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 · 2023
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
- 108
- 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 · 2023 · full board
| # | Player | Team | Pos | carrys | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | De'Von Achane◦ provisional | MIA | RB | 103 | 7.77 | 5.93 | 5.26 – 6.60 |
| 2 | Keaton Mitchell◦ provisional | BAL | RB | 47 | 8.43 | 5.46 | 4.68 – 6.25 |
| 3 | Christian McCaffrey | SF | RB | 272 | 5.36 | 5.03 | 4.53 – 5.53 |
| 4 | Jahmyr Gibbs | DET | RB | 182 | 5.19 | 4.81 | 4.24 – 5.39 |
| 5 | Jaylen Warren | PIT | RB | 149 | 5.26 | 4.81 | 4.20 – 5.41 |
| 6 | Kyren Williams | LA | RB | 229 | 5.00 | 4.74 | 4.21 – 5.27 |
| 7 | James Conner | ARI | RB | 210 | 4.95 | 4.69 | 4.14 – 5.23 |
| 8 | Jaleel McLaughlin◦ provisional | DEN | RB | 76 | 5.39 | 4.68 | 3.96 – 5.40 |
| 9 | Michael Carter◦ provisional | ARI | RB | 30 | 6.23 | 4.62 | 3.79 – 5.45 |
| 10 | Raheem Mostert | MIA | RB | 209 | 4.84 | 4.62 | 4.07 – 5.16 |
| 11 | Nick Chubb◦ provisional | CLE | RB | 28 | 6.07 | 4.57 | 3.73 – 5.40 |
| 12 | James Cook | BUF | RB | 237 | 4.73 | 4.56 | 4.04 – 5.08 |
| 13 | David Montgomery | DET | RB | 220 | 4.62 | 4.48 | 3.94 – 5.01 |
| 14 | D'Andre Swift | PHI | RB | 229 | 4.58 | 4.45 | 3.92 – 4.98 |
| 15 | Jordan Mason◦ provisional | SF | RB | 40 | 5.15 | 4.44 | 3.64 – 5.24 |
| 16 | Bijan Robinson | ATL | RB | 214 | 4.56 | 4.43 | 3.89 – 4.97 |
| 17 | Aaron Jones | GB | RB | 142 | 4.62 | 4.43 | 3.81 – 5.04 |
| 18 | Emari Demercado◦ provisional | ARI | RB | 58 | 4.90 | 4.43 | 3.67 – 5.18 |
| 19 | Khalil Herbert | CHI | RB | 133 | 4.61 | 4.42 | 3.79 – 5.04 |
| 20 | Isiah Pacheco | KC | RB | 206 | 4.54 | 4.41 | 3.86 – 4.96 |
| 21 | Ameer Abdullah◦ provisional | LV | RB | 15 | 5.93 | 4.39 | 3.51 – 5.27 |
| 22 | Chris Rodriguez Jr.◦ provisional | WAS | RB | 51 | 4.84 | 4.39 | 3.62 – 5.16 |
| 23 | Chris Brooks◦ provisional | MIA | RB | 19 | 5.58 | 4.39 | 3.52 – 5.25 |
| 24 | Justice Hill◦ provisional | BAL | RB | 84 | 4.61 | 4.36 | 3.66 – 5.07 |
| 25 | Breece Hall | NYJ | RB | 224 | 4.45 | 4.36 | 3.82 – 4.89 |
| 26 | Tyjae Spears◦ provisional | TEN | RB | 100 | 4.53 | 4.35 | 3.67 – 5.02 |
| 27 | Ty Chandler◦ provisional | MIN | RB | 102 | 4.52 | 4.34 | 3.67 – 5.01 |
| 28 | Pierre Strong◦ provisional | CLE | RB | 64 | 4.55 | 4.31 | 3.57 – 5.06 |
| 29 | Jonathan Taylor | IND | RB | 169 | 4.38 | 4.30 | 3.72 – 4.89 |
| 30 | Jeff Wilson◦ provisional | MIA | RB | 41 | 4.59 | 4.29 | 3.49 – 5.09 |
| 31 | Samaje Perine◦ provisional | DEN | RB | 53 | 4.49 | 4.28 | 3.51 – 5.05 |
| 32 | Zack Moss | IND | RB | 183 | 4.34 | 4.28 | 3.71 – 4.85 |
| 33 | Trey Sermon◦ provisional | IND | RB | 35 | 4.57 | 4.27 | 3.46 – 5.09 |
| 34 | Zamir White◦ provisional | LV | RB | 104 | 4.34 | 4.25 | 3.59 – 4.92 |
| 35 | Roschon Johnson◦ provisional | CHI | RB | 81 | 4.35 | 4.25 | 3.54 – 4.96 |
| 36 | Kenneth Gainwell◦ provisional | PHI | RB | 85 | 4.31 | 4.23 | 3.53 – 4.93 |
| 37 | Patrick Taylor◦ provisional | GB | RB | 32 | 4.41 | 4.23 | 3.41 – 5.05 |
| 38 | Craig Reynolds◦ provisional | DET | RB | 41 | 4.37 | 4.23 | 3.43 – 5.03 |
| 39 | Trayveon Williams◦ provisional | CIN | RB | 15 | 4.60 | 4.23 | 3.35 – 5.11 |
| 40 | Zach Charbonnet◦ provisional | SEA | RB | 108 | 4.28 | 4.23 | 3.56 – 4.89 |
| 41 | Ty Johnson◦ provisional | BUF | RB | 30 | 4.40 | 4.22 | 3.40 – 5.05 |
| 42 | Boston Scott◦ provisional | PHI | RB | 20 | 4.30 | 4.20 | 3.34 – 5.06 |
| 43 | Devin Singletary | HOU | RB | 216 | 4.20 | 4.19 | 3.65 – 4.74 |
| 44 | Derrick Henry | TEN | RB | 280 | 4.17 | 4.17 | 3.68 – 4.66 |
| 45 | Royce Freeman◦ provisional | LA | RB | 77 | 4.14 | 4.16 | 3.45 – 4.88 |
| 46 | Kevin Harris◦ provisional | NE | RB | 16 | 4.06 | 4.16 | 3.29 – 5.04 |
| 47 | Damien Harris◦ provisional | BUF | RB | 23 | 4.09 | 4.16 | 3.31 – 5.01 |
| 48 | Kenneth Walker III | SEA | RB | 219 | 4.13 | 4.15 | 3.61 – 4.69 |
| 49 | Chase Brown◦ provisional | CIN | RB | 44 | 4.07 | 4.14 | 3.36 – 4.93 |
| 50 | Ronnie Rivers◦ provisional | LA | RB | 32 | 4.03 | 4.14 | 3.32 – 4.97 |
| 51 | Antonio Gibson◦ provisional | WAS | RB | 65 | 4.08 | 4.14 | 3.40 – 4.88 |
| 52 | Brian Robinson | WAS | RB | 179 | 4.11 | 4.13 | 3.56 – 4.71 |
| 53 | Rico Dowdle◦ provisional | DAL | RB | 89 | 4.06 | 4.12 | 3.43 – 4.82 |
| 54 | Gus Edwards | BAL | RB | 199 | 4.08 | 4.11 | 3.56 – 4.67 |
| 55 | Darrynton Evans◦ provisional | MIA | RB | 32 | 3.78 | 4.09 | 3.26 – 4.91 |
| 56 | Najee Harris | PIT | RB | 256 | 4.04 | 4.08 | 3.57 – 4.59 |
| 57 | Tony Jones◦ provisional | ARI | RB | 26 | 3.65 | 4.08 | 3.23 – 4.92 |
| 58 | Kendre Miller◦ provisional | NO | RB | 41 | 3.80 | 4.07 | 3.28 – 4.87 |
| 59 | Joe Mixon | CIN | RB | 257 | 4.02 | 4.07 | 3.56 – 4.58 |
| 60 | La'Mical Perine◦ provisional | KC | RB | 22 | 3.50 | 4.06 | 3.21 – 4.92 |
| 61 | Raheem Blackshear◦ provisional | CAR | RB | 15 | 3.20 | 4.06 | 3.18 – 4.93 |
| 62 | Rhamondre Stevenson | NE | RB | 156 | 3.97 | 4.05 | 3.45 – 4.65 |
| 63 | Tony Pollard | DAL | RB | 253 | 3.98 | 4.04 | 3.53 – 4.55 |
| 64 | D'Onta Foreman | CHI | RB | 109 | 3.90 | 4.04 | 3.38 – 4.70 |
| 65 | Jerome Ford | CLE | RB | 206 | 3.96 | 4.03 | 3.48 – 4.58 |
| 66 | Latavius Murray◦ provisional | BUF | RB | 79 | 3.80 | 4.02 | 3.30 – 4.73 |
| 67 | Israel Abanikanda◦ provisional | NYJ | RB | 22 | 3.18 | 4.01 | 3.15 – 4.86 |
| 68 | Cordarrelle Patterson◦ provisional | ATL | RB | 50 | 3.62 | 4.00 | 3.23 – 4.77 |
| 69 | Elijah Mitchell◦ provisional | SF | RB | 75 | 3.75 | 4.00 | 3.28 – 4.72 |
| 70 | Alexander Mattison | MIN | RB | 180 | 3.89 | 4.00 | 3.42 – 4.57 |
| 71 | Chase Edmonds◦ provisional | TB | RB | 49 | 3.59 | 3.99 | 3.22 – 4.77 |
| 72 | Eric Gray◦ provisional | NYG | RB | 17 | 2.82 | 3.99 | 3.12 – 4.86 |
| 73 | Joshua Kelley◦ provisional | LAC | RB | 107 | 3.79 | 3.98 | 3.32 – 4.65 |
| 74 | Saquon Barkley | NYG | RB | 248 | 3.89 | 3.97 | 3.46 – 4.49 |
| 75 | Melvin Gordon◦ provisional | BAL | RB | 26 | 3.12 | 3.97 | 3.13 – 4.81 |
| 76 | Alvin Kamara | NO | RB | 182 | 3.84 | 3.96 | 3.39 – 4.53 |
| 77 | Jerick McKinnon◦ provisional | KC | RB | 21 | 2.86 | 3.96 | 3.11 – 4.82 |
| 78 | Salvon Ahmed◦ provisional | MIA | RB | 22 | 2.77 | 3.94 | 3.09 – 4.79 |
| 79 | Chuba Hubbard | CAR | RB | 238 | 3.79 | 3.91 | 3.39 – 4.43 |
| 80 | Travis Etienne | JAX | RB | 269 | 3.76 | 3.88 | 3.38 – 4.38 |
| 81 | Sean Tucker◦ provisional | TB | RB | 15 | 1.53 | 3.85 | 2.98 – 4.73 |
| 82 | Tyler Allgeier | ATL | RB | 187 | 3.65 | 3.84 | 3.28 – 4.41 |
| 83 | Dalvin Cook◦ provisional | NYJ | RB | 67 | 3.19 | 3.80 | 3.06 – 4.54 |
| 84 | Rachaad White | TB | RB | 272 | 3.64 | 3.79 | 3.29 – 4.29 |
| 85 | Clyde Edwards-Helaire◦ provisional | KC | RB | 70 | 3.19 | 3.79 | 3.06 – 4.52 |
| 86 | Isaiah Spiller◦ provisional | LAC | RB | 37 | 2.59 | 3.77 | 2.97 – 4.58 |
| 87 | Austin Ekeler | LAC | RB | 179 | 3.51 | 3.76 | 3.19 – 4.33 |
| 88 | Javonte Williams | DEN | RB | 219 | 3.54 | 3.75 | 3.21 – 4.29 |
| 89 | D'Ernest Johnson◦ provisional | JAX | RB | 41 | 2.63 | 3.75 | 2.96 – 4.55 |
| 90 | Deuce Vaughn◦ provisional | DAL | RB | 23 | 1.74 | 3.75 | 2.90 – 4.60 |
| 91 | Ezekiel Elliott | NE | RB | 184 | 3.49 | 3.74 | 3.17 – 4.31 |
| 92 | Ke'Shawn Vaughn◦ provisional | TB | RB | 24 | 1.75 | 3.74 | 2.89 – 4.58 |
| 93 | Miles Sanders | CAR | RB | 129 | 3.35 | 3.73 | 3.09 – 4.36 |
| 94 | AJ Dillon | GB | RB | 178 | 3.44 | 3.72 | 3.15 – 4.30 |
| 95 | Matt Breida◦ provisional | NYG | RB | 55 | 2.75 | 3.69 | 2.93 – 4.46 |
| 96 | Tank Bigsby◦ provisional | JAX | RB | 50 | 2.64 | 3.69 | 2.92 – 4.46 |
| 97 | Josh Jacobs | LV | RB | 233 | 3.45 | 3.68 | 3.16 – 4.21 |
| 98 | Cam Akers◦ provisional | MIN | RB | 60 | 2.78 | 3.68 | 2.93 – 4.43 |
| 99 | Keaontay Ingram◦ provisional | ARI | RB | 35 | 2.11 | 3.67 | 2.86 – 4.49 |
| 100 | Darrell Henderson◦ provisional | LA | RB | 46 | 2.43 | 3.66 | 2.87 – 4.44 |
| 101 | Kareem Hunt | CLE | RB | 135 | 3.04 | 3.55 | 2.92 – 4.17 |
| 102 | Jamaal Williams◦ provisional | NO | RB | 106 | 2.89 | 3.54 | 2.87 – 4.20 |
| 103 | Dameon Pierce | HOU | RB | 145 | 2.87 | 3.43 | 2.82 – 4.04 |
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).