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 · 2017
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
- 2071
- 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 · 2017 · full board
| # | Player | Team | Pos | carrys | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Alvin Kamara◦ provisional | NO | RB | 121 | 6.03 | 4.15 | 3.93 – 4.38 |
| 2 | Kareem Hunt◦ provisional | KC | RB | 272 | 4.88 | 4.14 | 3.93 – 4.36 |
| 3 | Mark Ingram◦ provisional | NO | RB | 230 | 4.89 | 4.13 | 3.91 – 4.35 |
| 4 | Todd Gurley◦ provisional | LA | RB | 279 | 4.68 | 4.12 | 3.90 – 4.33 |
| 5 | Dion Lewis◦ provisional | NE | RB | 180 | 4.98 | 4.12 | 3.90 – 4.34 |
| 6 | Corey Grant◦ provisional | JAX | RB | 30 | 8.27 | 4.10 | 3.88 – 4.33 |
| 7 | Aaron Jones◦ provisional | GB | RB | 81 | 5.53 | 4.10 | 3.88 – 4.33 |
| 8 | Alex Collins◦ provisional | BAL | RB | 212 | 4.59 | 4.10 | 3.88 – 4.31 |
| 9 | Kenyan Drake◦ provisional | MIA | RB | 134 | 4.82 | 4.09 | 3.87 – 4.31 |
| 10 | Alfred Morris◦ provisional | DAL | RB | 115 | 4.76 | 4.08 | 3.86 – 4.30 |
| 11 | Austin Ekeler◦ provisional | LAC | RB | 47 | 5.53 | 4.08 | 3.85 – 4.30 |
| 12 | Devonta Freeman◦ provisional | ATL | RB | 196 | 4.41 | 4.08 | 3.86 – 4.30 |
| 13 | LeGarrette Blount◦ provisional | PHI | RB | 174 | 4.41 | 4.07 | 3.85 – 4.29 |
| 14 | T.J. Yeldon◦ provisional | JAX | RB | 49 | 5.16 | 4.07 | 3.84 – 4.30 |
| 15 | Orleans Darkwa◦ provisional | NYG | RB | 172 | 4.38 | 4.07 | 3.85 – 4.29 |
| 16 | Dalvin Cook◦ provisional | MIN | RB | 74 | 4.78 | 4.07 | 3.84 – 4.29 |
| 17 | Marshawn Lynch◦ provisional | LV | RB | 207 | 4.30 | 4.07 | 3.85 – 4.29 |
| 18 | Bilal Powell◦ provisional | NYJ | RB | 178 | 4.34 | 4.07 | 3.85 – 4.29 |
| 19 | Jalen Richard◦ provisional | LV | RB | 56 | 4.91 | 4.07 | 3.84 – 4.29 |
| 20 | Matt Breida◦ provisional | SF | RB | 105 | 4.43 | 4.06 | 3.84 – 4.29 |
| 21 | Chris Thompson◦ provisional | WAS | RB | 64 | 4.59 | 4.06 | 3.84 – 4.29 |
| 22 | Giovani Bernard◦ provisional | CIN | RB | 105 | 4.36 | 4.06 | 3.84 – 4.28 |
| 23 | Derrick Henry◦ provisional | TEN | RB | 176 | 4.23 | 4.06 | 3.84 – 4.28 |
| 24 | Jay Ajayi◦ provisional | PHI | RB | 208 | 4.20 | 4.06 | 3.84 – 4.28 |
| 25 | Wayne Gallman◦ provisional | NYG | RB | 111 | 4.29 | 4.06 | 3.83 – 4.28 |
| 26 | Cameron Artis-Payne◦ provisional | CAR | RB | 18 | 5.28 | 4.06 | 3.83 – 4.28 |
| 27 | Corey Clement◦ provisional | PHI | RB | 75 | 4.31 | 4.05 | 3.83 – 4.28 |
| 28 | Tarik Cohen◦ provisional | CHI | RB | 87 | 4.25 | 4.05 | 3.83 – 4.28 |
| 29 | Jamaal Charles◦ provisional | DEN | RB | 69 | 4.29 | 4.05 | 3.83 – 4.28 |
| 30 | Isaiah Crowell◦ provisional | CLE | RB | 207 | 4.13 | 4.05 | 3.83 – 4.27 |
| 31 | Duke Johnson◦ provisional | CLE | RB | 82 | 4.24 | 4.05 | 3.83 – 4.28 |
| 32 | C.J. Anderson◦ provisional | DEN | RB | 245 | 4.11 | 4.05 | 3.83 – 4.27 |
| 33 | James Conner◦ provisional | PIT | RB | 32 | 4.50 | 4.05 | 3.82 – 4.28 |
| 34 | D'Onta Foreman◦ provisional | HOU | RB | 78 | 4.19 | 4.05 | 3.83 – 4.27 |
| 35 | Chris Carson◦ provisional | SEA | RB | 49 | 4.24 | 4.05 | 3.82 – 4.28 |
| 36 | Rod Smith◦ provisional | DAL | RB | 55 | 4.22 | 4.05 | 3.82 – 4.27 |
| 37 | Terron Ward◦ provisional | ATL | RB | 30 | 4.30 | 4.05 | 3.82 – 4.28 |
| 38 | Charles Sims◦ provisional | TB | RB | 22 | 4.32 | 4.05 | 3.82 – 4.28 |
| 39 | Rex Burkhead◦ provisional | NE | RB | 64 | 4.13 | 4.05 | 3.82 – 4.27 |
| 40 | Jordan Howard◦ provisional | CHI | RB | 276 | 4.07 | 4.05 | 3.83 – 4.26 |
| 41 | Ezekiel Elliott◦ provisional | DAL | RB | 242 | 4.06 | 4.05 | 3.83 – 4.26 |
| 42 | Travaris Cadet◦ provisional | BUF | RB | 23 | 4.17 | 4.05 | 3.82 – 4.27 |
| 43 | Stevan Ridley◦ provisional | PIT | RB | 26 | 4.15 | 4.05 | 3.82 – 4.27 |
| 44 | J.D. McKissic◦ provisional | SEA | RB | 46 | 4.07 | 4.04 | 3.82 – 4.27 |
| 45 | Darren Sproles◦ provisional | PHI | RB | 15 | 4.07 | 4.04 | 3.82 – 4.27 |
| 46 | Charcandrick West◦ provisional | KC | RB | 18 | 4.00 | 4.04 | 3.82 – 4.27 |
| 47 | Elijhaa Penny◦ provisional | ARI | RB | 31 | 4.00 | 4.04 | 3.82 – 4.27 |
| 48 | James White◦ provisional | NE | RB | 43 | 3.98 | 4.04 | 3.82 – 4.27 |
| 49 | Tevin Coleman◦ provisional | ATL | RB | 156 | 4.03 | 4.04 | 3.82 – 4.26 |
| 50 | Damien Williams◦ provisional | MIA | RB | 46 | 3.93 | 4.04 | 3.82 – 4.27 |
| 51 | Tion Green◦ provisional | DET | RB | 42 | 3.93 | 4.04 | 3.82 – 4.27 |
| 52 | Kapri Bibbs◦ provisional | WAS | RB | 21 | 3.76 | 4.04 | 3.81 – 4.27 |
| 53 | Kenjon Barner◦ provisional | PHI | RB | 16 | 3.56 | 4.04 | 3.81 – 4.27 |
| 54 | Malcolm Brown◦ provisional | LA | RB | 63 | 3.90 | 4.04 | 3.81 – 4.27 |
| 55 | Le'Veon Bell◦ provisional | PIT | RB | 322 | 4.01 | 4.04 | 3.83 – 4.25 |
| 56 | Peyton Barber◦ provisional | TB | RB | 108 | 3.92 | 4.04 | 3.81 – 4.26 |
| 57 | Jacquizz Rodgers◦ provisional | TB | RB | 64 | 3.81 | 4.04 | 3.81 – 4.26 |
| 58 | Wendell Smallwood◦ provisional | PHI | RB | 47 | 3.70 | 4.04 | 3.81 – 4.26 |
| 59 | Marlon Mack◦ provisional | IND | RB | 93 | 3.85 | 4.04 | 3.81 – 4.26 |
| 60 | Shane Vereen◦ provisional | NYG | RB | 45 | 3.64 | 4.04 | 3.81 – 4.26 |
| 61 | Mike Tolbert◦ provisional | BUF | RB | 66 | 3.74 | 4.04 | 3.81 – 4.26 |
| 62 | Devontae Booker◦ provisional | DEN | RB | 79 | 3.78 | 4.03 | 3.81 – 4.26 |
| 63 | LeSean McCoy◦ provisional | BUF | RB | 287 | 3.97 | 4.03 | 3.82 – 4.25 |
| 64 | Terrance West◦ provisional | BAL | RB | 40 | 3.45 | 4.03 | 3.81 – 4.26 |
| 65 | Alfred Blue◦ provisional | HOU | RB | 71 | 3.69 | 4.03 | 3.81 – 4.26 |
| 66 | Andre Ellington◦ provisional | HOU | RB | 20 | 2.75 | 4.03 | 3.80 – 4.26 |
| 67 | Javorius Allen◦ provisional | BAL | RB | 153 | 3.86 | 4.03 | 3.81 – 4.25 |
| 68 | Latavius Murray◦ provisional | MIN | RB | 216 | 3.90 | 4.03 | 3.81 – 4.25 |
| 69 | Carlos Hyde◦ provisional | SF | RB | 240 | 3.91 | 4.03 | 3.81 – 4.25 |
| 70 | Jeremy Hill◦ provisional | CIN | RB | 37 | 3.14 | 4.03 | 3.80 – 4.26 |
| 71 | Matt Forte◦ provisional | NYJ | RB | 103 | 3.70 | 4.03 | 3.80 – 4.25 |
| 72 | Mike Gillislee◦ provisional | NE | RB | 104 | 3.68 | 4.03 | 3.80 – 4.25 |
| 73 | Jerick McKinnon◦ provisional | MIN | RB | 151 | 3.79 | 4.03 | 3.81 – 4.25 |
| 74 | Christian McCaffrey◦ provisional | CAR | RB | 117 | 3.72 | 4.03 | 3.80 – 4.25 |
| 75 | Dwayne Washington◦ provisional | DET | RB | 20 | 2.20 | 4.03 | 3.80 – 4.25 |
| 76 | Melvin Gordon◦ provisional | LAC | RB | 284 | 3.89 | 4.03 | 3.81 – 4.24 |
| 77 | Robert Turbin◦ provisional | IND | RB | 23 | 2.30 | 4.03 | 3.80 – 4.25 |
| 78 | Leonard Fournette◦ provisional | JAX | RB | 269 | 3.87 | 4.02 | 3.81 – 4.24 |
| 79 | Elijah McGuire◦ provisional | NYJ | RB | 88 | 3.53 | 4.02 | 3.80 – 4.25 |
| 80 | Mike Davis◦ provisional | SEA | RB | 68 | 3.28 | 4.02 | 3.79 – 4.25 |
| 81 | Theo Riddick◦ provisional | DET | RB | 84 | 3.40 | 4.02 | 3.79 – 4.24 |
| 82 | Rob Kelley◦ provisional | WAS | RB | 62 | 3.13 | 4.02 | 3.79 – 4.24 |
| 83 | Kerwynn Williams◦ provisional | ARI | RB | 120 | 3.55 | 4.02 | 3.79 – 4.24 |
| 84 | Branden Oliver◦ provisional | LAC | RB | 35 | 2.37 | 4.02 | 3.79 – 4.24 |
| 85 | Jamaal Williams◦ provisional | GB | RB | 153 | 3.63 | 4.02 | 3.80 – 4.24 |
| 86 | Chris Johnson◦ provisional | ARI | RB | 45 | 2.53 | 4.01 | 3.79 – 4.24 |
| 87 | Lamar Miller◦ provisional | HOU | RB | 238 | 3.73 | 4.01 | 3.80 – 4.23 |
| 88 | Chris Ivory◦ provisional | JAX | RB | 112 | 3.41 | 4.01 | 3.79 – 4.24 |
| 89 | Paul Perkins◦ provisional | NYG | RB | 41 | 2.20 | 4.01 | 3.78 – 4.24 |
| 90 | Thomas Rawls◦ provisional | SEA | RB | 58 | 2.71 | 4.01 | 3.78 – 4.23 |
| 91 | DeAndre Washington◦ provisional | LV | RB | 57 | 2.68 | 4.01 | 3.78 – 4.23 |
| 92 | DeMarco Murray◦ provisional | TEN | RB | 184 | 3.58 | 4.01 | 3.79 – 4.23 |
| 93 | Frank Gore◦ provisional | IND | RB | 261 | 3.68 | 4.00 | 3.79 – 4.22 |
| 94 | Joe Mixon◦ provisional | CIN | RB | 178 | 3.52 | 4.00 | 3.78 – 4.22 |
| 95 | Adrian Peterson◦ provisional | ARI | RB | 156 | 3.39 | 4.00 | 3.78 – 4.22 |
| 96 | Samaje Perine◦ provisional | WAS | RB | 175 | 3.45 | 4.00 | 3.78 – 4.22 |
| 97 | Eddie Lacy◦ provisional | SEA | RB | 69 | 2.59 | 4.00 | 3.77 – 4.22 |
| 98 | Ameer Abdullah◦ provisional | DET | RB | 165 | 3.35 | 3.99 | 3.77 – 4.21 |
| 99 | Jonathan Stewart◦ provisional | CAR | RB | 198 | 3.43 | 3.99 | 3.77 – 4.21 |
| 100 | Doug Martin◦ provisional | TB | RB | 139 | 2.94 | 3.97 | 3.75 – 4.20 |
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).