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 · 2019
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
- 859
- 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 · 2019 · full board
| # | Player | Team | Pos | carrys | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Mark Ingram◦ provisional | BAL | RB | 204 | +0.08 | -0.05 | -0.10 – -0.00 |
| 2 | Dalvin Cook◦ provisional | MIN | RB | 250 | +0.02 | -0.06 | -0.10 – -0.01 |
| 3 | Marlon Mack◦ provisional | IND | RB | 248 | +0.01 | -0.06 | -0.11 – -0.02 |
| 4 | Gus Edwards◦ provisional | BAL | RB | 133 | +0.06 | -0.06 | -0.11 – -0.01 |
| 5 | Raheem Mostert◦ provisional | SF | RB | 137 | +0.05 | -0.06 | -0.11 – -0.02 |
| 6 | Derrick Henry◦ provisional | TEN | RB | 303 | -0.01 | -0.06 | -0.11 – -0.02 |
| 7 | Ezekiel Elliott◦ provisional | DAL | RB | 301 | -0.02 | -0.07 | -0.11 – -0.02 |
| 8 | Aaron Jones◦ provisional | GB | RB | 236 | -0.01 | -0.07 | -0.11 – -0.02 |
| 9 | Kenyan Drake◦ provisional | ARI | RB | 170 | +0.01 | -0.07 | -0.11 – -0.02 |
| 10 | Devin Singletary◦ provisional | BUF | RB | 151 | +0.02 | -0.07 | -0.11 – -0.02 |
| 11 | Jordan Wilkins◦ provisional | IND | RB | 51 | +0.14 | -0.07 | -0.12 – -0.02 |
| 12 | Rashaad Penny◦ provisional | SEA | RB | 65 | +0.07 | -0.07 | -0.12 – -0.02 |
| 13 | Jordan Howard◦ provisional | PHI | RB | 119 | -0.00 | -0.07 | -0.12 – -0.02 |
| 14 | Josh Jacobs◦ provisional | LV | RB | 242 | -0.04 | -0.07 | -0.12 – -0.03 |
| 15 | Justin Jackson◦ provisional | LAC | RB | 29 | +0.18 | -0.07 | -0.12 – -0.02 |
| 16 | Chase Edmonds◦ provisional | ARI | RB | 60 | +0.04 | -0.07 | -0.12 – -0.02 |
| 17 | Christian McCaffrey◦ provisional | CAR | RB | 288 | -0.05 | -0.07 | -0.12 – -0.03 |
| 18 | Latavius Murray◦ provisional | NO | RB | 146 | -0.03 | -0.07 | -0.12 – -0.03 |
| 19 | Jonathan Williams◦ provisional | IND | RB | 49 | +0.05 | -0.07 | -0.13 – -0.02 |
| 20 | Derrius Guice◦ provisional | WAS | RB | 42 | +0.07 | -0.07 | -0.13 – -0.02 |
| 21 | Rex Burkhead◦ provisional | NE | RB | 65 | +0.02 | -0.07 | -0.12 – -0.02 |
| 22 | Tony Pollard◦ provisional | DAL | RB | 87 | -0.01 | -0.08 | -0.12 – -0.03 |
| 23 | Phillip Lindsay◦ provisional | DEN | RB | 225 | -0.05 | -0.08 | -0.12 – -0.03 |
| 24 | Ito Smith◦ provisional | ATL | RB | 22 | +0.16 | -0.08 | -0.13 – -0.02 |
| 25 | Carlos Hyde◦ provisional | HOU | RB | 245 | -0.06 | -0.08 | -0.12 – -0.03 |
| 26 | Mike Boone◦ provisional | MIN | RB | 49 | +0.02 | -0.08 | -0.13 – -0.03 |
| 27 | Nyheim Hines◦ provisional | IND | RB | 52 | +0.01 | -0.08 | -0.13 – -0.03 |
| 28 | Travis Homer◦ provisional | SEA | RB | 18 | +0.17 | -0.08 | -0.13 – -0.03 |
| 29 | Brandon Bolden◦ provisional | NE | RB | 15 | +0.22 | -0.08 | -0.13 – -0.03 |
| 30 | Reggie Bonnafon◦ provisional | CAR | RB | 16 | +0.15 | -0.08 | -0.13 – -0.03 |
| 31 | Jeff Wilson◦ provisional | SF | RB | 27 | +0.04 | -0.08 | -0.13 – -0.03 |
| 32 | Kerrith Whyte◦ provisional | PIT | RB | 24 | +0.04 | -0.08 | -0.13 – -0.03 |
| 33 | Leonard Fournette◦ provisional | JAX | RB | 266 | -0.07 | -0.08 | -0.12 – -0.03 |
| 34 | Jamaal Williams◦ provisional | GB | RB | 107 | -0.06 | -0.08 | -0.13 – -0.03 |
| 35 | LeSean McCoy◦ provisional | KC | RB | 101 | -0.06 | -0.08 | -0.13 – -0.03 |
| 36 | Qadree Ollison◦ provisional | ATL | RB | 22 | +0.01 | -0.08 | -0.13 – -0.03 |
| 37 | Cordarrelle Patterson◦ provisional | CHI | RB | 17 | +0.02 | -0.08 | -0.13 – -0.03 |
| 38 | Nick Chubb◦ provisional | CLE | RB | 298 | -0.08 | -0.08 | -0.13 – -0.04 |
| 39 | Boston Scott◦ provisional | PHI | RB | 61 | -0.07 | -0.08 | -0.13 – -0.03 |
| 40 | Darwin Thompson◦ provisional | KC | RB | 37 | -0.06 | -0.08 | -0.13 – -0.03 |
| 41 | Miles Sanders◦ provisional | PHI | RB | 180 | -0.08 | -0.08 | -0.13 – -0.03 |
| 42 | Joe Mixon◦ provisional | CIN | RB | 278 | -0.08 | -0.08 | -0.13 – -0.04 |
| 43 | Austin Ekeler◦ provisional | LAC | RB | 132 | -0.08 | -0.08 | -0.13 – -0.03 |
| 44 | Myles Gaskin◦ provisional | MIA | RB | 36 | -0.07 | -0.08 | -0.13 – -0.03 |
| 45 | Spencer Ware◦ provisional | KC | RB | 17 | -0.07 | -0.08 | -0.13 – -0.03 |
| 46 | J.D. McKissic◦ provisional | DET | RB | 38 | -0.08 | -0.08 | -0.13 – -0.03 |
| 47 | Brian Hill◦ provisional | ATL | RB | 78 | -0.09 | -0.08 | -0.13 – -0.03 |
| 48 | Saquon Barkley◦ provisional | NYG | RB | 217 | -0.09 | -0.08 | -0.13 – -0.04 |
| 49 | Matt Breida◦ provisional | SF | RB | 123 | -0.09 | -0.08 | -0.13 – -0.03 |
| 50 | Justice Hill◦ provisional | BAL | RB | 58 | -0.10 | -0.08 | -0.13 – -0.03 |
| 51 | Ameer Abdullah◦ provisional | MIN | RB | 23 | -0.16 | -0.08 | -0.13 – -0.03 |
| 52 | Chris Carson◦ provisional | SEA | RB | 278 | -0.09 | -0.08 | -0.13 – -0.04 |
| 53 | Darren Sproles◦ provisional | PHI | RB | 18 | -0.21 | -0.08 | -0.14 – -0.03 |
| 54 | Kareem Hunt◦ provisional | CLE | RB | 43 | -0.14 | -0.08 | -0.14 – -0.03 |
| 55 | Melvin Gordon◦ provisional | LAC | RB | 162 | -0.10 | -0.08 | -0.13 – -0.04 |
| 56 | Sony Michel◦ provisional | NE | RB | 247 | -0.10 | -0.08 | -0.13 – -0.04 |
| 57 | Tarik Cohen◦ provisional | CHI | RB | 64 | -0.13 | -0.09 | -0.14 – -0.04 |
| 58 | Ty Johnson◦ provisional | DET | RB | 63 | -0.13 | -0.09 | -0.14 – -0.04 |
| 59 | Mark Walton◦ provisional | MIA | RB | 53 | -0.15 | -0.09 | -0.14 – -0.04 |
| 60 | Tevin Coleman◦ provisional | SF | RB | 137 | -0.11 | -0.09 | -0.13 – -0.04 |
| 61 | T.J. Yeldon◦ provisional | BUF | RB | 17 | -0.30 | -0.09 | -0.14 – -0.03 |
| 62 | Benny Snell◦ provisional | PIT | RB | 108 | -0.12 | -0.09 | -0.13 – -0.04 |
| 63 | Chris Thompson◦ provisional | WAS | RB | 37 | -0.20 | -0.09 | -0.14 – -0.04 |
| 64 | Damien Williams◦ provisional | KC | RB | 111 | -0.12 | -0.09 | -0.14 – -0.04 |
| 65 | Alexander Mattison◦ provisional | MIN | RB | 100 | -0.13 | -0.09 | -0.14 – -0.04 |
| 66 | Malcolm Brown◦ provisional | LA | RB | 69 | -0.15 | -0.09 | -0.14 – -0.04 |
| 67 | Elijhaa Penny◦ provisional | NYG | RB | 15 | -0.38 | -0.09 | -0.14 – -0.04 |
| 68 | Jalen Richard◦ provisional | LV | RB | 39 | -0.20 | -0.09 | -0.14 – -0.04 |
| 69 | Alvin Kamara◦ provisional | NO | RB | 171 | -0.11 | -0.09 | -0.13 – -0.04 |
| 70 | Duke Johnson◦ provisional | HOU | RB | 83 | -0.14 | -0.09 | -0.14 – -0.04 |
| 71 | Bilal Powell◦ provisional | NYJ | RB | 59 | -0.17 | -0.09 | -0.14 – -0.04 |
| 72 | Tra Carson◦ provisional | DET | RB | 18 | -0.35 | -0.09 | -0.14 – -0.04 |
| 73 | Trey Edmunds◦ provisional | PIT | RB | 22 | -0.30 | -0.09 | -0.14 – -0.04 |
| 74 | Bo Scarbrough◦ provisional | DET | RB | 89 | -0.15 | -0.09 | -0.14 – -0.04 |
| 75 | C.J. Anderson◦ provisional | DET | RB | 16 | -0.44 | -0.09 | -0.14 – -0.04 |
| 76 | David Johnson◦ provisional | ARI | RB | 94 | -0.15 | -0.09 | -0.14 – -0.04 |
| 77 | Wayne Gallman◦ provisional | NYG | RB | 29 | -0.28 | -0.09 | -0.14 – -0.04 |
| 78 | Royce Freeman◦ provisional | DEN | RB | 132 | -0.13 | -0.09 | -0.14 – -0.04 |
| 79 | Wendell Smallwood◦ provisional | WAS | RB | 22 | -0.35 | -0.09 | -0.14 – -0.04 |
| 80 | Ryquell Armstead◦ provisional | JAX | RB | 35 | -0.26 | -0.09 | -0.14 – -0.04 |
| 81 | Darrell Henderson◦ provisional | LA | RB | 39 | -0.25 | -0.09 | -0.14 – -0.04 |
| 82 | Darrel Williams◦ provisional | KC | RB | 41 | -0.25 | -0.09 | -0.14 – -0.04 |
| 83 | Adrian Peterson◦ provisional | WAS | RB | 211 | -0.12 | -0.09 | -0.14 – -0.04 |
| 84 | C.J. Prosise◦ provisional | SEA | RB | 24 | -0.37 | -0.09 | -0.14 – -0.04 |
| 85 | DeAndre Washington◦ provisional | LV | RB | 108 | -0.15 | -0.09 | -0.14 – -0.04 |
| 86 | Todd Gurley◦ provisional | LA | RB | 224 | -0.12 | -0.09 | -0.14 – -0.04 |
| 87 | Jon Hilliman◦ provisional | NYG | RB | 30 | -0.34 | -0.09 | -0.14 – -0.04 |
| 88 | Dion Lewis◦ provisional | TEN | RB | 54 | -0.25 | -0.09 | -0.14 – -0.04 |
| 89 | Ronald Jones◦ provisional | TB | RB | 172 | -0.14 | -0.09 | -0.14 – -0.04 |
| 90 | Jaylen Samuels◦ provisional | PIT | RB | 66 | -0.23 | -0.09 | -0.14 – -0.04 |
| 91 | James White◦ provisional | NE | RB | 69 | -0.23 | -0.09 | -0.14 – -0.04 |
| 92 | Kerryon Johnson◦ provisional | DET | RB | 113 | -0.18 | -0.09 | -0.14 – -0.04 |
| 93 | Giovani Bernard◦ provisional | CIN | RB | 53 | -0.29 | -0.09 | -0.14 – -0.04 |
| 94 | James Conner◦ provisional | PIT | RB | 116 | -0.21 | -0.10 | -0.15 – -0.05 |
| 95 | Kalen Ballage◦ provisional | MIA | RB | 73 | -0.28 | -0.10 | -0.15 – -0.05 |
| 96 | Patrick Laird◦ provisional | MIA | RB | 62 | -0.35 | -0.10 | -0.15 – -0.05 |
| 97 | Frank Gore◦ provisional | BUF | RB | 166 | -0.20 | -0.10 | -0.15 – -0.05 |
| 98 | David Montgomery◦ provisional | CHI | RB | 242 | -0.17 | -0.10 | -0.15 – -0.06 |
| 99 | Peyton Barber◦ provisional | TB | RB | 155 | -0.21 | -0.10 | -0.15 – -0.05 |
| 100 | Le'Veon Bell◦ provisional | NYJ | RB | 245 | -0.19 | -0.11 | -0.15 – -0.06 |
| 101 | Devonta Freeman◦ provisional | ATL | RB | 184 | -0.22 | -0.11 | -0.15 – -0.06 |
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).