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 · 2016
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
- 166
- 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 · 2016 · full board
| # | Player | Team | Pos | carrys | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | LeSean McCoy | BUF | RB | 235 | 5.40 | 4.89 | 4.39 – 5.40 |
| 2 | Jordan Howard | CHI | RB | 252 | 5.21 | 4.80 | 4.30 – 5.29 |
| 3 | Ezekiel Elliott | DAL | RB | 322 | 5.07 | 4.76 | 4.30 – 5.22 |
| 4 | Mike Gillislee◦ provisional | BUF | RB | 101 | 5.71 | 4.76 | 4.14 – 5.37 |
| 5 | Jalen Richard◦ provisional | LV | RB | 83 | 5.92 | 4.75 | 4.11 – 5.39 |
| 6 | Bilal Powell◦ provisional | NYJ | RB | 131 | 5.45 | 4.74 | 4.15 – 5.32 |
| 7 | Mark Ingram | NO | RB | 208 | 5.03 | 4.65 | 4.13 – 5.17 |
| 8 | Kerwynn Williams◦ provisional | ARI | RB | 18 | 8.72 | 4.62 | 3.87 – 5.36 |
| 9 | Jay Ajayi | MIA | RB | 260 | 4.89 | 4.61 | 4.12 – 5.10 |
| 10 | Le'Veon Bell | PIT | RB | 261 | 4.86 | 4.59 | 4.10 – 5.08 |
| 11 | DeAndre Washington◦ provisional | LV | RB | 87 | 5.37 | 4.58 | 3.95 – 5.22 |
| 12 | Isaiah Crowell | CLE | RB | 198 | 4.81 | 4.52 | 3.99 – 5.05 |
| 13 | Devonta Freeman | ATL | RB | 227 | 4.75 | 4.51 | 4.00 – 5.02 |
| 14 | Chris Thompson◦ provisional | WAS | RB | 69 | 5.16 | 4.46 | 3.80 – 5.12 |
| 15 | Eddie Lacy◦ provisional | GB | RB | 71 | 5.07 | 4.44 | 3.78 – 5.10 |
| 16 | C.J. Prosise◦ provisional | SEA | RB | 30 | 5.73 | 4.41 | 3.69 – 5.13 |
| 17 | Duke Johnson◦ provisional | CLE | RB | 73 | 4.90 | 4.40 | 3.74 – 5.05 |
| 18 | Carlos Hyde | SF | RB | 218 | 4.54 | 4.38 | 3.87 – 4.90 |
| 19 | Kenyan Drake◦ provisional | MIA | RB | 33 | 5.42 | 4.38 | 3.66 – 5.10 |
| 20 | Danny Woodhead◦ provisional | LAC | RB | 19 | 6.11 | 4.37 | 3.63 – 5.12 |
| 21 | Matt Jones◦ provisional | WAS | RB | 99 | 4.65 | 4.35 | 3.73 – 4.97 |
| 22 | Darren Sproles◦ provisional | PHI | RB | 94 | 4.66 | 4.35 | 3.72 – 4.98 |
| 23 | Corey Grant◦ provisional | JAX | RB | 32 | 5.13 | 4.33 | 3.61 – 5.05 |
| 24 | Rex Burkhead◦ provisional | CIN | RB | 74 | 4.65 | 4.32 | 3.67 – 4.97 |
| 25 | Ameer Abdullah◦ provisional | DET | RB | 18 | 5.61 | 4.31 | 3.57 – 5.06 |
| 26 | DeMarco Murray | TEN | RB | 293 | 4.39 | 4.31 | 3.84 – 4.79 |
| 27 | Akeem Hunt◦ provisional | HOU | RB | 20 | 5.45 | 4.31 | 3.57 – 5.05 |
| 28 | Fozzy Whittaker◦ provisional | CAR | RB | 57 | 4.65 | 4.29 | 3.62 – 4.97 |
| 29 | Derrick Henry◦ provisional | TEN | RB | 110 | 4.45 | 4.29 | 3.68 – 4.89 |
| 30 | Terron Ward◦ provisional | ATL | RB | 31 | 4.87 | 4.28 | 3.56 – 5.00 |
| 31 | Shane Vereen◦ provisional | NYG | RB | 33 | 4.79 | 4.27 | 3.56 – 4.99 |
| 32 | Tevin Coleman◦ provisional | ATL | RB | 118 | 4.41 | 4.27 | 3.67 – 4.87 |
| 33 | Kenjon Barner◦ provisional | PHI | RB | 27 | 4.78 | 4.26 | 3.53 – 4.99 |
| 34 | Spencer Ware | KC | RB | 214 | 4.30 | 4.25 | 3.73 – 4.77 |
| 35 | Jacquizz Rodgers◦ provisional | TB | RB | 129 | 4.34 | 4.25 | 3.66 – 4.84 |
| 36 | Benny Cunningham◦ provisional | LA | RB | 21 | 4.81 | 4.24 | 3.50 – 4.98 |
| 37 | Dion Lewis◦ provisional | NE | RB | 64 | 4.42 | 4.24 | 3.57 – 4.91 |
| 38 | Andre Williams◦ provisional | LAC | RB | 18 | 4.83 | 4.24 | 3.49 – 4.98 |
| 39 | Kenneth Dixon◦ provisional | BAL | RB | 88 | 4.34 | 4.23 | 3.60 – 4.87 |
| 40 | Jonathan Grimes◦ provisional | HOU | RB | 23 | 4.57 | 4.22 | 3.48 – 4.96 |
| 41 | Kapri Bibbs◦ provisional | DEN | RB | 29 | 4.45 | 4.21 | 3.49 – 4.94 |
| 42 | Aaron Ripkowski◦ provisional | GB | RB | 34 | 4.41 | 4.21 | 3.50 – 4.93 |
| 43 | David Johnson | ARI | RB | 293 | 4.23 | 4.21 | 3.74 – 4.68 |
| 44 | Ryan Mathews◦ provisional | PHI | RB | 157 | 4.24 | 4.20 | 3.64 – 4.77 |
| 45 | James White◦ provisional | NE | RB | 39 | 4.26 | 4.19 | 3.48 – 4.90 |
| 46 | Alfred Blue◦ provisional | HOU | RB | 100 | 4.20 | 4.18 | 3.56 – 4.80 |
| 47 | Rob Kelley | WAS | RB | 168 | 4.19 | 4.18 | 3.63 – 4.74 |
| 48 | Alex Collins◦ provisional | SEA | RB | 31 | 4.03 | 4.15 | 3.43 – 4.87 |
| 49 | Tim Hightower◦ provisional | NO | RB | 133 | 4.12 | 4.15 | 3.56 – 4.73 |
| 50 | Peyton Barber◦ provisional | TB | RB | 55 | 4.05 | 4.14 | 3.46 – 4.82 |
| 51 | Cameron Artis-Payne◦ provisional | CAR | RB | 36 | 4.00 | 4.14 | 3.43 – 4.85 |
| 52 | Ka'Deem Carey◦ provisional | CHI | RB | 32 | 3.94 | 4.13 | 3.42 – 4.85 |
| 53 | Wendell Smallwood◦ provisional | PHI | RB | 77 | 4.05 | 4.13 | 3.49 – 4.78 |
| 54 | Paul Perkins◦ provisional | NYG | RB | 112 | 4.07 | 4.13 | 3.52 – 4.74 |
| 55 | Bobby Rainey◦ provisional | NYG | RB | 17 | 3.71 | 4.13 | 3.38 – 4.88 |
| 56 | Chris Johnson◦ provisional | ARI | RB | 25 | 3.80 | 4.12 | 3.39 – 4.86 |
| 57 | Darren McFadden◦ provisional | DAL | RB | 24 | 3.63 | 4.10 | 3.37 – 4.84 |
| 58 | Latavius Murray | LV | RB | 195 | 4.04 | 4.10 | 3.57 – 4.63 |
| 59 | Orleans Darkwa◦ provisional | NYG | RB | 30 | 3.70 | 4.10 | 3.38 – 4.82 |
| 60 | C.J. Anderson◦ provisional | DEN | RB | 110 | 3.97 | 4.09 | 3.48 – 4.70 |
| 61 | Byron Marshall◦ provisional | PHI | RB | 19 | 3.37 | 4.09 | 3.35 – 4.83 |
| 62 | Terrance West | BAL | RB | 193 | 4.01 | 4.09 | 3.55 – 4.62 |
| 63 | Jonathan Williams◦ provisional | BUF | RB | 27 | 3.48 | 4.08 | 3.35 – 4.80 |
| 64 | DuJuan Harris◦ provisional | SF | RB | 38 | 3.63 | 4.07 | 3.36 – 4.78 |
| 65 | Theo Riddick◦ provisional | DET | RB | 92 | 3.88 | 4.07 | 3.44 – 4.70 |
| 66 | Lamar Miller | HOU | RB | 268 | 4.00 | 4.07 | 3.58 – 4.55 |
| 67 | Christine Michael◦ provisional | GB | RB | 148 | 3.94 | 4.06 | 3.49 – 4.63 |
| 68 | Zach Zenner◦ provisional | DET | RB | 88 | 3.80 | 4.04 | 3.41 – 4.68 |
| 69 | Jamize Olawale◦ provisional | LV | RB | 17 | 2.76 | 4.04 | 3.29 – 4.79 |
| 70 | Denard Robinson◦ provisional | JAX | RB | 41 | 3.51 | 4.04 | 3.34 – 4.75 |
| 71 | Melvin Gordon | LAC | RB | 254 | 3.93 | 4.02 | 3.53 – 4.52 |
| 72 | Robert Turbin◦ provisional | IND | RB | 47 | 3.49 | 4.02 | 3.33 – 4.72 |
| 73 | Damien Williams◦ provisional | MIA | RB | 35 | 3.29 | 4.02 | 3.30 – 4.73 |
| 74 | Mike Davis◦ provisional | SF | RB | 19 | 2.63 | 4.01 | 3.27 – 4.76 |
| 75 | Mike Tolbert◦ provisional | CAR | RB | 35 | 3.26 | 4.01 | 3.30 – 4.73 |
| 76 | Giovani Bernard◦ provisional | CIN | RB | 91 | 3.70 | 4.01 | 3.38 – 4.64 |
| 77 | Frank Gore | IND | RB | 263 | 3.90 | 4.00 | 3.52 – 4.49 |
| 78 | Chris Ivory◦ provisional | JAX | RB | 117 | 3.75 | 4.00 | 3.40 – 4.60 |
| 79 | LeGarrette Blount | NE | RB | 299 | 3.88 | 3.99 | 3.52 – 4.46 |
| 80 | Alfred Morris◦ provisional | DAL | RB | 69 | 3.52 | 3.98 | 3.32 – 4.64 |
| 81 | Ronnie Hillman◦ provisional | LAC | RB | 41 | 3.20 | 3.98 | 3.28 – 4.68 |
| 82 | Arian Foster◦ provisional | MIA | RB | 22 | 2.50 | 3.98 | 3.24 – 4.71 |
| 83 | Malcolm Brown◦ provisional | LA | RB | 18 | 2.17 | 3.98 | 3.23 – 4.72 |
| 84 | John Kuhn◦ provisional | NO | RB | 18 | 2.06 | 3.97 | 3.22 – 4.71 |
| 85 | Jonathan Stewart | CAR | RB | 218 | 3.78 | 3.95 | 3.43 – 4.47 |
| 86 | Jeremy Hill | CIN | RB | 222 | 3.78 | 3.95 | 3.43 – 4.46 |
| 87 | Andre Ellington◦ provisional | ARI | RB | 34 | 2.82 | 3.94 | 3.23 – 4.66 |
| 88 | Josh Ferguson◦ provisional | IND | RB | 15 | 1.33 | 3.94 | 3.19 – 4.69 |
| 89 | DeAngelo Williams◦ provisional | PIT | RB | 98 | 3.50 | 3.92 | 3.30 – 4.55 |
| 90 | Matt Forte | NYJ | RB | 218 | 3.73 | 3.92 | 3.40 – 4.44 |
| 91 | Knile Davis◦ provisional | KC | RB | 18 | 1.56 | 3.92 | 3.17 – 4.66 |
| 92 | Jeremy Langford◦ provisional | CHI | RB | 62 | 3.23 | 3.92 | 3.24 – 4.59 |
| 93 | Kenneth Farrow◦ provisional | LAC | RB | 60 | 3.20 | 3.91 | 3.24 – 4.59 |
| 94 | T.J. Yeldon◦ provisional | JAX | RB | 130 | 3.58 | 3.91 | 3.32 – 4.50 |
| 95 | Justin Forsett◦ provisional | DEN | RB | 87 | 3.34 | 3.89 | 3.25 – 4.52 |
| 96 | Charcandrick West◦ provisional | KC | RB | 88 | 3.33 | 3.88 | 3.25 – 4.52 |
| 97 | Charles Sims◦ provisional | TB | RB | 51 | 2.92 | 3.88 | 3.19 – 4.57 |
| 98 | Devontae Booker | DEN | RB | 174 | 3.52 | 3.84 | 3.29 – 4.39 |
| 99 | Matt Asiata◦ provisional | MIN | RB | 121 | 3.32 | 3.81 | 3.22 – 4.41 |
| 100 | Thomas Rawls◦ provisional | SEA | RB | 109 | 3.20 | 3.79 | 3.18 – 4.40 |
| 101 | Jerick McKinnon◦ provisional | MIN | RB | 161 | 3.36 | 3.77 | 3.21 – 4.33 |
| 102 | Adrian Peterson◦ provisional | MIN | RB | 37 | 1.95 | 3.77 | 3.06 – 4.48 |
| 103 | Dwayne Washington◦ provisional | DET | RB | 90 | 2.94 | 3.74 | 3.11 – 4.37 |
| 104 | Shaun Draughn◦ provisional | SF | RB | 74 | 2.65 | 3.70 | 3.05 – 4.36 |
| 105 | Rashad Jennings | NYG | RB | 180 | 3.26 | 3.70 | 3.15 – 4.24 |
| 106 | James Starks◦ provisional | GB | RB | 64 | 2.27 | 3.64 | 2.97 – 4.31 |
| 107 | Doug Martin◦ provisional | TB | RB | 144 | 2.92 | 3.59 | 3.02 – 4.17 |
| 108 | Todd Gurley | LA | RB | 278 | 3.18 | 3.55 | 3.07 – 4.03 |
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).