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.
EPA per target · 2016
Mean EPA per target, shrunk within position.
- Beats raw by
- 24.4%
- lower out-of-sample error
- RMSE raw → shrunk
- 0.38 → 0.29
- odd vs. even weeks
- Split-half reliability
- 0.13
- how repeatable the raw stat is
- Stabilizes at
- 327
- targets to trust the number
shrunkrawthe shrink90% CI
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.
EPA per target · 2016 · full board
| # | Player | Team | Pos | targets | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Cole Beasley◦ provisional | DAL | WR | 98 | +0.63 | +0.31 | +0.18 – +0.43 |
| 2 | Jordy Nelson◦ provisional | GB | WR | 152 | +0.48 | +0.29 | +0.17 – +0.41 |
| 3 | Adam Thielen◦ provisional | MIN | WR | 92 | +0.55 | +0.28 | +0.15 – +0.41 |
| 4 | Julio Jones◦ provisional | ATL | WR | 130 | +0.47 | +0.28 | +0.16 – +0.41 |
| 5 | Doug Baldwin◦ provisional | SEA | WR | 126 | +0.47 | +0.28 | +0.16 – +0.40 |
| 6 | Brandin Cooks◦ provisional | NO | WR | 117 | +0.47 | +0.28 | +0.15 – +0.40 |
| 7 | Pierre Garcon◦ provisional | WAS | WR | 114 | +0.47 | +0.28 | +0.15 – +0.40 |
| 8 | A.J. Green◦ provisional | CIN | WR | 100 | +0.49 | +0.27 | +0.15 – +0.40 |
| 9 | T.Y. Hilton◦ provisional | IND | WR | 157 | +0.38 | +0.27 | +0.15 – +0.39 |
| 10 | Mike Evans◦ provisional | TB | WR | 175 | +0.37 | +0.26 | +0.15 – +0.38 |
| 11 | Stefon Diggs◦ provisional | MIN | WR | 112 | +0.41 | +0.26 | +0.13 – +0.39 |
| 12 | Taylor Gabriel◦ provisional | ATL | WR | 50 | +0.59 | +0.26 | +0.12 – +0.39 |
| 13 | Marvin Jones◦ provisional | DET | WR | 103 | +0.42 | +0.26 | +0.13 – +0.39 |
| 14 | Mohamed Sanu◦ provisional | ATL | WR | 82 | +0.44 | +0.26 | +0.13 – +0.39 |
| 15 | Terrance Williams◦ provisional | DAL | WR | 61 | +0.48 | +0.25 | +0.12 – +0.39 |
| 16 | Chris Hogan◦ provisional | NE | WR | 58 | +0.48 | +0.25 | +0.12 – +0.38 |
| 17 | Davante Adams◦ provisional | GB | WR | 123 | +0.35 | +0.25 | +0.12 – +0.37 |
| 18 | Steve Smith◦ provisional | BAL | WR | 104 | +0.36 | +0.25 | +0.12 – +0.37 |
| 19 | Willie Snead◦ provisional | NO | WR | 104 | +0.36 | +0.25 | +0.12 – +0.37 |
| 20 | Malcolm Mitchell◦ provisional | NE | WR | 48 | +0.50 | +0.25 | +0.11 – +0.38 |
| 21 | Danny Amendola◦ provisional | NE | WR | 29 | +0.62 | +0.24 | +0.10 – +0.38 |
| 22 | Antonio Brown◦ provisional | PIT | WR | 157 | +0.31 | +0.24 | +0.12 – +0.36 |
| 23 | Eli Rogers◦ provisional | PIT | WR | 66 | +0.39 | +0.24 | +0.11 – +0.37 |
| 24 | DeSean Jackson◦ provisional | WAS | WR | 100 | +0.33 | +0.24 | +0.11 – +0.36 |
| 25 | Aldrick Robinson◦ provisional | ATL | WR | 32 | +0.53 | +0.24 | +0.10 – +0.38 |
| 26 | Geronimo Allison◦ provisional | GB | WR | 22 | +0.64 | +0.24 | +0.10 – +0.38 |
| 27 | Cobi Hamilton◦ provisional | PIT | WR | 28 | +0.55 | +0.24 | +0.10 – +0.38 |
| 28 | Kenny Britt◦ provisional | LA | WR | 111 | +0.31 | +0.23 | +0.11 – +0.36 |
| 29 | Randall Cobb◦ provisional | GB | WR | 84 | +0.32 | +0.23 | +0.10 – +0.36 |
| 30 | Justin Hardy◦ provisional | ATL | WR | 31 | +0.47 | +0.23 | +0.09 – +0.37 |
| 31 | Mike Wallace◦ provisional | BAL | WR | 117 | +0.29 | +0.23 | +0.11 – +0.36 |
| 32 | Jarvis Landry◦ provisional | MIA | WR | 133 | +0.28 | +0.23 | +0.11 – +0.35 |
| 33 | Rod Streater◦ provisional | SF | WR | 27 | +0.48 | +0.23 | +0.09 – +0.37 |
| 34 | Jamison Crowder◦ provisional | WAS | WR | 99 | +0.30 | +0.23 | +0.10 – +0.36 |
| 35 | Anquan Boldin◦ provisional | DET | WR | 95 | +0.30 | +0.23 | +0.10 – +0.36 |
| 36 | Rishard Matthews◦ provisional | TEN | WR | 109 | +0.29 | +0.23 | +0.10 – +0.35 |
| 37 | Brandon LaFell◦ provisional | CIN | WR | 107 | +0.29 | +0.23 | +0.10 – +0.35 |
| 38 | Russell Shepard◦ provisional | TB | WR | 40 | +0.38 | +0.23 | +0.09 – +0.36 |
| 39 | Michael Crabtree◦ provisional | LV | WR | 147 | +0.26 | +0.23 | +0.10 – +0.35 |
| 40 | Terrelle Pryor◦ provisional | CLE | WR | 142 | +0.26 | +0.23 | +0.10 – +0.35 |
| 41 | Dez Bryant◦ provisional | DAL | WR | 98 | +0.28 | +0.22 | +0.10 – +0.35 |
| 42 | Eddie Royal◦ provisional | CHI | WR | 43 | +0.34 | +0.22 | +0.09 – +0.36 |
| 43 | Julian Edelman◦ provisional | NE | WR | 160 | +0.25 | +0.22 | +0.10 – +0.34 |
| 44 | Dontrelle Inman◦ provisional | LAC | WR | 97 | +0.27 | +0.22 | +0.09 – +0.35 |
| 45 | Paul Richardson◦ provisional | SEA | WR | 36 | +0.34 | +0.22 | +0.08 – +0.36 |
| 46 | Robert Woods◦ provisional | BUF | WR | 76 | +0.28 | +0.22 | +0.09 – +0.35 |
| 47 | Marquess Wilson◦ provisional | CHI | WR | 16 | +0.46 | +0.22 | +0.08 – +0.36 |
| 48 | Amari Cooper◦ provisional | LV | WR | 135 | +0.25 | +0.22 | +0.10 – +0.34 |
| 49 | Cameron Meredith◦ provisional | CHI | WR | 97 | +0.26 | +0.22 | +0.09 – +0.35 |
| 50 | Chris Harper◦ provisional | SF | WR | 21 | +0.39 | +0.22 | +0.08 – +0.36 |
| 51 | Tyler Lockett◦ provisional | SEA | WR | 66 | +0.27 | +0.22 | +0.09 – +0.35 |
| 52 | Deonte Thompson◦ provisional | CHI | WR | 36 | +0.31 | +0.22 | +0.08 – +0.36 |
| 53 | Eric Decker◦ provisional | NYJ | WR | 21 | +0.36 | +0.22 | +0.08 – +0.36 |
| 54 | Bryan Walters◦ provisional | JAX | WR | 34 | +0.30 | +0.22 | +0.08 – +0.36 |
| 55 | Jarius Wright◦ provisional | MIN | WR | 14 | +0.38 | +0.22 | +0.07 – +0.36 |
| 56 | Odell Beckham Jr.◦ provisional | NYG | WR | 169 | +0.23 | +0.21 | +0.10 – +0.33 |
| 57 | J.J. Nelson◦ provisional | ARI | WR | 75 | +0.24 | +0.21 | +0.08 – +0.35 |
| 58 | Travis Benjamin◦ provisional | LAC | WR | 75 | +0.24 | +0.21 | +0.08 – +0.35 |
| 59 | Sammy Watkins◦ provisional | BUF | WR | 52 | +0.25 | +0.21 | +0.08 – +0.35 |
| 60 | Paul Turner◦ provisional | PHI | WR | 14 | +0.34 | +0.21 | +0.07 – +0.36 |
| 61 | Jordan Taylor◦ provisional | DEN | WR | 25 | +0.28 | +0.21 | +0.07 – +0.35 |
| 62 | Michael Thomas◦ provisional | NO | WR | 121 | +0.23 | +0.21 | +0.09 – +0.34 |
| 63 | Brandon Coleman◦ provisional | NO | WR | 38 | +0.25 | +0.21 | +0.08 – +0.35 |
| 64 | Andre Roberts◦ provisional | DET | WR | 25 | +0.26 | +0.21 | +0.07 – +0.35 |
| 65 | DeMarcus Ayers◦ provisional | PIT | WR | 13 | +0.29 | +0.21 | +0.07 – +0.35 |
| 66 | DeVante Parker◦ provisional | MIA | WR | 87 | +0.22 | +0.21 | +0.08 – +0.34 |
| 67 | Chris Conley◦ provisional | KC | WR | 69 | +0.23 | +0.21 | +0.08 – +0.34 |
| 68 | Andrew Hawkins◦ provisional | CLE | WR | 54 | +0.22 | +0.21 | +0.08 – +0.34 |
| 69 | Kendall Wright◦ provisional | TEN | WR | 43 | +0.22 | +0.21 | +0.07 – +0.35 |
| 70 | Tyreek Hill◦ provisional | KC | WR | 83 | +0.21 | +0.21 | +0.08 – +0.34 |
| 71 | Larry Fitzgerald◦ provisional | ARI | WR | 150 | +0.20 | +0.21 | +0.09 – +0.33 |
| 72 | Sterling Shepard◦ provisional | NYG | WR | 105 | +0.20 | +0.21 | +0.08 – +0.33 |
| 73 | Justin Hunter◦ provisional | BUF | WR | 24 | +0.18 | +0.21 | +0.07 – +0.35 |
| 74 | Kamar Aiken◦ provisional | BAL | WR | 50 | +0.18 | +0.21 | +0.07 – +0.34 |
| 75 | Donte Moncrief◦ provisional | IND | WR | 56 | +0.18 | +0.21 | +0.07 – +0.34 |
| 76 | Cody Latimer◦ provisional | DEN | WR | 15 | +0.12 | +0.20 | +0.06 – +0.35 |
| 77 | Josh Bellamy◦ provisional | CHI | WR | 38 | +0.17 | +0.20 | +0.07 – +0.34 |
| 78 | Adam Humphries◦ provisional | TB | WR | 84 | +0.18 | +0.20 | +0.07 – +0.33 |
| 79 | Kelvin Benjamin◦ provisional | CAR | WR | 118 | +0.19 | +0.20 | +0.08 – +0.33 |
| 80 | Golden Tate◦ provisional | DET | WR | 136 | +0.18 | +0.20 | +0.08 – +0.32 |
| 81 | Victor Cruz◦ provisional | NYG | WR | 72 | +0.17 | +0.20 | +0.07 – +0.33 |
| 82 | Ted Ginn◦ provisional | CAR | WR | 95 | +0.17 | +0.20 | +0.07 – +0.33 |
| 83 | Keith Mumphery◦ provisional | HOU | WR | 12 | -0.02 | +0.20 | +0.06 – +0.34 |
| 84 | Andre Holmes◦ provisional | LV | WR | 25 | +0.09 | +0.20 | +0.06 – +0.34 |
| 85 | Jeff Janis◦ provisional | GB | WR | 19 | +0.05 | +0.20 | +0.06 – +0.34 |
| 86 | Kenny Stills◦ provisional | MIA | WR | 81 | +0.16 | +0.20 | +0.07 – +0.33 |
| 87 | Bennie Fowler◦ provisional | DEN | WR | 24 | +0.07 | +0.20 | +0.06 – +0.34 |
| 88 | Dorial Green-Beckham◦ provisional | PHI | WR | 74 | +0.16 | +0.20 | +0.07 – +0.33 |
| 89 | Demaryius Thomas◦ provisional | DEN | WR | 145 | +0.18 | +0.20 | +0.08 – +0.32 |
| 90 | Jaron Brown◦ provisional | ARI | WR | 23 | +0.06 | +0.20 | +0.06 – +0.34 |
| 91 | Tyrell Williams◦ provisional | LAC | WR | 119 | +0.17 | +0.20 | +0.07 – +0.32 |
| 92 | Maurice Harris◦ provisional | WAS | WR | 12 | -0.08 | +0.20 | +0.06 – +0.34 |
| 93 | James Wright◦ provisional | CIN | WR | 19 | +0.02 | +0.20 | +0.06 – +0.34 |
| 94 | Devin Funchess◦ provisional | CAR | WR | 59 | +0.14 | +0.20 | +0.06 – +0.33 |
| 95 | Brice Butler◦ provisional | DAL | WR | 32 | +0.07 | +0.20 | +0.06 – +0.34 |
| 96 | Brittan Golden◦ provisional | ARI | WR | 14 | -0.09 | +0.20 | +0.05 – +0.34 |
| 97 | Sammie Coates◦ provisional | PIT | WR | 49 | +0.11 | +0.20 | +0.06 – +0.33 |
| 98 | Cody Core◦ provisional | CIN | WR | 27 | +0.04 | +0.20 | +0.06 – +0.34 |
| 99 | Walt Powell◦ provisional | BUF | WR | 25 | +0.03 | +0.20 | +0.06 – +0.34 |
| 100 | Aaron Burbridge◦ provisional | SF | WR | 16 | -0.07 | +0.20 | +0.05 – +0.34 |
| 101 | Marqise Lee◦ provisional | JAX | WR | 105 | +0.15 | +0.19 | +0.07 – +0.32 |
| 102 | T.J. Jones◦ provisional | DET | WR | 15 | -0.13 | +0.19 | +0.05 – +0.34 |
| 103 | Josh Huff◦ provisional | TB | WR | 23 | -0.02 | +0.19 | +0.05 – +0.33 |
| 104 | Rashard Higgins◦ provisional | CLE | WR | 12 | -0.24 | +0.19 | +0.05 – +0.34 |
| 105 | Ricardo Louis◦ provisional | CLE | WR | 36 | +0.05 | +0.19 | +0.06 – +0.33 |
| 106 | Ryan Grant◦ provisional | WAS | WR | 19 | -0.09 | +0.19 | +0.05 – +0.33 |
| 107 | Cecil Shorts◦ provisional | TB | WR | 27 | -0.01 | +0.19 | +0.05 – +0.33 |
| 108 | Chester Rogers◦ provisional | IND | WR | 34 | +0.03 | +0.19 | +0.05 – +0.33 |
| 109 | Bryce Treggs◦ provisional | PHI | WR | 12 | -0.29 | +0.19 | +0.05 – +0.33 |
| 110 | Charles D. Johnson◦ provisional | MIN | WR | 37 | +0.03 | +0.19 | +0.05 – +0.33 |
| 111 | Phillip Dorsett◦ provisional | IND | WR | 59 | +0.09 | +0.19 | +0.06 – +0.32 |
| 112 | Emmanuel Sanders◦ provisional | DEN | WR | 137 | +0.15 | +0.19 | +0.07 – +0.31 |
| 113 | Harry Douglas◦ provisional | TEN | WR | 22 | -0.10 | +0.19 | +0.05 – +0.33 |
| 114 | Andre Johnson◦ provisional | TEN | WR | 23 | -0.09 | +0.19 | +0.05 – +0.33 |
| 115 | Darrius Heyward-Bey◦ provisional | PIT | WR | 19 | -0.15 | +0.19 | +0.05 – +0.33 |
| 116 | Michael Floyd◦ provisional | NE | WR | 77 | +0.09 | +0.19 | +0.06 – +0.32 |
| 117 | Ty Montgomery◦ provisional | GB | WR | 56 | +0.05 | +0.19 | +0.05 – +0.32 |
| 118 | Charone Peake◦ provisional | NYJ | WR | 35 | -0.03 | +0.19 | +0.05 – +0.32 |
| 119 | Brian Quick◦ provisional | LA | WR | 77 | +0.08 | +0.18 | +0.05 – +0.32 |
| 120 | Will Fuller◦ provisional | HOU | WR | 92 | +0.09 | +0.18 | +0.05 – +0.31 |
| 121 | Quinton Patton◦ provisional | SF | WR | 63 | +0.04 | +0.18 | +0.05 – +0.31 |
| 122 | Chris Moore◦ provisional | BAL | WR | 16 | -0.39 | +0.18 | +0.04 – +0.32 |
| 123 | Tajae Sharpe◦ provisional | TEN | WR | 83 | +0.07 | +0.18 | +0.05 – +0.31 |
| 124 | Tyler Boyd◦ provisional | CIN | WR | 81 | +0.07 | +0.18 | +0.05 – +0.31 |
| 125 | Jeremy Maclin◦ provisional | KC | WR | 76 | +0.05 | +0.18 | +0.05 – +0.31 |
| 126 | Jalin Marshall◦ provisional | NYJ | WR | 23 | -0.24 | +0.18 | +0.04 – +0.32 |
| 127 | Corey Coleman◦ provisional | CLE | WR | 73 | +0.04 | +0.18 | +0.05 – +0.31 |
| 128 | Marquise Goodwin◦ provisional | BUF | WR | 68 | +0.03 | +0.18 | +0.05 – +0.31 |
| 129 | Roger Lewis◦ provisional | NYG | WR | 19 | -0.39 | +0.18 | +0.03 – +0.32 |
| 130 | Jaelen Strong◦ provisional | HOU | WR | 24 | -0.28 | +0.18 | +0.04 – +0.32 |
| 131 | Seth Roberts◦ provisional | LV | WR | 79 | +0.03 | +0.17 | +0.04 – +0.30 |
| 132 | Quincy Enunwa◦ provisional | NYJ | WR | 105 | +0.05 | +0.17 | +0.04 – +0.30 |
| 133 | Vincent Jackson◦ provisional | TB | WR | 34 | -0.21 | +0.17 | +0.03 – +0.31 |
| 134 | Jordan Norwood◦ provisional | DEN | WR | 35 | -0.21 | +0.17 | +0.03 – +0.31 |
| 135 | Corey Brown◦ provisional | CAR | WR | 54 | -0.08 | +0.17 | +0.03 – +0.30 |
| 136 | John Brown◦ provisional | ARI | WR | 73 | -0.03 | +0.17 | +0.03 – +0.30 |
| 137 | Breshad Perriman◦ provisional | BAL | WR | 66 | -0.06 | +0.16 | +0.03 – +0.30 |
| 138 | Albert Wilson◦ provisional | KC | WR | 51 | -0.13 | +0.16 | +0.03 – +0.30 |
| 139 | Nelson Agholor◦ provisional | PHI | WR | 70 | -0.06 | +0.16 | +0.03 – +0.29 |
| 140 | Braxton Miller◦ provisional | HOU | WR | 28 | -0.39 | +0.16 | +0.02 – +0.30 |
| 141 | Kevin White◦ provisional | CHI | WR | 36 | -0.28 | +0.16 | +0.02 – +0.30 |
| 142 | Alshon Jeffery◦ provisional | CHI | WR | 94 | -0.04 | +0.15 | +0.03 – +0.28 |
| 143 | Brandon Marshall◦ provisional | NYJ | WR | 128 | -0.00 | +0.15 | +0.03 – +0.27 |
| 144 | Robbie Chosen◦ provisional | NYJ | WR | 78 | -0.11 | +0.15 | +0.02 – +0.28 |
| 145 | Torrey Smith◦ provisional | SF | WR | 49 | -0.29 | +0.14 | +0.01 – +0.28 |
| 146 | Pharoh Cooper◦ provisional | LA | WR | 20 | -0.98 | +0.14 | -0.00 – +0.28 |
| 147 | Allen Hurns◦ provisional | JAX | WR | 76 | -0.16 | +0.14 | +0.01 – +0.27 |
| 148 | DeAndre Hopkins◦ provisional | HOU | WR | 151 | -0.01 | +0.14 | +0.02 – +0.26 |
| 149 | Jermaine Kearse◦ provisional | SEA | WR | 89 | -0.22 | +0.12 | -0.01 – +0.25 |
| 150 | Allen Robinson◦ provisional | JAX | WR | 152 | -0.10 | +0.11 | -0.01 – +0.23 |
| 151 | Jeremy Kerley◦ provisional | SF | WR | 115 | -0.20 | +0.10 | -0.02 – +0.23 |
| 152 | Tavon Austin◦ provisional | LA | WR | 106 | -0.36 | +0.07 | -0.06 – +0.20 |
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).