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 · 2018
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
- 298
- 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 · 2018 · full board
| # | Player | Team | Pos | carrys | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Phillip Lindsay◦ provisional | DEN | RB | 193 | 5.37 | 4.77 | 4.29 – 5.26 |
| 2 | Raheem Mostert◦ provisional | SF | RB | 34 | 7.68 | 4.72 | 4.13 – 5.31 |
| 3 | Aaron Jones◦ provisional | GB | RB | 133 | 5.47 | 4.72 | 4.20 – 5.24 |
| 4 | Matt Breida◦ provisional | SF | RB | 153 | 5.32 | 4.70 | 4.19 – 5.21 |
| 5 | Nick Chubb◦ provisional | CLE | RB | 192 | 5.19 | 4.70 | 4.21 – 5.18 |
| 6 | C.J. Anderson◦ provisional | LA | RB | 67 | 6.01 | 4.68 | 4.12 – 5.24 |
| 7 | Kerryon Johnson◦ provisional | DET | RB | 118 | 5.43 | 4.68 | 4.15 – 5.21 |
| 8 | Saquon Barkley◦ provisional | NYG | RB | 263 | 4.98 | 4.66 | 4.21 – 5.11 |
| 9 | Christian McCaffrey◦ provisional | CAR | RB | 219 | 5.01 | 4.65 | 4.18 – 5.12 |
| 10 | Gus Edwards◦ provisional | BAL | RB | 139 | 5.18 | 4.64 | 4.12 – 5.15 |
| 11 | Melvin Gordon◦ provisional | LAC | RB | 176 | 5.04 | 4.63 | 4.13 – 5.12 |
| 12 | Joe Mixon◦ provisional | CIN | RB | 237 | 4.93 | 4.62 | 4.16 – 5.09 |
| 13 | Derrick Henry◦ provisional | TEN | RB | 215 | 4.93 | 4.61 | 4.14 – 5.08 |
| 14 | Austin Ekeler◦ provisional | LAC | RB | 106 | 5.23 | 4.60 | 4.07 – 5.14 |
| 15 | Brian Hill◦ provisional | ATL | RB | 20 | 7.85 | 4.60 | 4.00 – 5.20 |
| 16 | Todd Gurley◦ provisional | LA | RB | 260 | 4.83 | 4.59 | 4.13 – 5.04 |
| 17 | Jordan Wilkins◦ provisional | IND | RB | 60 | 5.60 | 4.59 | 4.02 – 5.15 |
| 18 | Kenneth Dixon◦ provisional | BAL | RB | 60 | 5.55 | 4.58 | 4.01 – 5.14 |
| 19 | Ezekiel Elliott | DAL | RB | 304 | 4.72 | 4.55 | 4.11 – 4.99 |
| 20 | Tevin Coleman◦ provisional | ATL | RB | 167 | 4.79 | 4.53 | 4.03 – 5.03 |
| 21 | Isaiah Crowell◦ provisional | NYJ | RB | 143 | 4.79 | 4.51 | 4.00 – 5.02 |
| 22 | Cordarrelle Patterson◦ provisional | NE | RB | 42 | 5.43 | 4.51 | 3.93 – 5.09 |
| 23 | Chris Carson◦ provisional | SEA | RB | 247 | 4.66 | 4.51 | 4.05 – 4.97 |
| 24 | Rashaad Penny◦ provisional | SEA | RB | 85 | 4.93 | 4.50 | 3.95 – 5.05 |
| 25 | Dwayne Washington◦ provisional | NO | RB | 27 | 5.70 | 4.49 | 3.90 – 5.09 |
| 26 | Damien Williams◦ provisional | KC | RB | 50 | 5.12 | 4.49 | 3.91 – 5.06 |
| 27 | Lamar Miller◦ provisional | HOU | RB | 210 | 4.63 | 4.49 | 4.01 – 4.96 |
| 28 | Devontae Booker◦ provisional | DEN | RB | 34 | 5.38 | 4.48 | 3.89 – 5.07 |
| 29 | Kalen Ballage◦ provisional | MIA | RB | 36 | 5.31 | 4.48 | 3.89 – 5.07 |
| 30 | Marlon Mack◦ provisional | IND | RB | 197 | 4.63 | 4.48 | 4.00 – 4.96 |
| 31 | Mark Ingram◦ provisional | NO | RB | 138 | 4.67 | 4.47 | 3.96 – 4.99 |
| 32 | Frank Gore◦ provisional | MIA | RB | 156 | 4.63 | 4.47 | 3.96 – 4.97 |
| 33 | Dalvin Cook◦ provisional | MIN | RB | 133 | 4.62 | 4.46 | 3.94 – 4.97 |
| 34 | Malcolm Brown◦ provisional | LA | RB | 43 | 4.93 | 4.45 | 3.87 – 5.03 |
| 35 | Zach Zenner◦ provisional | DET | RB | 55 | 4.82 | 4.45 | 3.88 – 5.02 |
| 36 | Kareem Hunt◦ provisional | KC | RB | 181 | 4.55 | 4.45 | 3.96 – 4.94 |
| 37 | Spencer Ware◦ provisional | KC | RB | 51 | 4.82 | 4.45 | 3.87 – 5.02 |
| 38 | Marcus Murphy◦ provisional | BUF | RB | 52 | 4.81 | 4.44 | 3.87 – 5.02 |
| 39 | Duke Johnson◦ provisional | CLE | RB | 42 | 4.88 | 4.44 | 3.86 – 5.03 |
| 40 | James Conner◦ provisional | PIT | RB | 215 | 4.53 | 4.44 | 3.97 – 4.92 |
| 41 | Mike Davis◦ provisional | SEA | RB | 112 | 4.59 | 4.44 | 3.91 – 4.97 |
| 42 | Alvin Kamara◦ provisional | NO | RB | 197 | 4.51 | 4.43 | 3.95 – 4.92 |
| 43 | Jalen Richard◦ provisional | LV | RB | 56 | 4.63 | 4.42 | 3.85 – 4.99 |
| 44 | Kapri Bibbs◦ provisional | GB | RB | 21 | 4.90 | 4.42 | 3.81 – 5.02 |
| 45 | James White◦ provisional | NE | RB | 94 | 4.52 | 4.41 | 3.87 – 4.96 |
| 46 | Sony Michel◦ provisional | NE | RB | 209 | 4.45 | 4.41 | 3.93 – 4.89 |
| 47 | Jaylen Samuels◦ provisional | PIT | RB | 56 | 4.57 | 4.41 | 3.84 – 4.98 |
| 48 | Tarik Cohen◦ provisional | CHI | RB | 99 | 4.48 | 4.41 | 3.87 – 4.95 |
| 49 | Kenyan Drake◦ provisional | MIA | RB | 120 | 4.46 | 4.40 | 3.88 – 4.93 |
| 50 | Theo Riddick◦ provisional | DET | RB | 40 | 4.28 | 4.37 | 3.78 – 4.95 |
| 51 | Bilal Powell◦ provisional | NYJ | RB | 80 | 4.29 | 4.36 | 3.81 – 4.91 |
| 52 | Darren Sproles◦ provisional | PHI | RB | 29 | 4.14 | 4.36 | 3.77 – 4.95 |
| 53 | Chris Thompson◦ provisional | WAS | RB | 43 | 4.14 | 4.35 | 3.77 – 4.93 |
| 54 | Justin Jackson◦ provisional | LAC | RB | 50 | 4.12 | 4.34 | 3.77 – 4.92 |
| 55 | Kenjon Barner◦ provisional | CAR | RB | 19 | 3.74 | 4.34 | 3.74 – 4.95 |
| 56 | Josh Adams◦ provisional | PHI | RB | 121 | 4.24 | 4.34 | 3.82 – 4.86 |
| 57 | Keith Ford◦ provisional | BUF | RB | 21 | 3.76 | 4.34 | 3.74 – 4.94 |
| 58 | Cameron Artis-Payne◦ provisional | CAR | RB | 19 | 3.63 | 4.34 | 3.73 – 4.94 |
| 59 | Jay Ajayi◦ provisional | PHI | RB | 46 | 4.04 | 4.34 | 3.76 – 4.91 |
| 60 | Marshawn Lynch◦ provisional | LV | RB | 90 | 4.18 | 4.33 | 3.79 – 4.88 |
| 61 | DeAndre Washington◦ provisional | LV | RB | 30 | 3.83 | 4.33 | 3.74 – 4.92 |
| 62 | Wendell Smallwood◦ provisional | PHI | RB | 88 | 4.16 | 4.33 | 3.78 – 4.88 |
| 63 | Jeff Wilson◦ provisional | SF | RB | 66 | 4.03 | 4.32 | 3.75 – 4.88 |
| 64 | Doug Martin◦ provisional | LV | RB | 172 | 4.20 | 4.32 | 3.82 – 4.81 |
| 65 | Latavius Murray◦ provisional | MIN | RB | 140 | 4.13 | 4.30 | 3.79 – 4.81 |
| 66 | Mike Gillislee◦ provisional | NO | RB | 16 | 2.69 | 4.29 | 3.69 – 4.90 |
| 67 | Giovani Bernard◦ provisional | CIN | RB | 56 | 3.77 | 4.28 | 3.71 – 4.85 |
| 68 | T.J. Yeldon◦ provisional | JAX | RB | 104 | 3.98 | 4.28 | 3.74 – 4.81 |
| 69 | Adrian Peterson◦ provisional | WAS | RB | 251 | 4.15 | 4.28 | 3.82 – 4.73 |
| 70 | Corey Clement◦ provisional | PHI | RB | 69 | 3.78 | 4.27 | 3.71 – 4.83 |
| 71 | Royce Freeman◦ provisional | DEN | RB | 130 | 4.01 | 4.27 | 3.75 – 4.79 |
| 72 | Jacquizz Rodgers◦ provisional | TB | RB | 33 | 3.21 | 4.26 | 3.67 – 4.85 |
| 73 | Wayne Gallman◦ provisional | NYG | RB | 51 | 3.45 | 4.25 | 3.67 – 4.82 |
| 74 | John Kelly◦ provisional | LA | RB | 27 | 2.74 | 4.24 | 3.65 – 4.84 |
| 75 | Alfred Morris◦ provisional | SF | RB | 111 | 3.86 | 4.24 | 3.71 – 4.77 |
| 76 | Stevan Ridley◦ provisional | PIT | RB | 29 | 2.76 | 4.24 | 3.64 – 4.83 |
| 77 | Nyheim Hines◦ provisional | IND | RB | 85 | 3.69 | 4.23 | 3.68 – 4.78 |
| 78 | Chase Edmonds◦ provisional | ARI | RB | 60 | 3.47 | 4.23 | 3.66 – 4.80 |
| 79 | Jamaal Williams◦ provisional | GB | RB | 121 | 3.83 | 4.22 | 3.70 – 4.75 |
| 80 | Trenton Cannon◦ provisional | NYJ | RB | 38 | 2.97 | 4.22 | 3.64 – 4.81 |
| 81 | Ronald Jones◦ provisional | TB | RB | 23 | 1.91 | 4.20 | 3.61 – 4.80 |
| 82 | Rex Burkhead◦ provisional | NE | RB | 57 | 3.26 | 4.20 | 3.63 – 4.77 |
| 83 | Rod Smith◦ provisional | DAL | RB | 44 | 2.89 | 4.19 | 3.61 – 4.77 |
| 84 | Ito Smith◦ provisional | ATL | RB | 90 | 3.50 | 4.18 | 3.63 – 4.72 |
| 85 | Javorius Allen◦ provisional | BAL | RB | 41 | 2.68 | 4.18 | 3.59 – 4.76 |
| 86 | Alex Collins◦ provisional | BAL | RB | 114 | 3.61 | 4.17 | 3.64 – 4.70 |
| 87 | Chris Ivory◦ provisional | BUF | RB | 115 | 3.35 | 4.09 | 3.57 – 4.62 |
| 88 | Peyton Barber◦ provisional | TB | RB | 234 | 3.72 | 4.09 | 3.63 – 4.56 |
| 89 | Jordan Howard◦ provisional | CHI | RB | 250 | 3.74 | 4.09 | 3.63 – 4.55 |
| 90 | Elijah McGuire◦ provisional | NYJ | RB | 92 | 3.00 | 4.06 | 3.51 – 4.60 |
| 91 | Leonard Fournette◦ provisional | JAX | RB | 133 | 3.30 | 4.05 | 3.53 – 4.56 |
| 92 | David Johnson◦ provisional | ARI | RB | 259 | 3.64 | 4.04 | 3.58 – 4.49 |
| 93 | Alfred Blue◦ provisional | HOU | RB | 150 | 3.33 | 4.03 | 3.52 – 4.54 |
| 94 | Dion Lewis◦ provisional | TEN | RB | 155 | 3.34 | 4.02 | 3.52 – 4.53 |
| 95 | Carlos Hyde◦ provisional | JAX | RB | 172 | 3.32 | 3.99 | 3.50 – 4.49 |
| 96 | LeSean McCoy◦ provisional | BUF | RB | 161 | 3.19 | 3.96 | 3.46 – 4.47 |
| 97 | LeGarrette Blount◦ provisional | DET | RB | 155 | 2.70 | 3.80 | 3.30 – 4.31 |
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).