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 · 2016
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
- 183
- 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 · 2016 · full board
| # | Player | Team | Pos | carrys | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Mike Gillislee◦ provisional | BUF | RB | 101 | +0.23 | +0.04 | -0.05 – +0.12 |
| 2 | LeSean McCoy | BUF | RB | 235 | +0.06 | +0.00 | -0.07 – +0.08 |
| 3 | Ezekiel Elliott | DAL | RB | 322 | +0.04 | -0.00 | -0.07 – +0.06 |
| 4 | Jay Ajayi | MIA | RB | 260 | +0.03 | -0.01 | -0.08 – +0.06 |
| 5 | Robert Turbin◦ provisional | IND | RB | 47 | +0.21 | -0.02 | -0.11 – +0.08 |
| 6 | Bilal Powell◦ provisional | NYJ | RB | 131 | +0.06 | -0.02 | -0.10 – +0.06 |
| 7 | Le'Veon Bell | PIT | RB | 261 | +0.02 | -0.02 | -0.09 – +0.05 |
| 8 | Rex Burkhead◦ provisional | CIN | RB | 74 | +0.11 | -0.02 | -0.11 – +0.07 |
| 9 | Devonta Freeman | ATL | RB | 227 | +0.02 | -0.02 | -0.09 – +0.05 |
| 10 | Kenneth Dixon◦ provisional | BAL | RB | 88 | +0.08 | -0.02 | -0.11 – +0.06 |
| 11 | Kerwynn Williams◦ provisional | ARI | RB | 18 | +0.39 | -0.03 | -0.14 – +0.07 |
| 12 | Jordan Howard | CHI | RB | 252 | -0.00 | -0.03 | -0.10 – +0.04 |
| 13 | Chris Thompson◦ provisional | WAS | RB | 69 | +0.07 | -0.03 | -0.13 – +0.06 |
| 14 | Kenyan Drake◦ provisional | MIA | RB | 33 | +0.16 | -0.04 | -0.14 – +0.06 |
| 15 | Tevin Coleman◦ provisional | ATL | RB | 118 | +0.01 | -0.04 | -0.12 – +0.04 |
| 16 | Jalen Richard◦ provisional | LV | RB | 83 | +0.03 | -0.04 | -0.13 – +0.05 |
| 17 | Mark Ingram | NO | RB | 208 | -0.02 | -0.05 | -0.12 – +0.03 |
| 18 | Eddie Lacy◦ provisional | GB | RB | 71 | +0.03 | -0.05 | -0.14 – +0.05 |
| 19 | John Kuhn◦ provisional | NO | RB | 18 | +0.24 | -0.05 | -0.15 – +0.06 |
| 20 | Dion Lewis◦ provisional | NE | RB | 64 | +0.03 | -0.05 | -0.14 – +0.05 |
| 21 | Derrick Henry◦ provisional | TEN | RB | 110 | -0.00 | -0.05 | -0.13 – +0.04 |
| 22 | Tim Hightower◦ provisional | NO | RB | 133 | -0.02 | -0.05 | -0.13 – +0.03 |
| 23 | Latavius Murray | LV | RB | 195 | -0.03 | -0.05 | -0.12 – +0.03 |
| 24 | Danny Woodhead◦ provisional | LAC | RB | 19 | +0.19 | -0.05 | -0.15 – +0.05 |
| 25 | DeAndre Washington◦ provisional | LV | RB | 87 | +0.00 | -0.05 | -0.14 – +0.04 |
| 26 | Jeremy Hill | CIN | RB | 222 | -0.03 | -0.05 | -0.12 – +0.02 |
| 27 | Andre Williams◦ provisional | LAC | RB | 18 | +0.16 | -0.05 | -0.16 – +0.05 |
| 28 | Benny Cunningham◦ provisional | LA | RB | 21 | +0.12 | -0.05 | -0.16 – +0.05 |
| 29 | C.J. Prosise◦ provisional | SEA | RB | 30 | +0.06 | -0.06 | -0.16 – +0.04 |
| 30 | DeMarco Murray | TEN | RB | 293 | -0.04 | -0.06 | -0.12 – +0.01 |
| 31 | Jacquizz Rodgers◦ provisional | TB | RB | 129 | -0.03 | -0.06 | -0.14 – +0.03 |
| 32 | Darren Sproles◦ provisional | PHI | RB | 94 | -0.03 | -0.06 | -0.15 – +0.03 |
| 33 | Rob Kelley◦ provisional | WAS | RB | 168 | -0.04 | -0.06 | -0.14 – +0.02 |
| 34 | Corey Grant◦ provisional | JAX | RB | 32 | +0.03 | -0.06 | -0.16 – +0.04 |
| 35 | Ameer Abdullah◦ provisional | DET | RB | 18 | +0.07 | -0.06 | -0.16 – +0.04 |
| 36 | Kenjon Barner◦ provisional | PHI | RB | 27 | +0.02 | -0.06 | -0.16 – +0.04 |
| 37 | Ryan Mathews◦ provisional | PHI | RB | 157 | -0.06 | -0.07 | -0.15 – +0.01 |
| 38 | Alfred Morris◦ provisional | DAL | RB | 69 | -0.05 | -0.07 | -0.16 – +0.03 |
| 39 | Kapri Bibbs◦ provisional | DEN | RB | 29 | -0.02 | -0.07 | -0.17 – +0.03 |
| 40 | Aaron Ripkowski◦ provisional | GB | RB | 34 | -0.03 | -0.07 | -0.17 – +0.03 |
| 41 | LeGarrette Blount | NE | RB | 299 | -0.06 | -0.07 | -0.13 – -0.00 |
| 42 | David Johnson | ARI | RB | 293 | -0.06 | -0.07 | -0.14 – -0.00 |
| 43 | Paul Perkins◦ provisional | NYG | RB | 112 | -0.06 | -0.07 | -0.15 – +0.01 |
| 44 | Terron Ward◦ provisional | ATL | RB | 31 | -0.05 | -0.07 | -0.17 – +0.03 |
| 45 | Chris Johnson◦ provisional | ARI | RB | 25 | -0.05 | -0.07 | -0.17 – +0.03 |
| 46 | DeAngelo Williams◦ provisional | PIT | RB | 98 | -0.07 | -0.07 | -0.16 – +0.01 |
| 47 | Darren McFadden◦ provisional | DAL | RB | 24 | -0.06 | -0.07 | -0.17 – +0.03 |
| 48 | Cameron Artis-Payne◦ provisional | CAR | RB | 36 | -0.07 | -0.07 | -0.17 – +0.02 |
| 49 | James White◦ provisional | NE | RB | 39 | -0.07 | -0.07 | -0.17 – +0.02 |
| 50 | Akeem Hunt◦ provisional | HOU | RB | 20 | -0.07 | -0.07 | -0.18 – +0.03 |
| 51 | Orleans Darkwa◦ provisional | NYG | RB | 30 | -0.07 | -0.07 | -0.17 – +0.03 |
| 52 | Christine Michael◦ provisional | GB | RB | 148 | -0.08 | -0.07 | -0.16 – +0.01 |
| 53 | Jonathan Grimes◦ provisional | HOU | RB | 23 | -0.08 | -0.08 | -0.18 – +0.03 |
| 54 | Ka'Deem Carey◦ provisional | CHI | RB | 32 | -0.08 | -0.08 | -0.18 – +0.02 |
| 55 | Matt Jones◦ provisional | WAS | RB | 99 | -0.08 | -0.08 | -0.16 – +0.01 |
| 56 | Jonathan Stewart | CAR | RB | 218 | -0.08 | -0.08 | -0.15 – -0.00 |
| 57 | Carlos Hyde | SF | RB | 218 | -0.08 | -0.08 | -0.15 – -0.00 |
| 58 | Peyton Barber◦ provisional | TB | RB | 55 | -0.09 | -0.08 | -0.17 – +0.02 |
| 59 | Theo Riddick◦ provisional | DET | RB | 92 | -0.08 | -0.08 | -0.17 – +0.01 |
| 60 | Melvin Gordon | LAC | RB | 254 | -0.08 | -0.08 | -0.15 – -0.01 |
| 61 | Alex Collins◦ provisional | SEA | RB | 31 | -0.11 | -0.08 | -0.18 – +0.02 |
| 62 | Byron Marshall◦ provisional | PHI | RB | 19 | -0.14 | -0.08 | -0.18 – +0.02 |
| 63 | Matt Forte | NYJ | RB | 218 | -0.09 | -0.08 | -0.15 – -0.01 |
| 64 | Shane Vereen◦ provisional | NYG | RB | 33 | -0.12 | -0.08 | -0.18 – +0.02 |
| 65 | Alfred Blue◦ provisional | HOU | RB | 100 | -0.10 | -0.08 | -0.17 – +0.00 |
| 66 | Jamize Olawale◦ provisional | LV | RB | 17 | -0.18 | -0.08 | -0.19 – +0.02 |
| 67 | Bobby Rainey◦ provisional | NYG | RB | 17 | -0.19 | -0.08 | -0.19 – +0.02 |
| 68 | Frank Gore | IND | RB | 263 | -0.09 | -0.09 | -0.15 – -0.02 |
| 69 | Wendell Smallwood◦ provisional | PHI | RB | 77 | -0.11 | -0.09 | -0.18 – +0.01 |
| 70 | Denard Robinson◦ provisional | JAX | RB | 41 | -0.14 | -0.09 | -0.18 – +0.01 |
| 71 | Giovani Bernard◦ provisional | CIN | RB | 91 | -0.11 | -0.09 | -0.17 – +0.00 |
| 72 | Isaiah Crowell | CLE | RB | 198 | -0.10 | -0.09 | -0.16 – -0.01 |
| 73 | Damien Williams◦ provisional | MIA | RB | 35 | -0.17 | -0.09 | -0.19 – +0.01 |
| 74 | Fozzy Whittaker◦ provisional | CAR | RB | 57 | -0.14 | -0.09 | -0.18 – +0.00 |
| 75 | Andre Ellington◦ provisional | ARI | RB | 34 | -0.19 | -0.09 | -0.19 – +0.01 |
| 76 | Mike Tolbert◦ provisional | CAR | RB | 35 | -0.19 | -0.09 | -0.19 – +0.01 |
| 77 | C.J. Anderson◦ provisional | DEN | RB | 110 | -0.13 | -0.10 | -0.18 – -0.01 |
| 78 | Terrance West | BAL | RB | 193 | -0.12 | -0.10 | -0.17 – -0.02 |
| 79 | Duke Johnson◦ provisional | CLE | RB | 73 | -0.17 | -0.10 | -0.19 – -0.01 |
| 80 | Spencer Ware | KC | RB | 214 | -0.12 | -0.10 | -0.17 – -0.03 |
| 81 | Ronnie Hillman◦ provisional | LAC | RB | 41 | -0.23 | -0.10 | -0.20 – -0.01 |
| 82 | Zach Zenner◦ provisional | DET | RB | 88 | -0.17 | -0.10 | -0.19 – -0.02 |
| 83 | Kenneth Farrow◦ provisional | LAC | RB | 60 | -0.19 | -0.10 | -0.20 – -0.01 |
| 84 | Shaun Draughn◦ provisional | SF | RB | 74 | -0.19 | -0.11 | -0.20 – -0.02 |
| 85 | Knile Davis◦ provisional | KC | RB | 18 | -0.47 | -0.11 | -0.21 – -0.01 |
| 86 | Thomas Rawls◦ provisional | SEA | RB | 109 | -0.17 | -0.11 | -0.20 – -0.03 |
| 87 | Charcandrick West◦ provisional | KC | RB | 88 | -0.19 | -0.11 | -0.20 – -0.02 |
| 88 | Arian Foster◦ provisional | MIA | RB | 22 | -0.43 | -0.11 | -0.21 – -0.01 |
| 89 | Lamar Miller | HOU | RB | 268 | -0.14 | -0.11 | -0.18 – -0.05 |
| 90 | Devontae Booker◦ provisional | DEN | RB | 174 | -0.16 | -0.12 | -0.19 – -0.04 |
| 91 | Charles Sims◦ provisional | TB | RB | 51 | -0.26 | -0.12 | -0.21 – -0.02 |
| 92 | Mike Davis◦ provisional | SF | RB | 19 | -0.55 | -0.12 | -0.22 – -0.02 |
| 93 | T.J. Yeldon◦ provisional | JAX | RB | 130 | -0.18 | -0.12 | -0.20 – -0.04 |
| 94 | Rashad Jennings◦ provisional | NYG | RB | 180 | -0.18 | -0.12 | -0.20 – -0.05 |
| 95 | Malcolm Brown◦ provisional | LA | RB | 18 | -0.64 | -0.13 | -0.23 – -0.02 |
| 96 | Jeremy Langford◦ provisional | CHI | RB | 62 | -0.29 | -0.13 | -0.22 – -0.04 |
| 97 | Jonathan Williams◦ provisional | BUF | RB | 27 | -0.51 | -0.13 | -0.23 – -0.03 |
| 98 | Dwayne Washington◦ provisional | DET | RB | 90 | -0.24 | -0.13 | -0.22 – -0.04 |
| 99 | Matt Asiata◦ provisional | MIN | RB | 121 | -0.22 | -0.13 | -0.22 – -0.05 |
| 100 | Jerick McKinnon◦ provisional | MIN | RB | 161 | -0.20 | -0.13 | -0.21 – -0.05 |
| 101 | DuJuan Harris◦ provisional | SF | RB | 38 | -0.42 | -0.13 | -0.23 – -0.04 |
| 102 | Josh Ferguson◦ provisional | IND | RB | 15 | -0.86 | -0.13 | -0.24 – -0.03 |
| 103 | Adrian Peterson◦ provisional | MIN | RB | 37 | -0.49 | -0.14 | -0.24 – -0.05 |
| 104 | Todd Gurley | LA | RB | 278 | -0.19 | -0.15 | -0.21 – -0.08 |
| 105 | James Starks◦ provisional | GB | RB | 64 | -0.37 | -0.15 | -0.24 – -0.06 |
| 106 | Doug Martin◦ provisional | TB | RB | 144 | -0.25 | -0.15 | -0.23 – -0.07 |
| 107 | Justin Forsett◦ provisional | DEN | RB | 87 | -0.32 | -0.15 | -0.24 – -0.07 |
| 108 | Chris Ivory◦ provisional | JAX | RB | 117 | -0.29 | -0.16 | -0.24 – -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).