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 · 2024
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
- 165
- 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 · 2024 · full board
| # | Player | Team | Pos | carrys | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Derrick Henry | BAL | RB | 325 | 5.91 | 5.39 | 4.93 – 5.86 |
| 2 | Saquon Barkley | PHI | RB | 348 | 5.78 | 5.33 | 4.87 – 5.78 |
| 3 | Jahmyr Gibbs | DET | RB | 250 | 5.65 | 5.14 | 4.64 – 5.65 |
| 4 | Emari Demercado◦ provisional | ARI | RB | 24 | 9.29 | 5.00 | 4.25 – 5.75 |
| 5 | Bucky Irving | TB | RB | 207 | 5.42 | 4.96 | 4.42 – 5.49 |
| 6 | Dameon Pierce◦ provisional | HOU | RB | 40 | 7.33 | 4.95 | 4.23 – 5.67 |
| 7 | Sean Tucker◦ provisional | TB | RB | 50 | 6.16 | 4.79 | 4.09 – 5.49 |
| 8 | Jerome Ford◦ provisional | CLE | RB | 104 | 5.43 | 4.78 | 4.16 – 5.41 |
| 9 | Jordan Mason◦ provisional | SF | RB | 153 | 5.16 | 4.75 | 4.17 – 5.33 |
| 10 | James Cook | BUF | RB | 207 | 4.87 | 4.65 | 4.12 – 5.19 |
| 11 | Bijan Robinson | ATL | RB | 305 | 4.78 | 4.64 | 4.16 – 5.11 |
| 12 | Chuba Hubbard | CAR | RB | 251 | 4.77 | 4.61 | 4.11 – 5.12 |
| 13 | Isaiah Davis◦ provisional | NYJ | RB | 30 | 5.80 | 4.59 | 3.86 – 5.33 |
| 14 | Isaac Guerendo◦ provisional | SF | RB | 84 | 5.00 | 4.58 | 3.93 – 5.24 |
| 15 | Jonathan Taylor | IND | RB | 305 | 4.69 | 4.58 | 4.11 – 5.06 |
| 16 | Emanuel Wilson◦ provisional | GB | RB | 103 | 4.87 | 4.57 | 3.94 – 5.19 |
| 17 | Kenny McIntosh◦ provisional | SEA | RB | 31 | 5.55 | 4.56 | 3.82 – 5.29 |
| 18 | Ty Johnson◦ provisional | BUF | RB | 41 | 5.20 | 4.54 | 3.82 – 5.25 |
| 19 | J.K. Dobbins | LAC | RB | 195 | 4.64 | 4.52 | 3.98 – 5.06 |
| 20 | Tyler Allgeier◦ provisional | ATL | RB | 138 | 4.68 | 4.51 | 3.92 – 5.11 |
| 21 | James Conner | ARI | RB | 239 | 4.59 | 4.50 | 3.99 – 5.02 |
| 22 | Rico Dowdle | DAL | RB | 235 | 4.59 | 4.50 | 3.99 – 5.02 |
| 23 | Chris Brooks◦ provisional | GB | RB | 36 | 5.08 | 4.50 | 3.77 – 5.23 |
| 24 | Austin Ekeler◦ provisional | WAS | RB | 77 | 4.77 | 4.50 | 3.84 – 5.16 |
| 25 | Chris Rodriguez Jr.◦ provisional | WAS | RB | 35 | 4.94 | 4.47 | 3.75 – 5.20 |
| 26 | Ameer Abdullah◦ provisional | LV | RB | 66 | 4.71 | 4.47 | 3.79 – 5.15 |
| 27 | Tank Bigsby | JAX | RB | 168 | 4.56 | 4.47 | 3.90 – 5.03 |
| 28 | Justice Hill◦ provisional | BAL | RB | 47 | 4.74 | 4.46 | 3.75 – 5.16 |
| 29 | Jeremy McNichols◦ provisional | WAS | RB | 56 | 4.70 | 4.46 | 3.76 – 5.15 |
| 30 | Raheem Blackshear◦ provisional | CAR | RB | 15 | 5.33 | 4.45 | 3.69 – 5.22 |
| 31 | Trey Benson◦ provisional | ARI | RB | 63 | 4.62 | 4.44 | 3.76 – 5.12 |
| 32 | Tyler Goodson◦ provisional | IND | RB | 32 | 4.78 | 4.44 | 3.71 – 5.17 |
| 33 | Sincere McCormick◦ provisional | LV | RB | 39 | 4.69 | 4.43 | 3.71 – 5.16 |
| 34 | Aaron Jones | MIN | RB | 255 | 4.46 | 4.43 | 3.93 – 4.93 |
| 35 | De'Von Achane | MIA | RB | 203 | 4.47 | 4.43 | 3.89 – 4.96 |
| 36 | Antonio Gibson◦ provisional | NE | RB | 120 | 4.48 | 4.42 | 3.81 – 5.03 |
| 37 | Patrick Taylor◦ provisional | SF | RB | 40 | 4.58 | 4.41 | 3.69 – 5.13 |
| 38 | Julius Chestnut◦ provisional | TEN | RB | 22 | 4.64 | 4.41 | 3.65 – 5.16 |
| 39 | Samaje Perine◦ provisional | KC | RB | 20 | 4.60 | 4.40 | 3.64 – 5.16 |
| 40 | Craig Reynolds◦ provisional | DET | RB | 31 | 4.48 | 4.39 | 3.66 – 5.13 |
| 41 | D'Ernest Johnson◦ provisional | JAX | RB | 32 | 4.47 | 4.39 | 3.66 – 5.12 |
| 42 | Ronnie Rivers◦ provisional | LA | RB | 22 | 4.50 | 4.39 | 3.64 – 5.14 |
| 43 | Josh Jacobs | GB | RB | 303 | 4.39 | 4.38 | 3.91 – 4.86 |
| 44 | Jaleel McLaughlin◦ provisional | DEN | RB | 113 | 4.39 | 4.38 | 3.76 – 5.00 |
| 45 | Tyrone Tracy Jr. | NYG | RB | 192 | 4.37 | 4.37 | 3.83 – 4.92 |
| 46 | Deuce Vaughn◦ provisional | DAL | RB | 17 | 4.12 | 4.35 | 3.59 – 5.11 |
| 47 | Cordarrelle Patterson◦ provisional | PIT | RB | 32 | 4.22 | 4.35 | 3.62 – 5.08 |
| 48 | Pierre Strong◦ provisional | CLE | RB | 26 | 4.15 | 4.34 | 3.60 – 5.09 |
| 49 | Chase Brown | CIN | RB | 230 | 4.31 | 4.34 | 3.82 – 4.86 |
| 50 | Cam Akers◦ provisional | MIN | RB | 104 | 4.27 | 4.33 | 3.71 – 4.96 |
| 51 | Jaylen Warren◦ provisional | PIT | RB | 120 | 4.26 | 4.33 | 3.72 – 4.94 |
| 52 | Brian Robinson | WAS | RB | 187 | 4.27 | 4.32 | 3.77 – 4.87 |
| 53 | Rachaad White◦ provisional | TB | RB | 144 | 4.26 | 4.32 | 3.73 – 4.91 |
| 54 | Jeff Wilson◦ provisional | MIA | RB | 16 | 3.56 | 4.30 | 3.54 – 5.07 |
| 55 | Zach Charbonnet◦ provisional | SEA | RB | 135 | 4.21 | 4.30 | 3.71 – 4.90 |
| 56 | Christian McCaffrey◦ provisional | SF | RB | 50 | 4.04 | 4.30 | 3.59 – 5.00 |
| 57 | Audric Estimé◦ provisional | DEN | RB | 76 | 4.08 | 4.28 | 3.62 – 4.94 |
| 58 | Jordan Mims◦ provisional | NO | RB | 20 | 3.50 | 4.28 | 3.52 – 5.04 |
| 59 | Dare Ogunbowale◦ provisional | HOU | RB | 30 | 3.73 | 4.28 | 3.54 – 5.01 |
| 60 | JaMycal Hasty◦ provisional | NE | RB | 20 | 3.45 | 4.27 | 3.52 – 5.03 |
| 61 | David Montgomery | DET | RB | 186 | 4.17 | 4.26 | 3.71 – 4.81 |
| 62 | Michael Carter◦ provisional | ARI | RB | 35 | 3.74 | 4.26 | 3.54 – 4.99 |
| 63 | Kendre Miller◦ provisional | NO | RB | 39 | 3.79 | 4.26 | 3.54 – 4.98 |
| 64 | Alvin Kamara | NO | RB | 228 | 4.17 | 4.25 | 3.73 – 4.77 |
| 65 | Breece Hall | NYJ | RB | 212 | 4.15 | 4.25 | 3.72 – 4.78 |
| 66 | Khalil Herbert◦ provisional | CIN | RB | 36 | 3.61 | 4.24 | 3.51 – 4.96 |
| 67 | Tony Pollard | TEN | RB | 261 | 4.14 | 4.23 | 3.73 – 4.73 |
| 68 | Joe Mixon | HOU | RB | 247 | 4.11 | 4.22 | 3.71 – 4.73 |
| 69 | Kenneth Gainwell◦ provisional | PHI | RB | 75 | 3.87 | 4.22 | 3.55 – 4.88 |
| 70 | Kimani Vidal◦ provisional | LAC | RB | 43 | 3.60 | 4.22 | 3.50 – 4.93 |
| 71 | Miles Sanders◦ provisional | CAR | RB | 55 | 3.73 | 4.21 | 3.52 – 4.91 |
| 72 | Kyren Williams | LA | RB | 316 | 4.11 | 4.20 | 3.73 – 4.67 |
| 73 | Ray Davis◦ provisional | BUF | RB | 113 | 3.91 | 4.19 | 3.57 – 4.80 |
| 74 | Keaton Mitchell◦ provisional | BAL | RB | 15 | 2.00 | 4.18 | 3.41 – 4.94 |
| 75 | Devin Singletary◦ provisional | NYG | RB | 113 | 3.87 | 4.17 | 3.55 – 4.79 |
| 76 | Jaylen Wright◦ provisional | MIA | RB | 68 | 3.66 | 4.17 | 3.49 – 4.84 |
| 77 | Blake Corum◦ provisional | LA | RB | 58 | 3.57 | 4.17 | 3.48 – 4.85 |
| 78 | Isiah Pacheco◦ provisional | KC | RB | 83 | 3.73 | 4.16 | 3.51 – 4.81 |
| 79 | Jamaal Williams◦ provisional | NO | RB | 48 | 3.42 | 4.16 | 3.45 – 4.86 |
| 80 | Tyjae Spears◦ provisional | TEN | RB | 84 | 3.71 | 4.15 | 3.50 – 4.80 |
| 81 | Najee Harris | PIT | RB | 263 | 3.97 | 4.12 | 3.63 – 4.62 |
| 82 | Will Shipley◦ provisional | PHI | RB | 30 | 2.73 | 4.12 | 3.39 – 4.86 |
| 83 | Braelon Allen◦ provisional | NYJ | RB | 92 | 3.63 | 4.11 | 3.47 – 4.75 |
| 84 | Carson Steele◦ provisional | KC | RB | 56 | 3.27 | 4.09 | 3.40 – 4.79 |
| 85 | Rhamondre Stevenson | NE | RB | 207 | 3.87 | 4.09 | 3.56 – 4.63 |
| 86 | Ty Chandler◦ provisional | MIN | RB | 56 | 3.25 | 4.09 | 3.40 – 4.78 |
| 87 | Hassan Haskins◦ provisional | LAC | RB | 34 | 2.62 | 4.07 | 3.34 – 4.80 |
| 88 | Kenneth Walker III◦ provisional | SEA | RB | 153 | 3.75 | 4.07 | 3.49 – 4.65 |
| 89 | Gus Edwards◦ provisional | LAC | RB | 102 | 3.58 | 4.07 | 3.44 – 4.70 |
| 90 | Travis Etienne◦ provisional | JAX | RB | 150 | 3.72 | 4.06 | 3.48 – 4.64 |
| 91 | Javonte Williams◦ provisional | DEN | RB | 139 | 3.69 | 4.06 | 3.47 – 4.65 |
| 92 | D'Onta Foreman◦ provisional | CLE | RB | 71 | 3.27 | 4.04 | 3.37 – 4.71 |
| 93 | Zack Moss◦ provisional | CIN | RB | 74 | 3.27 | 4.03 | 3.37 – 4.70 |
| 94 | D'Andre Swift | CHI | RB | 253 | 3.79 | 4.02 | 3.52 – 4.52 |
| 95 | Raheem Mostert◦ provisional | MIA | RB | 85 | 3.27 | 4.00 | 3.35 – 4.65 |
| 96 | Trey Sermon◦ provisional | IND | RB | 56 | 2.84 | 3.99 | 3.29 – 4.68 |
| 97 | Kareem Hunt | KC | RB | 200 | 3.64 | 3.97 | 3.43 – 4.51 |
| 98 | Ezekiel Elliott◦ provisional | DAL | RB | 74 | 3.05 | 3.97 | 3.30 – 4.63 |
| 99 | Roschon Johnson◦ provisional | CHI | RB | 55 | 2.73 | 3.96 | 3.27 – 4.66 |
| 100 | Nick Chubb◦ provisional | CLE | RB | 102 | 3.25 | 3.95 | 3.32 – 4.58 |
| 101 | Zamir White◦ provisional | LV | RB | 65 | 2.82 | 3.93 | 3.26 – 4.61 |
| 102 | Alexander Mattison◦ provisional | LV | RB | 134 | 3.15 | 3.83 | 3.23 – 4.42 |
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).