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 · 2017
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
- 324
- 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 · 2017 · full board
| # | Player | Team | Pos | carrys | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Alvin Kamara◦ provisional | NO | RB | 121 | +0.25 | -0.00 | -0.07 – +0.07 |
| 2 | Dion Lewis◦ provisional | NE | RB | 180 | +0.10 | -0.03 | -0.09 – +0.04 |
| 3 | Kareem Hunt◦ provisional | KC | RB | 272 | +0.01 | -0.05 | -0.11 – +0.01 |
| 4 | Corey Grant◦ provisional | JAX | RB | 30 | +0.44 | -0.05 | -0.13 – +0.03 |
| 5 | Aaron Jones◦ provisional | GB | RB | 81 | +0.12 | -0.05 | -0.13 – +0.02 |
| 6 | Alex Collins◦ provisional | BAL | RB | 212 | -0.01 | -0.06 | -0.13 – +0.00 |
| 7 | Ezekiel Elliott◦ provisional | DAL | RB | 242 | -0.02 | -0.06 | -0.13 – -0.00 |
| 8 | Corey Clement◦ provisional | PHI | RB | 75 | +0.07 | -0.07 | -0.14 – +0.01 |
| 9 | Duke Johnson◦ provisional | CLE | RB | 82 | +0.05 | -0.07 | -0.14 – +0.01 |
| 10 | Rod Smith◦ provisional | DAL | RB | 55 | +0.10 | -0.07 | -0.14 – +0.01 |
| 11 | Mark Ingram◦ provisional | NO | RB | 230 | -0.03 | -0.07 | -0.13 – -0.01 |
| 12 | Alfred Morris◦ provisional | DAL | RB | 115 | +0.01 | -0.07 | -0.14 – +0.00 |
| 13 | Jamaal Williams◦ provisional | GB | RB | 153 | -0.01 | -0.07 | -0.14 – -0.00 |
| 14 | Todd Gurley◦ provisional | LA | RB | 279 | -0.04 | -0.07 | -0.13 – -0.01 |
| 15 | Matt Breida◦ provisional | SF | RB | 105 | +0.00 | -0.07 | -0.14 – -0.00 |
| 16 | Rex Burkhead◦ provisional | NE | RB | 64 | +0.03 | -0.08 | -0.15 – -0.00 |
| 17 | Le'Veon Bell◦ provisional | PIT | RB | 322 | -0.06 | -0.08 | -0.14 – -0.02 |
| 18 | Jordan Howard◦ provisional | CHI | RB | 276 | -0.05 | -0.08 | -0.14 – -0.02 |
| 19 | Elijhaa Penny◦ provisional | ARI | RB | 31 | +0.10 | -0.08 | -0.16 – -0.00 |
| 20 | Orleans Darkwa◦ provisional | NYG | RB | 172 | -0.05 | -0.08 | -0.15 – -0.01 |
| 21 | Peyton Barber◦ provisional | TB | RB | 108 | -0.03 | -0.08 | -0.15 – -0.01 |
| 22 | Leonard Fournette◦ provisional | JAX | RB | 269 | -0.06 | -0.08 | -0.14 – -0.02 |
| 23 | Devonta Freeman◦ provisional | ATL | RB | 196 | -0.06 | -0.08 | -0.15 – -0.02 |
| 24 | Austin Ekeler◦ provisional | LAC | RB | 47 | +0.00 | -0.08 | -0.16 – -0.01 |
| 25 | Wayne Gallman◦ provisional | NYG | RB | 111 | -0.05 | -0.09 | -0.16 – -0.01 |
| 26 | Tion Green◦ provisional | DET | RB | 42 | -0.00 | -0.09 | -0.16 – -0.01 |
| 27 | Cameron Artis-Payne◦ provisional | CAR | RB | 18 | +0.09 | -0.09 | -0.17 – -0.01 |
| 28 | Marshawn Lynch◦ provisional | LV | RB | 207 | -0.07 | -0.09 | -0.15 – -0.02 |
| 29 | Devontae Booker◦ provisional | DEN | RB | 79 | -0.06 | -0.09 | -0.16 – -0.02 |
| 30 | James Conner◦ provisional | PIT | RB | 32 | -0.01 | -0.09 | -0.17 – -0.01 |
| 31 | Javorius Allen◦ provisional | BAL | RB | 153 | -0.07 | -0.09 | -0.16 – -0.02 |
| 32 | Melvin Gordon◦ provisional | LAC | RB | 284 | -0.08 | -0.09 | -0.15 – -0.03 |
| 33 | Derrick Henry◦ provisional | TEN | RB | 176 | -0.08 | -0.09 | -0.16 – -0.02 |
| 34 | Travaris Cadet◦ provisional | BUF | RB | 23 | -0.02 | -0.09 | -0.17 – -0.01 |
| 35 | Robert Turbin◦ provisional | IND | RB | 23 | -0.04 | -0.09 | -0.17 – -0.01 |
| 36 | Charles Sims◦ provisional | TB | RB | 22 | -0.04 | -0.09 | -0.17 – -0.01 |
| 37 | T.J. Yeldon◦ provisional | JAX | RB | 49 | -0.07 | -0.09 | -0.17 – -0.02 |
| 38 | Latavius Murray◦ provisional | MIN | RB | 216 | -0.09 | -0.09 | -0.16 – -0.03 |
| 39 | Dalvin Cook◦ provisional | MIN | RB | 74 | -0.08 | -0.09 | -0.17 – -0.02 |
| 40 | Frank Gore◦ provisional | IND | RB | 261 | -0.09 | -0.09 | -0.16 – -0.03 |
| 41 | Charcandrick West◦ provisional | KC | RB | 18 | -0.06 | -0.09 | -0.18 – -0.01 |
| 42 | J.D. McKissic◦ provisional | SEA | RB | 46 | -0.08 | -0.09 | -0.17 – -0.02 |
| 43 | Stevan Ridley◦ provisional | PIT | RB | 26 | -0.07 | -0.10 | -0.17 – -0.02 |
| 44 | Chris Carson◦ provisional | SEA | RB | 49 | -0.09 | -0.10 | -0.17 – -0.02 |
| 45 | Giovani Bernard◦ provisional | CIN | RB | 105 | -0.09 | -0.10 | -0.17 – -0.02 |
| 46 | Kenyan Drake◦ provisional | MIA | RB | 134 | -0.09 | -0.10 | -0.17 – -0.03 |
| 47 | Kapri Bibbs◦ provisional | WAS | RB | 21 | -0.10 | -0.10 | -0.18 – -0.02 |
| 48 | C.J. Anderson◦ provisional | DEN | RB | 245 | -0.10 | -0.10 | -0.16 – -0.04 |
| 49 | Marlon Mack◦ provisional | IND | RB | 93 | -0.10 | -0.10 | -0.17 – -0.02 |
| 50 | Bilal Powell◦ provisional | NYJ | RB | 178 | -0.10 | -0.10 | -0.16 – -0.03 |
| 51 | Darren Sproles◦ provisional | PHI | RB | 15 | -0.14 | -0.10 | -0.18 – -0.02 |
| 52 | Jeremy Hill◦ provisional | CIN | RB | 37 | -0.12 | -0.10 | -0.18 – -0.02 |
| 53 | Alfred Blue◦ provisional | HOU | RB | 71 | -0.11 | -0.10 | -0.17 – -0.03 |
| 54 | Christian McCaffrey◦ provisional | CAR | RB | 117 | -0.11 | -0.10 | -0.17 – -0.03 |
| 55 | Chris Thompson◦ provisional | WAS | RB | 64 | -0.12 | -0.10 | -0.18 – -0.03 |
| 56 | Joe Mixon◦ provisional | CIN | RB | 178 | -0.11 | -0.10 | -0.17 – -0.03 |
| 57 | Kenjon Barner◦ provisional | PHI | RB | 16 | -0.19 | -0.10 | -0.18 – -0.02 |
| 58 | Rob Kelley◦ provisional | WAS | RB | 62 | -0.13 | -0.10 | -0.18 – -0.03 |
| 59 | Jalen Richard◦ provisional | LV | RB | 56 | -0.14 | -0.10 | -0.18 – -0.03 |
| 60 | Jay Ajayi◦ provisional | PHI | RB | 208 | -0.11 | -0.10 | -0.17 – -0.04 |
| 61 | Jacquizz Rodgers◦ provisional | TB | RB | 64 | -0.14 | -0.10 | -0.18 – -0.03 |
| 62 | Malcolm Brown◦ provisional | LA | RB | 63 | -0.14 | -0.10 | -0.18 – -0.03 |
| 63 | Tevin Coleman◦ provisional | ATL | RB | 156 | -0.12 | -0.10 | -0.17 – -0.04 |
| 64 | James White◦ provisional | NE | RB | 43 | -0.16 | -0.10 | -0.18 – -0.03 |
| 65 | Andre Ellington◦ provisional | HOU | RB | 20 | -0.24 | -0.11 | -0.19 – -0.03 |
| 66 | D'Onta Foreman◦ provisional | HOU | RB | 78 | -0.14 | -0.11 | -0.18 – -0.03 |
| 67 | Tarik Cohen◦ provisional | CHI | RB | 87 | -0.14 | -0.11 | -0.18 – -0.03 |
| 68 | Lamar Miller◦ provisional | HOU | RB | 238 | -0.12 | -0.11 | -0.17 – -0.04 |
| 69 | Carlos Hyde◦ provisional | SF | RB | 240 | -0.12 | -0.11 | -0.17 – -0.04 |
| 70 | DeAndre Washington◦ provisional | LV | RB | 57 | -0.18 | -0.11 | -0.19 – -0.03 |
| 71 | Wendell Smallwood◦ provisional | PHI | RB | 47 | -0.19 | -0.11 | -0.19 – -0.03 |
| 72 | Branden Oliver◦ provisional | LAC | RB | 35 | -0.23 | -0.11 | -0.19 – -0.03 |
| 73 | LeGarrette Blount◦ provisional | PHI | RB | 174 | -0.13 | -0.11 | -0.18 – -0.04 |
| 74 | Mike Gillislee◦ provisional | NE | RB | 104 | -0.15 | -0.11 | -0.18 – -0.04 |
| 75 | Terrance West◦ provisional | BAL | RB | 40 | -0.23 | -0.11 | -0.19 – -0.03 |
| 76 | Kerwynn Williams◦ provisional | ARI | RB | 120 | -0.15 | -0.11 | -0.18 – -0.04 |
| 77 | Isaiah Crowell◦ provisional | CLE | RB | 207 | -0.14 | -0.11 | -0.18 – -0.05 |
| 78 | Elijah McGuire◦ provisional | NYJ | RB | 88 | -0.18 | -0.11 | -0.19 – -0.04 |
| 79 | Mike Tolbert◦ provisional | BUF | RB | 66 | -0.20 | -0.12 | -0.19 – -0.04 |
| 80 | Terron Ward◦ provisional | ATL | RB | 30 | -0.31 | -0.12 | -0.19 – -0.04 |
| 81 | Jamaal Charles◦ provisional | DEN | RB | 69 | -0.20 | -0.12 | -0.19 – -0.04 |
| 82 | Chris Johnson◦ provisional | ARI | RB | 45 | -0.26 | -0.12 | -0.19 – -0.04 |
| 83 | LeSean McCoy◦ provisional | BUF | RB | 287 | -0.14 | -0.12 | -0.18 – -0.06 |
| 84 | Dwayne Washington◦ provisional | DET | RB | 20 | -0.45 | -0.12 | -0.20 – -0.04 |
| 85 | Matt Forte◦ provisional | NYJ | RB | 103 | -0.18 | -0.12 | -0.19 – -0.05 |
| 86 | Theo Riddick◦ provisional | DET | RB | 84 | -0.21 | -0.12 | -0.19 – -0.05 |
| 87 | Paul Perkins◦ provisional | NYG | RB | 41 | -0.31 | -0.12 | -0.20 – -0.04 |
| 88 | Shane Vereen◦ provisional | NYG | RB | 45 | -0.30 | -0.12 | -0.20 – -0.04 |
| 89 | DeMarco Murray◦ provisional | TEN | RB | 184 | -0.17 | -0.12 | -0.19 – -0.06 |
| 90 | Damien Williams◦ provisional | MIA | RB | 46 | -0.32 | -0.13 | -0.20 – -0.05 |
| 91 | Mike Davis◦ provisional | SEA | RB | 68 | -0.29 | -0.13 | -0.21 – -0.06 |
| 92 | Eddie Lacy◦ provisional | SEA | RB | 69 | -0.29 | -0.13 | -0.21 – -0.06 |
| 93 | Doug Martin◦ provisional | TB | RB | 139 | -0.21 | -0.13 | -0.20 – -0.06 |
| 94 | Chris Ivory◦ provisional | JAX | RB | 112 | -0.24 | -0.13 | -0.21 – -0.06 |
| 95 | Jonathan Stewart◦ provisional | CAR | RB | 198 | -0.20 | -0.14 | -0.20 – -0.07 |
| 96 | Samaje Perine◦ provisional | WAS | RB | 175 | -0.21 | -0.14 | -0.20 – -0.07 |
| 97 | Ameer Abdullah◦ provisional | DET | RB | 165 | -0.22 | -0.14 | -0.21 – -0.07 |
| 98 | Thomas Rawls◦ provisional | SEA | RB | 58 | -0.39 | -0.14 | -0.22 – -0.07 |
| 99 | Jerick McKinnon◦ provisional | MIN | RB | 151 | -0.24 | -0.14 | -0.21 – -0.07 |
| 100 | Adrian Peterson◦ provisional | ARI | RB | 156 | -0.26 | -0.15 | -0.22 – -0.08 |
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).