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 · 2021
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
- 198
- 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 · 2021 · full board
| # | Player | Team | Pos | targets | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Cooper Kupp◦ provisional | LA | WR | 192 | +0.59 | +0.41 | +0.28 – +0.55 |
| 2 | Mike Evans◦ provisional | TB | WR | 114 | +0.58 | +0.37 | +0.21 – +0.52 |
| 3 | Mike Williams◦ provisional | LAC | WR | 130 | +0.51 | +0.35 | +0.20 – +0.50 |
| 4 | Ja'Marr Chase◦ provisional | CIN | WR | 128 | +0.51 | +0.35 | +0.20 – +0.50 |
| 5 | DeAndre Hopkins◦ provisional | ARI | WR | 64 | +0.66 | +0.35 | +0.18 – +0.51 |
| 6 | Tee Higgins◦ provisional | CIN | WR | 111 | +0.52 | +0.34 | +0.19 – +0.50 |
| 7 | Justin Jefferson◦ provisional | MIN | WR | 170 | +0.46 | +0.34 | +0.20 – +0.48 |
| 8 | Henry Ruggs III◦ provisional | LV | WR | 36 | +0.86 | +0.34 | +0.16 – +0.52 |
| 9 | Kendrick Bourne◦ provisional | NE | WR | 70 | +0.61 | +0.34 | +0.17 – +0.50 |
| 10 | Tyler Lockett◦ provisional | SEA | WR | 108 | +0.50 | +0.33 | +0.18 – +0.49 |
| 11 | Christian Kirk◦ provisional | ARI | WR | 103 | +0.50 | +0.33 | +0.18 – +0.49 |
| 12 | Byron Pringle◦ provisional | KC | WR | 60 | +0.61 | +0.33 | +0.16 – +0.50 |
| 13 | Allen Lazard◦ provisional | GB | WR | 60 | +0.61 | +0.33 | +0.16 – +0.50 |
| 14 | Davante Adams◦ provisional | GB | WR | 169 | +0.43 | +0.33 | +0.19 – +0.47 |
| 15 | Deebo Samuel Sr.◦ provisional | SF | WR | 121 | +0.46 | +0.32 | +0.17 – +0.48 |
| 16 | Cedrick Wilson Jr.◦ provisional | DAL | WR | 62 | +0.58 | +0.32 | +0.16 – +0.49 |
| 17 | Amari Cooper◦ provisional | DAL | WR | 104 | +0.46 | +0.32 | +0.16 – +0.47 |
| 18 | Amon-Ra St. Brown◦ provisional | DET | WR | 121 | +0.44 | +0.32 | +0.17 – +0.47 |
| 19 | Antonio Brown◦ provisional | TB | WR | 62 | +0.55 | +0.32 | +0.15 – +0.48 |
| 20 | Brandon Aiyuk◦ provisional | SF | WR | 86 | +0.47 | +0.31 | +0.15 – +0.47 |
| 21 | Cyril Grayson◦ provisional | TB | WR | 12 | +1.44 | +0.31 | +0.13 – +0.50 |
| 22 | Tyreek Hill◦ provisional | KC | WR | 159 | +0.39 | +0.31 | +0.17 – +0.45 |
| 23 | Jalen Guyton◦ provisional | LAC | WR | 48 | +0.56 | +0.31 | +0.13 – +0.48 |
| 24 | Tim Patrick◦ provisional | DEN | WR | 85 | +0.44 | +0.30 | +0.14 – +0.46 |
| 25 | Quez Watkins◦ provisional | PHI | WR | 63 | +0.49 | +0.30 | +0.14 – +0.47 |
| 26 | Hunter Renfrow◦ provisional | LV | WR | 129 | +0.39 | +0.30 | +0.15 – +0.45 |
| 27 | Robert Woods◦ provisional | LA | WR | 70 | +0.44 | +0.29 | +0.13 – +0.46 |
| 28 | Randall Cobb◦ provisional | GB | WR | 39 | +0.55 | +0.29 | +0.12 – +0.47 |
| 29 | Michael Pittman◦ provisional | IND | WR | 130 | +0.37 | +0.29 | +0.15 – +0.44 |
| 30 | T.Y. Hilton◦ provisional | IND | WR | 37 | +0.55 | +0.29 | +0.12 – +0.47 |
| 31 | Isaiah McKenzie◦ provisional | BUF | WR | 26 | +0.65 | +0.29 | +0.11 – +0.47 |
| 32 | James Proche◦ provisional | BAL | WR | 20 | +0.72 | +0.29 | +0.10 – +0.47 |
| 33 | Laquon Treadwell◦ provisional | JAX | WR | 51 | +0.45 | +0.29 | +0.12 – +0.46 |
| 34 | Donovan Peoples-Jones◦ provisional | CLE | WR | 59 | +0.42 | +0.29 | +0.12 – +0.45 |
| 35 | Van Jefferson◦ provisional | LA | WR | 89 | +0.38 | +0.28 | +0.13 – +0.44 |
| 36 | Jauan Jennings◦ provisional | SF | WR | 38 | +0.48 | +0.28 | +0.11 – +0.46 |
| 37 | John Ross◦ provisional | NYG | WR | 20 | +0.61 | +0.28 | +0.10 – +0.46 |
| 38 | Nick Westbrook-Ikhine◦ provisional | TEN | WR | 57 | +0.38 | +0.27 | +0.11 – +0.44 |
| 39 | Isaiah Ford◦ provisional | MIA | WR | 17 | +0.62 | +0.27 | +0.09 – +0.46 |
| 40 | Josh Reynolds◦ provisional | DET | WR | 49 | +0.39 | +0.27 | +0.10 – +0.44 |
| 41 | Mohamed Sanu◦ provisional | SF | WR | 24 | +0.50 | +0.27 | +0.09 – +0.45 |
| 42 | A.J. Brown◦ provisional | TEN | WR | 105 | +0.32 | +0.27 | +0.12 – +0.43 |
| 43 | Marquez Callaway◦ provisional | NO | WR | 84 | +0.33 | +0.27 | +0.11 – +0.43 |
| 44 | Emmanuel Sanders◦ provisional | BUF | WR | 73 | +0.34 | +0.27 | +0.11 – +0.43 |
| 45 | Mack Hollins◦ provisional | MIA | WR | 29 | +0.43 | +0.27 | +0.09 – +0.45 |
| 46 | DeVante Parker◦ provisional | MIA | WR | 73 | +0.33 | +0.27 | +0.10 – +0.43 |
| 47 | Gabe Davis◦ provisional | BUF | WR | 63 | +0.33 | +0.26 | +0.10 – +0.43 |
| 48 | Kendall Hinton◦ provisional | DEN | WR | 23 | +0.44 | +0.26 | +0.08 – +0.45 |
| 49 | A.J. Green◦ provisional | ARI | WR | 93 | +0.31 | +0.26 | +0.11 – +0.42 |
| 50 | Quintez Cephus◦ provisional | DET | WR | 23 | +0.41 | +0.26 | +0.08 – +0.44 |
| 51 | Chris Godwin Jr.◦ provisional | TB | WR | 127 | +0.28 | +0.26 | +0.11 – +0.41 |
| 52 | Cam Sims◦ provisional | WAS | WR | 23 | +0.39 | +0.26 | +0.08 – +0.44 |
| 53 | Julio Jones◦ provisional | TEN | WR | 48 | +0.32 | +0.26 | +0.09 – +0.43 |
| 54 | Brandon Zylstra◦ provisional | CAR | WR | 25 | +0.37 | +0.26 | +0.08 – +0.44 |
| 55 | DeVonta Smith◦ provisional | PHI | WR | 105 | +0.28 | +0.26 | +0.10 – +0.41 |
| 56 | Michael Gallup◦ provisional | DAL | WR | 62 | +0.30 | +0.26 | +0.09 – +0.42 |
| 57 | Malik Turner◦ provisional | DAL | WR | 16 | +0.41 | +0.26 | +0.07 – +0.44 |
| 58 | Breshad Perriman◦ provisional | TB | WR | 18 | +0.39 | +0.26 | +0.07 – +0.44 |
| 59 | DeSean Jackson◦ provisional | LV | WR | 34 | +0.32 | +0.26 | +0.08 – +0.43 |
| 60 | Chris Moore◦ provisional | HOU | WR | 22 | +0.36 | +0.26 | +0.07 – +0.44 |
| 61 | Bryan Edwards◦ provisional | LV | WR | 60 | +0.29 | +0.25 | +0.09 – +0.42 |
| 62 | Freddie Swain◦ provisional | SEA | WR | 41 | +0.30 | +0.25 | +0.08 – +0.43 |
| 63 | Marquise Goodwin◦ provisional | CHI | WR | 40 | +0.30 | +0.25 | +0.08 – +0.43 |
| 64 | Chris Conley◦ provisional | HOU | WR | 37 | +0.29 | +0.25 | +0.08 – +0.43 |
| 65 | Jerry Jeudy◦ provisional | DEN | WR | 56 | +0.28 | +0.25 | +0.08 – +0.42 |
| 66 | Jeff Smith◦ provisional | NYJ | WR | 17 | +0.32 | +0.25 | +0.07 – +0.43 |
| 67 | Adam Thielen◦ provisional | MIN | WR | 95 | +0.25 | +0.25 | +0.09 – +0.40 |
| 68 | Ashton Dulin◦ provisional | IND | WR | 22 | +0.27 | +0.25 | +0.07 – +0.43 |
| 69 | Equanimeous St. Brown◦ provisional | GB | WR | 17 | +0.28 | +0.25 | +0.06 – +0.43 |
| 70 | Josh Palmer◦ provisional | LAC | WR | 49 | +0.26 | +0.25 | +0.07 – +0.42 |
| 71 | Kadarius Toney◦ provisional | NYG | WR | 57 | +0.25 | +0.25 | +0.08 – +0.41 |
| 72 | Lil'Jordan Humphrey◦ provisional | NO | WR | 19 | +0.26 | +0.24 | +0.06 – +0.43 |
| 73 | Tre'Quan Smith◦ provisional | NO | WR | 51 | +0.25 | +0.24 | +0.07 – +0.41 |
| 74 | Demarcus Robinson◦ provisional | KC | WR | 41 | +0.24 | +0.24 | +0.07 – +0.42 |
| 75 | Kalif Raymond◦ provisional | DET | WR | 71 | +0.24 | +0.24 | +0.08 – +0.41 |
| 76 | Damiere Byrd◦ provisional | CHI | WR | 39 | +0.23 | +0.24 | +0.07 – +0.42 |
| 77 | DeAndre Carter◦ provisional | WAS | WR | 44 | +0.23 | +0.24 | +0.07 – +0.41 |
| 78 | CeeDee Lamb◦ provisional | DAL | WR | 121 | +0.23 | +0.24 | +0.09 – +0.39 |
| 79 | Olamide Zaccheaus◦ provisional | ATL | WR | 54 | +0.21 | +0.24 | +0.07 – +0.41 |
| 80 | Rashod Bateman◦ provisional | BAL | WR | 68 | +0.22 | +0.24 | +0.07 – +0.40 |
| 81 | Jakeem Grant◦ provisional | CHI | WR | 17 | +0.14 | +0.24 | +0.05 – +0.42 |
| 82 | Mecole Hardman◦ provisional | KC | WR | 83 | +0.22 | +0.24 | +0.08 – +0.40 |
| 83 | DK Metcalf◦ provisional | SEA | WR | 129 | +0.22 | +0.24 | +0.09 – +0.38 |
| 84 | Parris Campbell◦ provisional | IND | WR | 20 | +0.12 | +0.23 | +0.05 – +0.41 |
| 85 | Marvin Jones◦ provisional | JAX | WR | 120 | +0.21 | +0.23 | +0.08 – +0.38 |
| 86 | Tyler Boyd◦ provisional | CIN | WR | 95 | +0.20 | +0.23 | +0.07 – +0.39 |
| 87 | Courtland Sutton◦ provisional | DEN | WR | 100 | +0.20 | +0.23 | +0.07 – +0.39 |
| 88 | Marquez Valdes-Scantling◦ provisional | GB | WR | 56 | +0.18 | +0.23 | +0.06 – +0.40 |
| 89 | Ben Skowronek◦ provisional | LA | WR | 20 | +0.07 | +0.23 | +0.05 – +0.41 |
| 90 | Devin Duvernay◦ provisional | BAL | WR | 47 | +0.16 | +0.23 | +0.06 – +0.40 |
| 91 | Jamal Agnew◦ provisional | JAX | WR | 40 | +0.14 | +0.23 | +0.05 – +0.40 |
| 92 | Deonte Harty◦ provisional | NO | WR | 59 | +0.17 | +0.23 | +0.06 – +0.39 |
| 93 | Tajae Sharpe◦ provisional | ATL | WR | 37 | +0.13 | +0.23 | +0.05 – +0.40 |
| 94 | Calvin Ridley◦ provisional | ATL | WR | 52 | +0.15 | +0.22 | +0.05 – +0.40 |
| 95 | K.J. Osborn◦ provisional | MIN | WR | 82 | +0.18 | +0.22 | +0.06 – +0.39 |
| 96 | Marcus Johnson◦ provisional | TEN | WR | 19 | +0.01 | +0.22 | +0.04 – +0.41 |
| 97 | Phillip Dorsett◦ provisional | HOU | WR | 14 | -0.06 | +0.22 | +0.04 – +0.41 |
| 98 | Keelan Cole◦ provisional | NYJ | WR | 52 | +0.14 | +0.22 | +0.05 – +0.39 |
| 99 | Keenan Allen◦ provisional | LAC | WR | 158 | +0.19 | +0.22 | +0.08 – +0.36 |
| 100 | Stefon Diggs◦ provisional | BUF | WR | 164 | +0.20 | +0.22 | +0.08 – +0.36 |
| 101 | Juwann Winfree◦ provisional | GB | WR | 13 | -0.13 | +0.22 | +0.04 – +0.41 |
| 102 | Brandin Cooks◦ provisional | HOU | WR | 134 | +0.18 | +0.22 | +0.07 – +0.37 |
| 103 | Allen Robinson◦ provisional | CHI | WR | 67 | +0.15 | +0.22 | +0.05 – +0.38 |
| 104 | Rashard Higgins◦ provisional | CLE | WR | 47 | +0.11 | +0.22 | +0.05 – +0.39 |
| 105 | Dede Westbrook◦ provisional | MIN | WR | 15 | -0.13 | +0.22 | +0.03 – +0.40 |
| 106 | Noah Brown◦ provisional | DAL | WR | 25 | +0.01 | +0.22 | +0.04 – +0.40 |
| 107 | Dante Pettis◦ provisional | NYG | WR | 16 | -0.12 | +0.22 | +0.03 – +0.40 |
| 108 | Tyler Johnson◦ provisional | TB | WR | 56 | +0.12 | +0.22 | +0.05 – +0.38 |
| 109 | DJ Chark◦ provisional | JAX | WR | 23 | -0.03 | +0.22 | +0.03 – +0.40 |
| 110 | Penny Hart◦ provisional | SEA | WR | 12 | -0.26 | +0.21 | +0.03 – +0.40 |
| 111 | Braxton Berrios◦ provisional | NYJ | WR | 65 | +0.12 | +0.21 | +0.05 – +0.38 |
| 112 | Chester Rogers◦ provisional | TEN | WR | 43 | +0.07 | +0.21 | +0.04 – +0.39 |
| 113 | Dyami Brown◦ provisional | WAS | WR | 25 | -0.06 | +0.21 | +0.03 – +0.39 |
| 114 | Dee Eskridge◦ provisional | SEA | WR | 20 | -0.14 | +0.21 | +0.03 – +0.39 |
| 115 | Danny Amendola◦ provisional | HOU | WR | 39 | +0.02 | +0.21 | +0.03 – +0.38 |
| 116 | Jakobi Meyers◦ provisional | NE | WR | 128 | +0.15 | +0.21 | +0.06 – +0.36 |
| 117 | Jamison Crowder◦ provisional | NYJ | WR | 73 | +0.09 | +0.20 | +0.04 – +0.37 |
| 118 | Jaylen Waddle◦ provisional | MIA | WR | 140 | +0.14 | +0.20 | +0.06 – +0.35 |
| 119 | Zay Jones◦ provisional | LV | WR | 70 | +0.09 | +0.20 | +0.04 – +0.37 |
| 120 | Odell Beckham Jr.◦ provisional | LA | WR | 83 | +0.10 | +0.20 | +0.04 – +0.36 |
| 121 | Dax Milne◦ provisional | WAS | WR | 14 | -0.40 | +0.20 | +0.02 – +0.39 |
| 122 | Preston Williams◦ provisional | MIA | WR | 16 | -0.34 | +0.20 | +0.02 – +0.38 |
| 123 | Sterling Shepard◦ provisional | NYG | WR | 53 | +0.03 | +0.20 | +0.03 – +0.37 |
| 124 | Nelson Agholor◦ provisional | NE | WR | 64 | +0.06 | +0.20 | +0.03 – +0.36 |
| 125 | Russell Gage◦ provisional | ATL | WR | 94 | +0.10 | +0.20 | +0.04 – +0.36 |
| 126 | Ty Montgomery◦ provisional | NO | WR | 26 | -0.17 | +0.20 | +0.02 – +0.38 |
| 127 | Trent Sherfield◦ provisional | SF | WR | 20 | -0.28 | +0.20 | +0.01 – +0.38 |
| 128 | Antoine Wesley◦ provisional | ARI | WR | 32 | -0.11 | +0.19 | +0.02 – +0.37 |
| 129 | Chase Claypool◦ provisional | PIT | WR | 105 | +0.09 | +0.19 | +0.04 – +0.35 |
| 130 | Rondale Moore◦ provisional | ARI | WR | 64 | +0.02 | +0.19 | +0.02 – +0.36 |
| 131 | Diontae Johnson◦ provisional | PIT | WR | 173 | +0.13 | +0.19 | +0.05 – +0.33 |
| 132 | Denzel Mims◦ provisional | NYJ | WR | 23 | -0.29 | +0.19 | +0.01 – +0.37 |
| 133 | Sammy Watkins◦ provisional | BAL | WR | 49 | -0.04 | +0.19 | +0.02 – +0.36 |
| 134 | Nico Collins◦ provisional | HOU | WR | 60 | -0.00 | +0.19 | +0.02 – +0.35 |
| 135 | KhaDarel Hodge◦ provisional | DET | WR | 28 | -0.23 | +0.19 | +0.01 – +0.36 |
| 136 | Jaelon Darden◦ provisional | TB | WR | 12 | -0.78 | +0.19 | -0.00 – +0.37 |
| 137 | Corey Davis◦ provisional | NYJ | WR | 59 | -0.01 | +0.18 | +0.02 – +0.35 |
| 138 | Terry McLaurin◦ provisional | WAS | WR | 130 | +0.09 | +0.18 | +0.04 – +0.33 |
| 139 | Anthony Schwartz◦ provisional | CLE | WR | 23 | -0.34 | +0.18 | +0.00 – +0.36 |
| 140 | Albert Wilson◦ provisional | MIA | WR | 39 | -0.14 | +0.18 | +0.01 – +0.36 |
| 141 | JuJu Smith-Schuster◦ provisional | PIT | WR | 28 | -0.29 | +0.18 | -0.00 – +0.36 |
| 142 | Kenny Stills◦ provisional | NO | WR | 23 | -0.41 | +0.18 | -0.01 – +0.36 |
| 143 | Terrace Marshall Jr.◦ provisional | CAR | WR | 31 | -0.26 | +0.18 | -0.00 – +0.35 |
| 144 | Anthony Miller◦ provisional | PIT | WR | 12 | -0.95 | +0.18 | -0.01 – +0.36 |
| 145 | Trinity Benson◦ provisional | DET | WR | 22 | -0.44 | +0.18 | -0.01 – +0.36 |
| 146 | Cole Beasley◦ provisional | BUF | WR | 113 | +0.05 | +0.18 | +0.02 – +0.33 |
| 147 | Marquise Brown◦ provisional | BAL | WR | 147 | +0.08 | +0.17 | +0.03 – +0.32 |
| 148 | Laviska Shenault Jr.◦ provisional | JAX | WR | 100 | +0.04 | +0.17 | +0.02 – +0.33 |
| 149 | Elijah Moore◦ provisional | NYJ | WR | 78 | -0.02 | +0.17 | +0.01 – +0.33 |
| 150 | James Washington◦ provisional | PIT | WR | 44 | -0.16 | +0.17 | -0.00 – +0.34 |
| 151 | Josh Gordon◦ provisional | KC | WR | 14 | -0.89 | +0.17 | -0.02 – +0.35 |
| 152 | Tavon Austin◦ provisional | JAX | WR | 37 | -0.25 | +0.17 | -0.01 – +0.34 |
| 153 | Collin Johnson◦ provisional | NYG | WR | 21 | -0.58 | +0.17 | -0.02 – +0.35 |
| 154 | Kenny Golladay◦ provisional | NYG | WR | 77 | -0.04 | +0.16 | +0.00 – +0.33 |
| 155 | Adam Humphries◦ provisional | WAS | WR | 62 | -0.10 | +0.16 | -0.01 – +0.33 |
| 156 | DJ Moore◦ provisional | CAR | WR | 164 | +0.06 | +0.16 | +0.02 – +0.30 |
| 157 | Jalen Reagor◦ provisional | PHI | WR | 57 | -0.19 | +0.15 | -0.02 – +0.32 |
| 158 | Darnell Mooney◦ provisional | CHI | WR | 141 | +0.00 | +0.14 | -0.00 – +0.29 |
| 159 | Darius Slayton◦ provisional | NYG | WR | 58 | -0.25 | +0.13 | -0.04 – +0.30 |
| 160 | Zach Pascal◦ provisional | IND | WR | 69 | -0.19 | +0.13 | -0.03 – +0.30 |
| 161 | Ray-Ray McCloud◦ provisional | PIT | WR | 66 | -0.22 | +0.13 | -0.04 – +0.29 |
| 162 | Jarvis Landry◦ provisional | CLE | WR | 87 | -0.15 | +0.12 | -0.04 – +0.28 |
| 163 | Robbie Chosen◦ provisional | CAR | WR | 110 | -0.26 | +0.06 | -0.09 – +0.22 |
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).