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 · 2021
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
- 211
- 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 · 2021 · full board
| # | Player | Team | Pos | carrys | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Rashaad Penny◦ provisional | SEA | RB | 119 | 6.29 | 5.00 | 4.48 – 5.52 |
| 2 | Jonathan Taylor | IND | RB | 332 | 5.45 | 5.00 | 4.59 – 5.40 |
| 3 | Nick Chubb | CLE | RB | 228 | 5.52 | 4.92 | 4.47 – 5.37 |
| 4 | Tony Pollard◦ provisional | DAL | RB | 130 | 5.53 | 4.75 | 4.24 – 5.26 |
| 5 | Miles Sanders◦ provisional | PHI | RB | 138 | 5.48 | 4.75 | 4.24 – 5.26 |
| 6 | Dontrell Hilliard◦ provisional | TEN | RB | 56 | 6.25 | 4.69 | 4.11 – 5.27 |
| 7 | Travis Homer◦ provisional | SEA | RB | 21 | 8.43 | 4.65 | 4.03 – 5.27 |
| 8 | D'Ernest Johnson◦ provisional | CLE | RB | 100 | 5.34 | 4.62 | 4.08 – 5.15 |
| 9 | Chase Edmonds◦ provisional | ARI | RB | 116 | 5.10 | 4.57 | 4.04 – 5.09 |
| 10 | Justin Jackson◦ provisional | LAC | RB | 69 | 5.28 | 4.52 | 3.95 – 5.08 |
| 11 | Dalvin Cook | MIN | RB | 251 | 4.63 | 4.46 | 4.02 – 4.90 |
| 12 | Elijah Mitchell◦ provisional | SF | RB | 207 | 4.65 | 4.46 | 4.00 – 4.92 |
| 13 | Godwin Igwebuike◦ provisional | DET | RB | 18 | 6.56 | 4.45 | 3.83 – 5.08 |
| 14 | Aaron Jones◦ provisional | GB | RB | 171 | 4.67 | 4.45 | 3.97 – 4.93 |
| 15 | James Robinson◦ provisional | JAX | RB | 164 | 4.68 | 4.45 | 3.96 – 4.94 |
| 16 | Kareem Hunt◦ provisional | CLE | RB | 79 | 4.91 | 4.45 | 3.89 – 5.00 |
| 17 | Devin Singletary◦ provisional | BUF | RB | 188 | 4.63 | 4.44 | 3.97 – 4.91 |
| 18 | Damien Harris◦ provisional | NE | RB | 202 | 4.60 | 4.43 | 3.97 – 4.90 |
| 19 | Derrick Gore◦ provisional | KC | RB | 51 | 5.02 | 4.42 | 3.83 – 5.00 |
| 20 | Ty'Son Williams◦ provisional | BAL | RB | 35 | 5.29 | 4.42 | 3.81 – 5.02 |
| 21 | Darrell Henderson◦ provisional | LA | RB | 149 | 4.62 | 4.41 | 3.92 – 4.91 |
| 22 | Brandon Bolden◦ provisional | NE | RB | 45 | 5.07 | 4.41 | 3.82 – 5.00 |
| 23 | Nyheim Hines◦ provisional | IND | RB | 56 | 4.93 | 4.41 | 3.83 – 4.99 |
| 24 | Jordan Howard◦ provisional | PHI | RB | 86 | 4.72 | 4.40 | 3.85 – 4.95 |
| 25 | Melvin Gordon◦ provisional | DEN | RB | 203 | 4.52 | 4.39 | 3.93 – 4.86 |
| 26 | Leonard Fournette◦ provisional | TB | RB | 180 | 4.51 | 4.38 | 3.90 – 4.86 |
| 27 | Rhamondre Stevenson◦ provisional | NE | RB | 133 | 4.56 | 4.38 | 3.87 – 4.89 |
| 28 | Ke'Shawn Vaughn◦ provisional | TB | RB | 36 | 5.00 | 4.38 | 3.78 – 4.98 |
| 29 | Duke Johnson◦ provisional | MIA | RB | 71 | 4.65 | 4.37 | 3.80 – 4.93 |
| 30 | Javonte Williams◦ provisional | DEN | RB | 203 | 4.45 | 4.36 | 3.89 – 4.82 |
| 31 | Ryquell Armstead◦ provisional | JAX | RB | 15 | 5.33 | 4.34 | 3.71 – 4.97 |
| 32 | Qadree Ollison◦ provisional | ATL | RB | 21 | 5.00 | 4.34 | 3.72 – 4.96 |
| 33 | Christian McCaffrey◦ provisional | CAR | RB | 99 | 4.46 | 4.33 | 3.80 – 4.87 |
| 34 | Matt Breida◦ provisional | BUF | RB | 26 | 4.81 | 4.33 | 3.72 – 4.94 |
| 35 | Austin Ekeler◦ provisional | LAC | RB | 208 | 4.39 | 4.33 | 3.87 – 4.79 |
| 36 | Jermar Jefferson◦ provisional | DET | RB | 15 | 4.93 | 4.32 | 3.69 – 4.94 |
| 37 | Samaje Perine◦ provisional | CIN | RB | 55 | 4.47 | 4.31 | 3.73 – 4.89 |
| 38 | Jonathan Williams◦ provisional | WAS | RB | 17 | 4.65 | 4.30 | 3.67 – 4.93 |
| 39 | Clyde Edwards-Helaire◦ provisional | KC | RB | 119 | 4.34 | 4.30 | 3.78 – 4.82 |
| 40 | Devonta Freeman◦ provisional | BAL | RB | 133 | 4.33 | 4.29 | 3.78 – 4.80 |
| 41 | Chris Evans◦ provisional | CIN | RB | 17 | 4.53 | 4.29 | 3.66 – 4.92 |
| 42 | Michael Carter◦ provisional | NYJ | RB | 148 | 4.32 | 4.29 | 3.79 – 4.79 |
| 43 | AJ Dillon◦ provisional | GB | RB | 187 | 4.29 | 4.28 | 3.81 – 4.76 |
| 44 | J.D. McKissic◦ provisional | WAS | RB | 49 | 4.33 | 4.28 | 3.70 – 4.87 |
| 45 | Chris Carson◦ provisional | SEA | RB | 54 | 4.30 | 4.28 | 3.70 – 4.86 |
| 46 | Boston Scott◦ provisional | PHI | RB | 87 | 4.29 | 4.28 | 3.73 – 4.82 |
| 47 | JaMycal Hasty◦ provisional | SF | RB | 16 | 4.25 | 4.27 | 3.64 – 4.90 |
| 48 | Derrick Henry | TEN | RB | 220 | 4.27 | 4.27 | 3.81 – 4.73 |
| 49 | Corey Clement◦ provisional | DAL | RB | 33 | 4.24 | 4.27 | 3.66 – 4.87 |
| 50 | D'Onta Foreman◦ provisional | TEN | RB | 133 | 4.26 | 4.27 | 3.76 – 4.78 |
| 51 | Kenneth Gainwell◦ provisional | PHI | RB | 69 | 4.25 | 4.27 | 3.70 – 4.83 |
| 52 | Tevin Coleman◦ provisional | NYJ | RB | 84 | 4.24 | 4.26 | 3.71 – 4.81 |
| 53 | Ronald Jones◦ provisional | TB | RB | 101 | 4.24 | 4.26 | 3.73 – 4.80 |
| 54 | DeeJay Dallas◦ provisional | SEA | RB | 33 | 4.18 | 4.26 | 3.65 – 4.86 |
| 55 | Craig Reynolds◦ provisional | DET | RB | 55 | 4.18 | 4.25 | 3.67 – 4.83 |
| 56 | Latavius Murray◦ provisional | BAL | RB | 119 | 4.21 | 4.25 | 3.73 – 4.77 |
| 57 | Khalil Herbert◦ provisional | CHI | RB | 103 | 4.20 | 4.25 | 3.72 – 4.78 |
| 58 | Elijhaa Penny◦ provisional | NYG | RB | 25 | 4.04 | 4.25 | 3.63 – 4.86 |
| 59 | Damien Williams◦ provisional | CHI | RB | 40 | 4.10 | 4.24 | 3.65 – 4.84 |
| 60 | Trey Sermon◦ provisional | SF | RB | 41 | 4.07 | 4.24 | 3.64 – 4.84 |
| 61 | Ezekiel Elliott | DAL | RB | 240 | 4.20 | 4.23 | 3.79 – 4.68 |
| 62 | Patrick Taylor◦ provisional | GB | RB | 23 | 3.87 | 4.23 | 3.61 – 4.85 |
| 63 | Austin Walter◦ provisional | NYJ | RB | 26 | 3.88 | 4.23 | 3.61 – 4.84 |
| 64 | Kenyan Drake◦ provisional | LV | RB | 63 | 4.03 | 4.22 | 3.64 – 4.79 |
| 65 | Trayveon Williams◦ provisional | CIN | RB | 15 | 3.40 | 4.21 | 3.58 – 4.84 |
| 66 | Wayne Gallman◦ provisional | MIN | RB | 28 | 3.71 | 4.21 | 3.59 – 4.82 |
| 67 | Malcolm Brown◦ provisional | MIA | RB | 33 | 3.79 | 4.21 | 3.60 – 4.81 |
| 68 | Devontae Booker◦ provisional | NYG | RB | 145 | 4.09 | 4.20 | 3.70 – 4.70 |
| 69 | Jeremy McNichols◦ provisional | TEN | RB | 41 | 3.80 | 4.20 | 3.60 – 4.79 |
| 70 | D'Andre Swift◦ provisional | DET | RB | 151 | 4.09 | 4.19 | 3.70 – 4.69 |
| 71 | Marlon Mack◦ provisional | IND | RB | 28 | 3.61 | 4.19 | 3.58 – 4.81 |
| 72 | Ty Johnson◦ provisional | NYJ | RB | 61 | 3.90 | 4.19 | 3.61 – 4.76 |
| 73 | Peyton Barber◦ provisional | LV | RB | 55 | 3.85 | 4.19 | 3.61 – 4.77 |
| 74 | Jaret Patterson◦ provisional | WAS | RB | 68 | 3.91 | 4.18 | 3.62 – 4.75 |
| 75 | Cordarrelle Patterson◦ provisional | ATL | RB | 153 | 4.04 | 4.17 | 3.68 – 4.67 |
| 76 | Joe Mixon | CIN | RB | 294 | 4.10 | 4.17 | 3.75 – 4.59 |
| 77 | Sony Michel◦ provisional | LA | RB | 208 | 4.06 | 4.17 | 3.71 – 4.63 |
| 78 | Eno Benjamin◦ provisional | ARI | RB | 34 | 3.47 | 4.16 | 3.56 – 4.76 |
| 79 | Josh Jacobs | LV | RB | 217 | 4.02 | 4.14 | 3.69 – 4.60 |
| 80 | Antonio Gibson | WAS | RB | 259 | 4.01 | 4.13 | 3.69 – 4.56 |
| 81 | Jamaal Williams◦ provisional | DET | RB | 153 | 3.93 | 4.13 | 3.63 – 4.62 |
| 82 | Jeff Wilson◦ provisional | SF | RB | 79 | 3.72 | 4.12 | 3.57 – 4.68 |
| 83 | Alex Collins◦ provisional | SEA | RB | 108 | 3.81 | 4.11 | 3.58 – 4.64 |
| 84 | Joshua Kelley◦ provisional | LAC | RB | 33 | 3.09 | 4.11 | 3.51 – 4.72 |
| 85 | Darrel Williams◦ provisional | KC | RB | 144 | 3.88 | 4.11 | 3.61 – 4.61 |
| 86 | J.J. Taylor◦ provisional | NE | RB | 19 | 1.95 | 4.08 | 3.46 – 4.70 |
| 87 | Carlos Hyde◦ provisional | JAX | RB | 72 | 3.51 | 4.08 | 3.52 – 4.64 |
| 88 | Ameer Abdullah◦ provisional | CAR | RB | 51 | 3.25 | 4.07 | 3.49 – 4.66 |
| 89 | Dare Ogunbowale◦ provisional | JAX | RB | 44 | 3.11 | 4.07 | 3.48 – 4.66 |
| 90 | David Johnson◦ provisional | HOU | RB | 67 | 3.40 | 4.06 | 3.49 – 4.63 |
| 91 | Zack Moss◦ provisional | BUF | RB | 96 | 3.59 | 4.06 | 3.52 – 4.60 |
| 92 | Najee Harris | PIT | RB | 307 | 3.91 | 4.06 | 3.64 – 4.47 |
| 93 | Benny Snell◦ provisional | PIT | RB | 36 | 2.72 | 4.05 | 3.44 – 4.65 |
| 94 | Alexander Mattison◦ provisional | MIN | RB | 135 | 3.64 | 4.02 | 3.52 – 4.53 |
| 95 | Mike Davis◦ provisional | ATL | RB | 138 | 3.64 | 4.02 | 3.52 – 4.53 |
| 96 | David Montgomery | CHI | RB | 225 | 3.77 | 4.01 | 3.56 – 4.47 |
| 97 | Adrian Peterson◦ provisional | SEA | RB | 38 | 2.58 | 4.01 | 3.41 – 4.61 |
| 98 | Royce Freeman◦ provisional | HOU | RB | 56 | 3.02 | 4.01 | 3.43 – 4.59 |
| 99 | Saquon Barkley◦ provisional | NYG | RB | 162 | 3.66 | 4.01 | 3.52 – 4.50 |
| 100 | James Conner◦ provisional | ARI | RB | 202 | 3.72 | 4.00 | 3.54 – 4.47 |
| 101 | Le'Veon Bell◦ provisional | TB | RB | 40 | 2.58 | 4.00 | 3.40 – 4.60 |
| 102 | Larry Rountree III◦ provisional | LAC | RB | 36 | 2.42 | 4.00 | 3.40 – 4.60 |
| 103 | Rex Burkhead◦ provisional | HOU | RB | 122 | 3.50 | 3.99 | 3.47 – 4.51 |
| 104 | Alvin Kamara | NO | RB | 241 | 3.73 | 3.98 | 3.54 – 4.43 |
| 105 | Salvon Ahmed◦ provisional | MIA | RB | 54 | 2.76 | 3.96 | 3.38 – 4.54 |
| 106 | Chuba Hubbard◦ provisional | CAR | RB | 172 | 3.56 | 3.95 | 3.47 – 4.43 |
| 107 | Myles Gaskin◦ provisional | MIA | RB | 173 | 3.54 | 3.94 | 3.46 – 4.42 |
| 108 | Tony Jones◦ provisional | NO | RB | 54 | 2.63 | 3.94 | 3.36 – 4.52 |
| 109 | Mark Ingram◦ provisional | NO | RB | 160 | 3.46 | 3.92 | 3.43 – 4.41 |
| 110 | Phillip Lindsay◦ provisional | MIA | RB | 88 | 2.83 | 3.85 | 3.30 – 4.39 |
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).