +0.06 |
| 23 | James Conner | PIT | RB | 215 | -0.02 | -0.04 | -0.12 – +0.03 |
| 24 | Ezekiel Elliott | DAL | RB | 304 | -0.03 | -0.05 | -0.11 – +0.02 |
| 25 | Saquon Barkley | NYG | RB | 263 | -0.03 | -0.05 | -0.12 – +0.02 |
| 26 | Malcolm Brown◦ provisional | LA | RB | 43 | +0.05 | -0.05 | -0.14 – +0.05 |
| 27 | Kenneth Dixon◦ provisional | BAL | RB | 60 | +0.02 | -0.05 | -0.14 – +0.05 |
| 28 | Devontae Booker◦ provisional | DEN | RB | 34 | +0.07 | -0.05 | -0.15 – +0.05 |
| 29 | Frank Gore◦ provisional | MIA | RB | 156 | -0.03 | -0.05 | -0.13 – +0.03 |
| 30 | Kerryon Johnson◦ provisional | DET | RB | 118 | -0.02 | -0.05 | -0.13 – +0.04 |
| 31 | Damien Williams◦ provisional | KC | RB | 50 | -0.01 | -0.06 | -0.15 – +0.04 |
| 32 | Joe Mixon | CIN | RB | 237 | -0.05 | -0.06 | -0.13 – +0.02 |
| 33 | Marshawn Lynch◦ provisional | LV | RB | 90 | -0.03 | -0.06 | -0.14 – +0.03 |
| 34 | Raheem Mostert◦ provisional | SF | RB | 34 | +0.01 | -0.06 | -0.16 – +0.04 |
| 35 | Rashaad Penny◦ provisional | SEA | RB | 85 | -0.03 | -0.06 | -0.15 – +0.03 |
| 36 | Darren Sproles◦ provisional | PHI | RB | 29 | +0.01 | -0.06 | -0.16 – +0.04 |
| 37 | Duke Johnson◦ provisional | CLE | RB | 42 | -0.02 | -0.06 | -0.16 – +0.04 |
| 38 | Spencer Ware◦ provisional | KC | RB | 51 | -0.03 | -0.06 | -0.15 – +0.04 |
| 39 | Lamar Miller | HOU | RB | 210 | -0.06 | -0.06 | -0.14 – +0.01 |
| 40 | James White◦ provisional | NE | RB | 94 | -0.05 | -0.06 | -0.15 – +0.03 |
| 41 | Jaylen Samuels◦ provisional | PIT | RB | 56 | -0.05 | -0.06 | -0.16 – +0.03 |
| 42 | Cameron Artis-Payne◦ provisional | CAR | RB | 19 | -0.02 | -0.06 | -0.17 – +0.04 |
| 43 | Dwayne Washington◦ provisional | NO | RB | 27 | -0.04 | -0.06 | -0.17 – +0.04 |
| 44 | Mark Ingram◦ provisional | NO | RB | 138 | -0.06 | -0.07 | -0.15 – +0.02 |
| 45 | Isaiah Crowell◦ provisional | NYJ | RB | 143 | -0.07 | -0.07 | -0.15 – +0.01 |
| 46 | Justin Jackson◦ provisional | LAC | RB | 50 | -0.07 | -0.07 | -0.16 – +0.03 |
| 47 | Tevin Coleman◦ provisional | ATL | RB | 167 | -0.07 | -0.07 | -0.15 – +0.01 |
| 48 | Giovani Bernard◦ provisional | CIN | RB | 56 | -0.08 | -0.07 | -0.16 – +0.03 |
| 49 | Marcus Murphy◦ provisional | BUF | RB | 52 | -0.09 | -0.07 | -0.17 – +0.02 |
| 50 | Keith Ford◦ provisional | BUF | RB | 21 | -0.11 | -0.07 | -0.17 – +0.03 |
| 51 | Corey Clement◦ provisional | PHI | RB | 69 | -0.09 | -0.07 | -0.17 – +0.02 |
| 52 | Jay Ajayi◦ provisional | PHI | RB | 46 | -0.11 | -0.07 | -0.17 – +0.02 |
| 53 | Doug Martin◦ provisional | LV | RB | 172 | -0.09 | -0.08 | -0.16 – +0.00 |
| 54 | Chase Edmonds◦ provisional | ARI | RB | 60 | -0.11 | -0.08 | -0.17 – +0.02 |
| 55 | Brian Hill◦ provisional | ATL | RB | 20 | -0.18 | -0.08 | -0.18 – +0.02 |
| 56 | Jacquizz Rodgers◦ provisional | TB | RB | 33 | -0.15 | -0.08 | -0.18 – +0.02 |
| 57 | Theo Riddick◦ provisional | DET | RB | 40 | -0.14 | -0.08 | -0.18 – +0.02 |
| 58 | Javorius Allen◦ provisional | BAL | RB | 41 | -0.14 | -0.08 | -0.18 – +0.02 |
| 59 | Kenjon Barner◦ provisional | CAR | RB | 19 | -0.22 | -0.08 | -0.18 – +0.02 |
| 60 | Tarik Cohen◦ provisional | CHI | RB | 99 | -0.11 | -0.08 | -0.17 – +0.00 |
| 61 | Adrian Peterson | WAS | RB | 251 | -0.10 | -0.08 | -0.16 – -0.01 |
| 62 | Jordan Howard | CHI | RB | 250 | -0.10 | -0.09 | -0.16 – -0.01 |
| 63 | Wayne Gallman◦ provisional | NYG | RB | 51 | -0.16 | -0.09 | -0.18 – +0.01 |
| 64 | Trenton Cannon◦ provisional | NYJ | RB | 38 | -0.19 | -0.09 | -0.19 – +0.01 |
| 65 | Rod Smith◦ provisional | DAL | RB | 44 | -0.17 | -0.09 | -0.18 – +0.01 |
| 66 | Kalen Ballage◦ provisional | MIA | RB | 36 | -0.19 | -0.09 | -0.19 – +0.01 |
| 67 | Bilal Powell◦ provisional | NYJ | RB | 80 | -0.14 | -0.09 | -0.18 – +0.00 |
| 68 | Kenyan Drake◦ provisional | MIA | RB | 120 | -0.13 | -0.09 | -0.18 – -0.01 |
| 69 | Nyheim Hines◦ provisional | IND | RB | 85 | -0.14 | -0.09 | -0.18 – -0.00 |
| 70 | Ronald Jones◦ provisional | TB | RB | 23 | -0.32 | -0.09 | -0.20 – +0.01 |
| 71 | Jamaal Williams◦ provisional | GB | RB | 121 | -0.14 | -0.09 | -0.18 – -0.01 |
| 72 | Leonard Fournette◦ provisional | JAX | RB | 133 | -0.13 | -0.09 | -0.18 – -0.01 |
| 73 | Royce Freeman◦ provisional | DEN | RB | 130 | -0.14 | -0.10 | -0.18 – -0.01 |
| 74 | Chris Thompson◦ provisional | WAS | RB | 43 | -0.22 | -0.10 | -0.19 – +0.00 |
| 75 | DeAndre Washington◦ provisional | LV | RB | 30 | -0.30 | -0.10 | -0.20 – +0.00 |
| 76 | John Kelly◦ provisional | LA | RB | 27 | -0.33 | -0.10 | -0.20 – +0.00 |
| 77 | Alfred Morris◦ provisional | SF | RB | 111 | -0.16 | -0.10 | -0.19 – -0.01 |
| 78 | Latavius Murray◦ provisional | MIN | RB | 140 | -0.15 | -0.10 | -0.18 – -0.02 |
| 79 | Rex Burkhead◦ provisional | NE | RB | 57 | -0.21 | -0.10 | -0.20 – -0.01 |
| 80 | T.J. Yeldon◦ provisional | JAX | RB | 104 | -0.17 | -0.10 | -0.19 – -0.02 |
| 81 | Ito Smith◦ provisional | ATL | RB | 90 | -0.18 | -0.10 | -0.19 – -0.01 |
| 82 | Chris Ivory◦ provisional | BUF | RB | 115 | -0.16 | -0.10 | -0.19 – -0.02 |
| 83 | Alex Collins◦ provisional | BAL | RB | 114 | -0.18 | -0.11 | -0.19 – -0.02 |
| 84 | Dalvin Cook◦ provisional | MIN | RB | 133 | -0.17 | -0.11 | -0.19 – -0.02 |
| 85 | Jeff Wilson◦ provisional | SF | RB | 66 | -0.24 | -0.11 | -0.21 – -0.02 |
| 86 | Josh Adams◦ provisional | PHI | RB | 121 | -0.19 | -0.11 | -0.20 – -0.03 |
| 87 | Stevan Ridley◦ provisional | PIT | RB | 29 | -0.43 | -0.12 | -0.22 – -0.01 |
| 88 | Jalen Richard◦ provisional | LV | RB | 56 | -0.30 | -0.12 | -0.22 – -0.03 |
| 89 | Mike Gillislee◦ provisional | NO | RB | 16 | -0.89 | -0.13 | -0.23 – -0.03 |
| 90 | Peyton Barber | TB | RB | 234 | -0.18 | -0.13 | -0.20 – -0.06 |
| 91 | Alfred Blue◦ provisional | HOU | RB | 150 | -0.22 | -0.13 | -0.21 – -0.05 |
| 92 | LeSean McCoy◦ provisional | BUF | RB | 161 | -0.22 | -0.14 | -0.22 – -0.06 |
| 93 | Carlos Hyde◦ provisional | JAX | RB | 172 | -0.23 | -0.14 | -0.22 – -0.06 |
| 94 | Dion Lewis◦ provisional | TEN | RB | 155 | -0.24 | -0.14 | -0.23 – -0.06 |
| 95 | LeGarrette Blount◦ provisional | DET | RB | 155 | -0.24 | -0.15 | -0.23 – -0.07 |
| 96 | David Johnson | ARI | RB | 259 | -0.20 | -0.15 | -0.22 – -0.08 |
| 97 | Elijah McGuire◦ provisional | NYJ | RB | 92 | -0.36 | -0.16 | -0.25 – -0.07 |
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).