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.
Yards per carry · 2022
Mean rushing yards per carry. Heavy-tailed (one long run moves it); the band reflects that.
- Beats raw by
- 18.1%
- lower out-of-sample error
- RMSE raw → shrunk
- 1.04 → 0.85
- odd vs. even weeks
- Split-half reliability
- 0.23
- how repeatable the raw stat is
- Stabilizes at
- 524
- 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.
Yards per carry · 2022 · full board
| # | Player | Team | Pos | carrys | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Khalil Herbert◦ provisional | CHI | RB | 129 | 5.67 | 4.70 | 4.30 – 5.10 |
| 2 | Aaron Jones◦ provisional | GB | RB | 213 | 5.26 | 4.69 | 4.31 – 5.07 |
| 3 | Nick Chubb◦ provisional | CLE | RB | 303 | 5.04 | 4.67 | 4.32 – 5.03 |
| 4 | Tony Pollard◦ provisional | DAL | RB | 193 | 5.22 | 4.66 | 4.28 – 5.05 |
| 5 | Travis Etienne◦ provisional | JAX | RB | 221 | 5.10 | 4.65 | 4.27 – 5.03 |
| 6 | James Cook◦ provisional | BUF | RB | 89 | 5.70 | 4.64 | 4.22 – 5.05 |
| 7 | J.K. Dobbins◦ provisional | BAL | RB | 92 | 5.65 | 4.64 | 4.22 – 5.05 |
| 8 | Breece Hall◦ provisional | NYJ | RB | 80 | 5.79 | 4.64 | 4.22 – 5.05 |
| 9 | Rashaad Penny◦ provisional | SEA | RB | 57 | 6.07 | 4.62 | 4.19 – 5.04 |
| 10 | D'Andre Swift◦ provisional | DET | RB | 100 | 5.44 | 4.62 | 4.21 – 5.03 |
| 11 | Josh Jacobs◦ provisional | LV | RB | 341 | 4.85 | 4.61 | 4.26 – 4.96 |
| 12 | Miles Sanders◦ provisional | PHI | RB | 260 | 4.88 | 4.60 | 4.23 – 4.97 |
| 13 | Elijah Mitchell◦ provisional | SF | RB | 45 | 6.20 | 4.60 | 4.17 – 5.03 |
| 14 | Tyler Allgeier◦ provisional | ATL | RB | 211 | 4.91 | 4.59 | 4.21 – 4.97 |
| 15 | Raheem Mostert◦ provisional | MIA | RB | 181 | 4.92 | 4.58 | 4.19 – 4.96 |
| 16 | Jordan Mason◦ provisional | SF | RB | 43 | 6.00 | 4.58 | 4.15 – 5.01 |
| 17 | Rhamondre Stevenson◦ provisional | NE | RB | 210 | 4.86 | 4.57 | 4.19 – 4.95 |
| 18 | Jeff Wilson◦ provisional | MIA | RB | 176 | 4.89 | 4.57 | 4.18 – 4.95 |
| 19 | Isiah Pacheco◦ provisional | KC | RB | 170 | 4.88 | 4.56 | 4.17 – 4.95 |
| 20 | Dontrell Hilliard◦ provisional | TEN | RB | 22 | 6.59 | 4.55 | 4.11 – 4.98 |
| 21 | Cordarrelle Patterson◦ provisional | ATL | RB | 144 | 4.83 | 4.54 | 4.14 – 4.94 |
| 22 | Justice Hill◦ provisional | BAL | RB | 49 | 5.35 | 4.54 | 4.11 – 4.96 |
| 23 | Gus Edwards◦ provisional | BAL | RB | 87 | 4.98 | 4.53 | 4.12 – 4.95 |
| 24 | Chuba Hubbard◦ provisional | CAR | RB | 95 | 4.91 | 4.53 | 4.12 – 4.94 |
| 25 | Zack Moss◦ provisional | IND | RB | 93 | 4.90 | 4.53 | 4.11 – 4.94 |
| 26 | Jaylen Warren◦ provisional | PIT | RB | 77 | 4.92 | 4.52 | 4.10 – 4.94 |
| 27 | Christian McCaffrey◦ provisional | SF | RB | 246 | 4.63 | 4.51 | 4.14 – 4.88 |
| 28 | DeeJay Dallas◦ provisional | SEA | RB | 35 | 5.31 | 4.51 | 4.08 – 4.95 |
| 29 | Ty Johnson◦ provisional | NYJ | RB | 30 | 5.33 | 4.51 | 4.07 – 4.94 |
| 30 | Caleb Huntley◦ provisional | ATL | RB | 76 | 4.82 | 4.50 | 4.09 – 4.92 |
| 31 | Kenneth Walker III◦ provisional | SEA | RB | 228 | 4.61 | 4.50 | 4.13 – 4.88 |
| 32 | Devin Singletary◦ provisional | BUF | RB | 177 | 4.63 | 4.50 | 4.11 – 4.89 |
| 33 | Marlon Mack◦ provisional | DEN | RB | 16 | 5.25 | 4.48 | 4.04 – 4.92 |
| 34 | Avery Williams◦ provisional | ATL | RB | 22 | 4.95 | 4.48 | 4.04 – 4.92 |
| 35 | Darrel Williams◦ provisional | ARI | RB | 21 | 4.86 | 4.47 | 4.04 – 4.91 |
| 36 | D'Onta Foreman◦ provisional | CAR | RB | 204 | 4.49 | 4.47 | 4.09 – 4.85 |
| 37 | Austin Ekeler◦ provisional | LAC | RB | 204 | 4.49 | 4.47 | 4.09 – 4.85 |
| 38 | Jonathan Taylor◦ provisional | IND | RB | 192 | 4.48 | 4.47 | 4.08 – 4.85 |
| 39 | Kenneth Gainwell◦ provisional | PHI | RB | 53 | 4.53 | 4.47 | 4.04 – 4.89 |
| 40 | Gary Brightwell◦ provisional | NYG | RB | 31 | 4.55 | 4.46 | 4.03 – 4.90 |
| 41 | Jaret Patterson◦ provisional | WAS | RB | 17 | 4.59 | 4.46 | 4.02 – 4.90 |
| 42 | Benny Snell◦ provisional | PIT | RB | 20 | 4.50 | 4.46 | 4.02 – 4.90 |
| 43 | Malcolm Brown◦ provisional | LA | RB | 18 | 4.50 | 4.46 | 4.02 – 4.90 |
| 44 | Craig Reynolds◦ provisional | DET | RB | 23 | 4.43 | 4.46 | 4.02 – 4.90 |
| 45 | Saquon Barkley◦ provisional | NYG | RB | 295 | 4.45 | 4.46 | 4.10 – 4.81 |
| 46 | Dalvin Cook◦ provisional | MIN | RB | 264 | 4.44 | 4.45 | 4.09 – 4.82 |
| 47 | J.D. McKissic◦ provisional | WAS | RB | 22 | 4.32 | 4.45 | 4.01 – 4.89 |
| 48 | Kenyan Drake◦ provisional | BAL | RB | 109 | 4.42 | 4.45 | 4.05 – 4.86 |
| 49 | Latavius Murray◦ provisional | DEN | RB | 172 | 4.43 | 4.45 | 4.06 – 4.84 |
| 50 | Mike Boone◦ provisional | DEN | RB | 24 | 4.25 | 4.45 | 4.01 – 4.89 |
| 51 | Javonte Williams◦ provisional | DEN | RB | 47 | 4.34 | 4.45 | 4.02 – 4.88 |
| 52 | Ronald Jones◦ provisional | KC | RB | 17 | 4.12 | 4.45 | 4.01 – 4.89 |
| 53 | Zamir White◦ provisional | LV | RB | 17 | 4.12 | 4.45 | 4.01 – 4.89 |
| 54 | Brandon Bolden◦ provisional | LV | RB | 17 | 4.00 | 4.45 | 4.00 – 4.89 |
| 55 | Malik Davis◦ provisional | DAL | RB | 38 | 4.24 | 4.44 | 4.01 – 4.88 |
| 56 | Damien Harris◦ provisional | NE | RB | 106 | 4.36 | 4.44 | 4.03 – 4.85 |
| 57 | JaMycal Hasty◦ provisional | JAX | RB | 46 | 4.22 | 4.44 | 4.01 – 4.87 |
| 58 | Travis Homer◦ provisional | SEA | RB | 19 | 3.89 | 4.44 | 4.00 – 4.88 |
| 59 | Derrick Henry◦ provisional | TEN | RB | 349 | 4.41 | 4.44 | 4.09 – 4.79 |
| 60 | Corey Clement◦ provisional | ARI | RB | 15 | 3.67 | 4.44 | 4.00 – 4.88 |
| 61 | Jonathan Williams◦ provisional | WAS | RB | 37 | 4.11 | 4.44 | 4.00 – 4.87 |
| 62 | Clyde Edwards-Helaire◦ provisional | KC | RB | 71 | 4.25 | 4.44 | 4.01 – 4.86 |
| 63 | Kyren Williams◦ provisional | LA | RB | 35 | 3.97 | 4.43 | 4.00 – 4.86 |
| 64 | Hassan Haskins◦ provisional | TEN | RB | 25 | 3.72 | 4.43 | 3.99 – 4.86 |
| 65 | Joshua Kelley◦ provisional | LAC | RB | 69 | 4.16 | 4.42 | 4.00 – 4.85 |
| 66 | Matt Breida◦ provisional | NYG | RB | 54 | 4.07 | 4.42 | 4.00 – 4.85 |
| 67 | Phillip Lindsay◦ provisional | IND | RB | 16 | 3.19 | 4.42 | 3.98 – 4.86 |
| 68 | Justin Jackson◦ provisional | DET | RB | 43 | 3.95 | 4.42 | 3.99 – 4.85 |
| 69 | Boston Scott◦ provisional | PHI | RB | 54 | 4.02 | 4.42 | 3.99 – 4.85 |
| 70 | Ke'Shawn Vaughn◦ provisional | TB | RB | 17 | 3.12 | 4.42 | 3.98 – 4.86 |
| 71 | Raheem Blackshear◦ provisional | CAR | RB | 23 | 3.35 | 4.41 | 3.97 – 4.85 |
| 72 | James Conner◦ provisional | ARI | RB | 183 | 4.27 | 4.41 | 4.03 – 4.80 |
| 73 | Darrell Henderson◦ provisional | LA | RB | 70 | 4.04 | 4.41 | 3.99 – 4.83 |
| 74 | Jerick McKinnon◦ provisional | KC | RB | 72 | 4.04 | 4.41 | 3.99 – 4.83 |
| 75 | Kevin Harris◦ provisional | NE | RB | 18 | 2.89 | 4.41 | 3.97 – 4.85 |
| 76 | Eno Benjamin◦ provisional | NO | RB | 78 | 4.04 | 4.41 | 3.99 – 4.82 |
| 77 | Samaje Perine◦ provisional | CIN | RB | 96 | 4.10 | 4.40 | 3.99 – 4.82 |
| 78 | Dameon Pierce◦ provisional | HOU | RB | 220 | 4.27 | 4.40 | 4.03 – 4.78 |
| 79 | Rex Burkhead◦ provisional | HOU | RB | 26 | 3.08 | 4.39 | 3.96 – 4.83 |
| 80 | Isaiah Spiller◦ provisional | LAC | RB | 18 | 2.28 | 4.39 | 3.95 – 4.83 |
| 81 | Cam Akers◦ provisional | LA | RB | 188 | 4.18 | 4.39 | 4.00 – 4.77 |
| 82 | Alexander Mattison◦ provisional | MIN | RB | 74 | 3.82 | 4.38 | 3.96 – 4.80 |
| 83 | AJ Dillon◦ provisional | GB | RB | 186 | 4.14 | 4.38 | 3.99 – 4.76 |
| 84 | Mark Ingram◦ provisional | NO | RB | 64 | 3.67 | 4.37 | 3.95 – 4.80 |
| 85 | Tyrion Davis-Price◦ provisional | SF | RB | 34 | 2.91 | 4.37 | 3.93 – 4.80 |
| 86 | Trestan Ebner◦ provisional | CHI | RB | 24 | 2.25 | 4.36 | 3.92 – 4.80 |
| 87 | Sony Michel◦ provisional | LAC | RB | 36 | 2.94 | 4.36 | 3.93 – 4.80 |
| 88 | Chase Edmonds◦ provisional | DEN | RB | 68 | 3.60 | 4.36 | 3.94 – 4.78 |
| 89 | James Robinson◦ provisional | NYJ | RB | 110 | 3.86 | 4.36 | 3.95 – 4.76 |
| 90 | Keaontay Ingram◦ provisional | ARI | RB | 27 | 2.22 | 4.35 | 3.91 – 4.79 |
| 91 | Deon Jackson◦ provisional | IND | RB | 68 | 3.47 | 4.35 | 3.92 – 4.77 |
| 92 | Royce Freeman◦ provisional | HOU | RB | 41 | 2.85 | 4.34 | 3.91 – 4.77 |
| 93 | Dare Ogunbowale◦ provisional | HOU | RB | 43 | 2.86 | 4.34 | 3.91 – 4.77 |
| 94 | Kareem Hunt◦ provisional | CLE | RB | 123 | 3.80 | 4.34 | 3.93 – 4.74 |
| 95 | Bam Knight◦ provisional | NYJ | RB | 85 | 3.53 | 4.33 | 3.91 – 4.75 |
| 96 | Alvin Kamara◦ provisional | NO | RB | 223 | 4.02 | 4.33 | 3.95 – 4.70 |
| 97 | David Montgomery◦ provisional | CHI | RB | 201 | 3.99 | 4.33 | 3.95 – 4.71 |
| 98 | Jamaal Williams◦ provisional | DET | RB | 263 | 4.06 | 4.33 | 3.96 – 4.69 |
| 99 | Nyheim Hines◦ provisional | BUF | RB | 24 | 1.38 | 4.32 | 3.89 – 4.76 |
| 100 | Melvin Gordon◦ provisional | DEN | RB | 90 | 3.53 | 4.32 | 3.91 – 4.74 |
| 101 | Rachaad White◦ provisional | TB | RB | 130 | 3.70 | 4.31 | 3.91 – 4.71 |
| 102 | Brian Robinson◦ provisional | WAS | RB | 205 | 3.89 | 4.30 | 3.92 – 4.68 |
| 103 | Michael Carter◦ provisional | NYJ | RB | 114 | 3.53 | 4.29 | 3.89 – 4.70 |
| 104 | Joe Mixon◦ provisional | CIN | RB | 210 | 3.88 | 4.29 | 3.91 – 4.67 |
| 105 | Antonio Gibson◦ provisional | WAS | RB | 149 | 3.66 | 4.28 | 3.89 – 4.68 |
| 106 | Ezekiel Elliott◦ provisional | DAL | RB | 231 | 3.79 | 4.26 | 3.88 – 4.63 |
| 107 | Najee Harris◦ provisional | PIT | RB | 272 | 3.80 | 4.23 | 3.87 – 4.60 |
| 108 | Leonard Fournette◦ provisional | TB | RB | 189 | 3.53 | 4.21 | 3.83 – 4.60 |
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).