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.
Catch rate · 2016
Receptions per target, shrunk within position (WR vs TE separately). Depth-of-target confound; catchable-target rate not available here.
- Beats raw by
- 18.3%
- lower out-of-sample error
- RMSE raw → shrunk
- 11.1% → 9.1%
- odd vs. even weeks
- Split-half reliability
- 0.35
- how repeatable the raw stat is
- Stabilizes at
- 50
- 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.
Catch rate · 2016 · full board
| # | Player | Team | Pos | targets | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Michael Thomas | NO | WR | 121 | 76.0% | 71.3% | 65.5% – 76.8% |
| 2 | Cole Beasley | DAL | WR | 98 | 76.5% | 70.9% | 64.6% – 76.8% |
| 3 | Doug Baldwin | SEA | WR | 126 | 74.6% | 70.4% | 64.6% – 75.9% |
| 4 | Stefon Diggs | MIN | WR | 112 | 75.0% | 70.3% | 64.3% – 76.0% |
| 5 | Ty Montgomery | GB | WR | 56 | 78.6% | 69.7% | 62.2% – 76.8% |
| 6 | Adam Thielen | MIN | WR | 92 | 75.0% | 69.6% | 63.1% – 75.8% |
| 7 | Larry Fitzgerald | ARI | WR | 150 | 71.3% | 68.4% | 62.9% – 73.7% |
| 8 | Tyreek Hill | KC | WR | 83 | 73.5% | 68.3% | 61.6% – 74.8% |
| 9 | Jarvis Landry | MIA | WR | 133 | 70.7% | 67.7% | 61.9% – 73.3% |
| 10 | Eddie Royal◦ provisional | CHI | WR | 43 | 76.7% | 67.6% | 59.4% – 75.3% |
| 11 | Mohamed Sanu | ATL | WR | 82 | 72.0% | 67.3% | 60.5% – 73.9% |
| 12 | Eli Rogers | PIT | WR | 66 | 72.7% | 67.1% | 59.8% – 74.1% |
| 13 | Randall Cobb | GB | WR | 84 | 71.4% | 67.1% | 60.3% – 73.6% |
| 14 | Danny Amendola◦ provisional | NE | WR | 29 | 79.3% | 66.9% | 58.0% – 75.3% |
| 15 | Anquan Boldin | DET | WR | 95 | 70.5% | 66.8% | 60.3% – 73.1% |
| 16 | Terrance Williams | DAL | WR | 61 | 72.1% | 66.5% | 59.0% – 73.7% |
| 17 | Pierre Garcon | WAS | WR | 114 | 69.3% | 66.4% | 60.2% – 72.3% |
| 18 | Willie Snead | NO | WR | 104 | 69.2% | 66.1% | 59.8% – 72.3% |
| 19 | Antonio Brown | PIT | WR | 157 | 67.5% | 65.6% | 60.1% – 71.0% |
| 20 | Cameron Meredith | CHI | WR | 97 | 68.0% | 65.2% | 58.7% – 71.5% |
| 21 | Jamison Crowder | WAS | WR | 99 | 67.7% | 65.0% | 58.5% – 71.3% |
| 22 | Golden Tate | DET | WR | 136 | 66.9% | 65.0% | 59.2% – 70.6% |
| 23 | Taylor Gabriel | ATL | WR | 50 | 70.0% | 64.9% | 56.9% – 72.5% |
| 24 | Steve Smith | BAL | WR | 104 | 67.3% | 64.8% | 58.4% – 71.0% |
| 25 | Brandin Cooks | NO | WR | 117 | 66.7% | 64.6% | 58.4% – 70.6% |
| 26 | Keith Mumphery◦ provisional | HOU | WR | 12 | 83.3% | 64.3% | 54.1% – 74.0% |
| 27 | Robert Woods | BUF | WR | 76 | 67.1% | 64.2% | 57.0% – 71.0% |
| 28 | Bryan Walters◦ provisional | JAX | WR | 34 | 70.6% | 64.1% | 55.4% – 72.5% |
| 29 | Tyler Boyd | CIN | WR | 81 | 66.7% | 64.0% | 57.0% – 70.8% |
| 30 | A.J. Green | CIN | WR | 100 | 66.0% | 63.9% | 57.4% – 70.2% |
| 31 | Jarius Wright◦ provisional | MIN | WR | 14 | 78.6% | 63.8% | 53.8% – 73.4% |
| 32 | Brandon Coleman◦ provisional | NO | WR | 38 | 68.4% | 63.5% | 54.9% – 71.7% |
| 33 | Adam Humphries | TB | WR | 84 | 65.5% | 63.3% | 56.4% – 70.0% |
| 34 | Kendall Wright◦ provisional | TEN | WR | 43 | 67.4% | 63.3% | 54.9% – 71.3% |
| 35 | Malcolm Mitchell◦ provisional | NE | WR | 48 | 66.7% | 63.1% | 55.0% – 71.0% |
| 36 | Chris Hogan | NE | WR | 58 | 65.5% | 62.8% | 55.1% – 70.3% |
| 37 | Josh Huff◦ provisional | TB | WR | 23 | 69.6% | 62.8% | 53.4% – 71.9% |
| 38 | Jordy Nelson | GB | WR | 152 | 63.8% | 62.8% | 57.1% – 68.3% |
| 39 | Justin Hardy◦ provisional | ATL | WR | 31 | 67.7% | 62.8% | 53.8% – 71.4% |
| 40 | Julio Jones | ATL | WR | 130 | 63.8% | 62.7% | 56.7% – 68.5% |
| 41 | DeVante Parker | MIA | WR | 87 | 64.4% | 62.7% | 55.8% – 69.3% |
| 42 | Pharoh Cooper◦ provisional | LA | WR | 20 | 70.0% | 62.7% | 53.0% – 71.9% |
| 43 | Harry Douglas◦ provisional | TEN | WR | 22 | 68.2% | 62.3% | 52.8% – 71.5% |
| 44 | Rod Streater◦ provisional | SF | WR | 27 | 66.7% | 62.2% | 52.9% – 71.0% |
| 45 | James Wright◦ provisional | CIN | WR | 19 | 68.4% | 62.1% | 52.4% – 71.5% |
| 46 | Chris Conley | KC | WR | 69 | 63.8% | 62.1% | 54.7% – 69.3% |
| 47 | Travis Benjamin | LAC | WR | 75 | 62.7% | 61.5% | 54.3% – 68.5% |
| 48 | Demaryius Thomas | DEN | WR | 145 | 62.1% | 61.5% | 55.7% – 67.1% |
| 49 | Sterling Shepard | NYG | WR | 105 | 61.9% | 61.2% | 54.7% – 67.5% |
| 50 | Jordan Taylor◦ provisional | DEN | WR | 25 | 64.0% | 61.2% | 51.8% – 70.2% |
| 51 | Tyler Lockett | SEA | WR | 66 | 62.1% | 61.1% | 53.6% – 68.4% |
| 52 | Maurice Harris◦ provisional | WAS | WR | 12 | 66.7% | 61.1% | 50.8% – 71.0% |
| 53 | Amari Cooper | LV | WR | 135 | 61.5% | 61.0% | 55.1% – 66.8% |
| 54 | Mike Wallace | BAL | WR | 117 | 61.5% | 61.0% | 54.7% – 67.1% |
| 55 | Julian Edelman | NE | WR | 160 | 61.3% | 60.9% | 55.3% – 66.4% |
| 56 | Cody Core◦ provisional | CIN | WR | 27 | 63.0% | 60.9% | 51.6% – 69.8% |
| 57 | Aldrick Robinson◦ provisional | ATL | WR | 32 | 62.5% | 60.8% | 51.8% – 69.5% |
| 58 | Kenny Britt | LA | WR | 111 | 61.3% | 60.8% | 54.4% – 67.0% |
| 59 | Paul Turner◦ provisional | PHI | WR | 14 | 64.3% | 60.7% | 50.6% – 70.5% |
| 60 | Davante Adams | GB | WR | 123 | 61.0% | 60.6% | 54.4% – 66.6% |
| 61 | Andrew Hawkins | CLE | WR | 54 | 61.1% | 60.5% | 52.5% – 68.2% |
| 62 | Chris Harper◦ provisional | SF | WR | 21 | 61.9% | 60.4% | 50.7% – 69.7% |
| 63 | Michael Crabtree | LV | WR | 147 | 60.5% | 60.3% | 54.6% – 66.0% |
| 64 | Deonte Thompson◦ provisional | CHI | WR | 36 | 61.1% | 60.3% | 51.5% – 68.8% |
| 65 | Albert Wilson | KC | WR | 51 | 60.8% | 60.3% | 52.2% – 68.1% |
| 66 | Jalin Marshall◦ provisional | NYJ | WR | 23 | 60.9% | 60.1% | 50.6% – 69.3% |
| 67 | Cobi Hamilton◦ provisional | PIT | WR | 28 | 60.7% | 60.1% | 50.9% – 69.0% |
| 68 | Marqise Lee | JAX | WR | 105 | 60.0% | 59.9% | 53.4% – 66.3% |
| 69 | Jordan Norwood◦ provisional | DEN | WR | 35 | 60.0% | 59.8% | 51.0% – 68.4% |
| 70 | Brandon LaFell | CIN | WR | 107 | 59.8% | 59.8% | 53.3% – 66.1% |
| 71 | Dontrelle Inman | LAC | WR | 97 | 59.8% | 59.8% | 53.1% – 66.3% |
| 72 | Odell Beckham Jr. | NYG | WR | 169 | 59.8% | 59.8% | 54.3% – 65.1% |
| 73 | Rishard Matthews | TEN | WR | 109 | 59.6% | 59.7% | 53.2% – 66.0% |
| 74 | Jaelen Strong◦ provisional | HOU | WR | 24 | 58.3% | 59.3% | 49.8% – 68.5% |
| 75 | Jeff Janis◦ provisional | GB | WR | 19 | 57.9% | 59.2% | 49.4% – 68.7% |
| 76 | Quinton Patton | SF | WR | 63 | 58.7% | 59.2% | 51.5% – 66.7% |
| 77 | Brittan Golden◦ provisional | ARI | WR | 14 | 57.1% | 59.2% | 49.0% – 69.0% |
| 78 | Paul Richardson◦ provisional | SEA | WR | 36 | 58.3% | 59.2% | 50.3% – 67.7% |
| 79 | Marquess Wilson◦ provisional | CHI | WR | 16 | 56.3% | 58.9% | 48.8% – 68.6% |
| 80 | Kamar Aiken | BAL | WR | 50 | 58.0% | 58.9% | 50.7% – 66.8% |
| 81 | Russell Shepard◦ provisional | TB | WR | 40 | 57.5% | 58.7% | 50.1% – 67.1% |
| 82 | Jeremy Maclin | KC | WR | 76 | 57.9% | 58.6% | 51.3% – 65.7% |
| 83 | Tyrell Williams | LAC | WR | 119 | 58.0% | 58.5% | 52.2% – 64.7% |
| 84 | Andre Roberts◦ provisional | DET | WR | 25 | 56.0% | 58.5% | 49.0% – 67.7% |
| 85 | Andre Holmes◦ provisional | LV | WR | 25 | 56.0% | 58.5% | 49.0% – 67.7% |
| 86 | Walt Powell◦ provisional | BUF | WR | 25 | 56.0% | 58.5% | 49.0% – 67.7% |
| 87 | T.Y. Hilton | IND | WR | 157 | 58.0% | 58.4% | 52.7% – 64.0% |
| 88 | Cody Latimer◦ provisional | DEN | WR | 15 | 53.3% | 58.3% | 48.1% – 68.1% |
| 89 | Emmanuel Sanders | DEN | WR | 137 | 57.7% | 58.2% | 52.3% – 64.1% |
| 90 | Chester Rogers◦ provisional | IND | WR | 34 | 55.9% | 58.2% | 49.3% – 66.9% |
| 91 | Geronimo Allison◦ provisional | GB | WR | 22 | 54.5% | 58.1% | 48.5% – 67.5% |
| 92 | Rashard Higgins◦ provisional | CLE | WR | 12 | 50.0% | 57.9% | 47.5% – 68.0% |
| 93 | Ted Ginn | CAR | WR | 95 | 56.8% | 57.8% | 51.0% – 64.5% |
| 94 | Phillip Dorsett | IND | WR | 59 | 55.9% | 57.7% | 49.8% – 65.3% |
| 95 | Braxton Miller◦ provisional | HOU | WR | 28 | 53.6% | 57.5% | 48.3% – 66.6% |
| 96 | Charone Peake◦ provisional | NYJ | WR | 35 | 54.3% | 57.5% | 48.6% – 66.2% |
| 97 | Charles D. Johnson◦ provisional | MIN | WR | 37 | 54.0% | 57.3% | 48.5% – 65.9% |
| 98 | DeSean Jackson | WAS | WR | 100 | 56.0% | 57.2% | 50.6% – 63.8% |
| 99 | DeMarcus Ayers◦ provisional | PIT | WR | 13 | 46.2% | 56.9% | 46.6% – 67.0% |
| 100 | Jeremy Kerley | SF | WR | 115 | 55.6% | 56.9% | 50.5% – 63.2% |
| 101 | Alshon Jeffery | CHI | WR | 94 | 55.3% | 56.9% | 50.0% – 63.6% |
| 102 | Kevin White◦ provisional | CHI | WR | 36 | 52.8% | 56.8% | 48.0% – 65.5% |
| 103 | Sammy Watkins | BUF | WR | 52 | 53.8% | 56.7% | 48.6% – 64.7% |
| 104 | Quincy Enunwa | NYJ | WR | 105 | 55.2% | 56.7% | 50.1% – 63.2% |
| 105 | Donte Moncrief | IND | WR | 56 | 53.6% | 56.5% | 48.5% – 64.3% |
| 106 | Victor Cruz | NYG | WR | 72 | 54.2% | 56.5% | 49.0% – 63.7% |
| 107 | Ryan Grant◦ provisional | WAS | WR | 19 | 47.4% | 56.3% | 46.5% – 66.0% |
| 108 | Tavon Austin | LA | WR | 106 | 54.7% | 56.3% | 49.8% – 62.8% |
| 109 | Robbie Chosen | NYJ | WR | 78 | 53.8% | 56.1% | 48.9% – 63.3% |
| 110 | John Brown | ARI | WR | 73 | 53.4% | 56.0% | 48.6% – 63.3% |
| 111 | Jaron Brown◦ provisional | ARI | WR | 23 | 47.8% | 56.0% | 46.4% – 65.4% |
| 112 | Mike Evans | TB | WR | 175 | 54.9% | 55.9% | 50.5% – 61.3% |
| 113 | Brice Butler◦ provisional | DAL | WR | 32 | 50.0% | 55.9% | 46.9% – 64.8% |
| 114 | Chris Moore◦ provisional | BAL | WR | 16 | 43.8% | 55.9% | 45.8% – 65.7% |
| 115 | Aaron Burbridge◦ provisional | SF | WR | 16 | 43.8% | 55.9% | 45.8% – 65.7% |
| 116 | Brian Quick | LA | WR | 77 | 53.3% | 55.8% | 48.5% – 63.0% |
| 117 | Terrelle Pryor | CLE | WR | 142 | 54.2% | 55.7% | 49.7% – 61.5% |
| 118 | Ricardo Louis◦ provisional | CLE | WR | 36 | 50.0% | 55.7% | 46.8% – 64.3% |
| 119 | Josh Bellamy◦ provisional | CHI | WR | 38 | 50.0% | 55.5% | 46.8% – 64.1% |
| 120 | Marvin Jones | DET | WR | 103 | 53.4% | 55.5% | 48.8% – 62.0% |
| 121 | Kelvin Benjamin | CAR | WR | 118 | 53.4% | 55.3% | 48.9% – 61.5% |
| 122 | Bennie Fowler◦ provisional | DEN | WR | 24 | 45.8% | 55.2% | 45.7% – 64.6% |
| 123 | Nelson Agholor | PHI | WR | 70 | 51.4% | 54.9% | 47.4% – 62.3% |
| 124 | Kenny Stills | MIA | WR | 81 | 51.8% | 54.9% | 47.7% – 61.9% |
| 125 | Eric Decker◦ provisional | NYJ | WR | 21 | 42.9% | 54.7% | 45.0% – 64.3% |
| 126 | Corey Brown | CAR | WR | 54 | 50.0% | 54.7% | 46.6% – 62.6% |
| 127 | Breshad Perriman | BAL | WR | 66 | 50.0% | 54.2% | 46.6% – 61.7% |
| 128 | Will Fuller | HOU | WR | 92 | 51.1% | 54.1% | 47.2% – 61.0% |
| 129 | Dez Bryant | DAL | WR | 98 | 51.0% | 54.0% | 47.2% – 60.7% |
| 130 | Justin Hunter◦ provisional | BUF | WR | 24 | 41.7% | 53.9% | 44.3% – 63.3% |
| 131 | DeAndre Hopkins | HOU | WR | 151 | 51.7% | 53.7% | 47.9% – 59.4% |
| 132 | T.J. Jones◦ provisional | DET | WR | 15 | 33.3% | 53.6% | 43.5% – 63.7% |
| 133 | Roger Lewis◦ provisional | NYG | WR | 19 | 36.8% | 53.4% | 43.5% – 63.2% |
| 134 | Vincent Jackson◦ provisional | TB | WR | 34 | 44.1% | 53.4% | 44.5% – 62.3% |
| 135 | Tajae Sharpe | TEN | WR | 83 | 49.4% | 53.3% | 46.2% – 60.4% |
| 136 | Andre Johnson◦ provisional | TEN | WR | 23 | 39.1% | 53.2% | 43.6% – 62.7% |
| 137 | Dorial Green-Beckham | PHI | WR | 74 | 48.6% | 53.1% | 45.7% – 60.4% |
| 138 | Cecil Shorts◦ provisional | TB | WR | 27 | 40.7% | 53.1% | 43.7% – 62.3% |
| 139 | Bryce Treggs◦ provisional | PHI | WR | 12 | 25.0% | 53.0% | 42.6% – 63.3% |
| 140 | Michael Floyd | NE | WR | 77 | 48.0% | 52.6% | 45.4% – 59.9% |
| 141 | Seth Roberts | LV | WR | 79 | 48.1% | 52.6% | 45.4% – 59.8% |
| 142 | Darrius Heyward-Bey◦ provisional | PIT | WR | 19 | 31.6% | 52.0% | 42.1% – 61.8% |
| 143 | Allen Hurns | JAX | WR | 76 | 46.1% | 51.5% | 44.2% – 58.8% |
| 144 | Sammie Coates◦ provisional | PIT | WR | 49 | 42.9% | 51.4% | 43.1% – 59.6% |
| 145 | Corey Coleman | CLE | WR | 73 | 45.2% | 51.1% | 43.7% – 58.5% |
| 146 | J.J. Nelson | ARI | WR | 75 | 45.3% | 51.1% | 43.8% – 58.4% |
| 147 | Jermaine Kearse | SEA | WR | 89 | 46.1% | 51.0% | 44.0% – 57.9% |
| 148 | Allen Robinson | JAX | WR | 152 | 48.0% | 50.9% | 45.1% – 56.7% |
| 149 | Torrey Smith◦ provisional | SF | WR | 49 | 40.8% | 50.4% | 42.1% – 58.6% |
| 150 | Brandon Marshall | NYJ | WR | 128 | 46.1% | 49.9% | 43.8% – 56.1% |
| 151 | Marquise Goodwin | BUF | WR | 68 | 42.6% | 49.9% | 42.3% – 57.4% |
| 152 | Devin Funchess | CAR | WR | 59 | 39.0% | 48.5% | 40.7% – 56.4% |
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).