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
- 121
- targets 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.
EPA per target · 2016 · full board
| # | Player | Team | Pos | targets | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Travis Kelce◦ provisional | KC | TE | 118 | +0.60 | +0.41 | +0.25 – +0.57 |
| 2 | Rob Gronkowski◦ provisional | NE | TE | 38 | +0.93 | +0.39 | +0.20 – +0.58 |
| 3 | Hunter Henry◦ provisional | LAC | TE | 54 | +0.64 | +0.35 | +0.17 – +0.54 |
| 4 | Martellus Bennett◦ provisional | NE | TE | 73 | +0.53 | +0.34 | +0.17 – +0.51 |
| 5 | Erik Swoope◦ provisional | IND | TE | 22 | +0.96 | +0.34 | +0.14 – +0.54 |
| 6 | Cameron Brate◦ provisional | TB | TE | 81 | +0.50 | +0.33 | +0.17 – +0.50 |
| 7 | Levine Toilolo◦ provisional | ATL | TE | 19 | +0.93 | +0.32 | +0.12 – +0.53 |
| 8 | Tyler Eifert◦ provisional | CIN | TE | 47 | +0.53 | +0.31 | +0.12 – +0.50 |
| 9 | Dwayne Allen◦ provisional | IND | TE | 53 | +0.47 | +0.30 | +0.12 – +0.48 |
| 10 | Jimmy Graham◦ provisional | SEA | TE | 95 | +0.39 | +0.30 | +0.13 – +0.46 |
| 11 | Austin Hooper◦ provisional | ATL | TE | 28 | +0.58 | +0.29 | +0.09 – +0.49 |
| 12 | Eric Ebron◦ provisional | DET | TE | 85 | +0.39 | +0.29 | +0.12 – +0.46 |
| 13 | Gary Barnidge◦ provisional | CLE | TE | 83 | +0.35 | +0.28 | +0.11 – +0.45 |
| 14 | Jordan Reed◦ provisional | WAS | TE | 90 | +0.33 | +0.27 | +0.10 – +0.44 |
| 15 | Vance McDonald◦ provisional | SF | TE | 45 | +0.37 | +0.26 | +0.08 – +0.45 |
| 16 | MarQueis Gray◦ provisional | MIA | TE | 17 | +0.49 | +0.26 | +0.05 – +0.46 |
| 17 | Zach Miller◦ provisional | CHI | TE | 64 | +0.32 | +0.26 | +0.08 – +0.43 |
| 18 | Neal Sterling◦ provisional | JAX | TE | 16 | +0.47 | +0.25 | +0.05 – +0.46 |
| 19 | Anthony Fasano◦ provisional | TEN | TE | 14 | +0.49 | +0.25 | +0.05 – +0.46 |
| 20 | Stephen Anderson◦ provisional | HOU | TE | 16 | +0.46 | +0.25 | +0.05 – +0.46 |
| 21 | Jared Cook◦ provisional | GB | TE | 51 | +0.30 | +0.25 | +0.06 – +0.43 |
| 22 | Dion Sims◦ provisional | MIA | TE | 35 | +0.33 | +0.25 | +0.05 – +0.44 |
| 23 | Darren Fells◦ provisional | ARI | TE | 18 | +0.38 | +0.25 | +0.04 – +0.45 |
| 24 | Nick O'Leary◦ provisional | BUF | TE | 15 | +0.41 | +0.24 | +0.04 – +0.45 |
| 25 | Daniel Brown◦ provisional | CHI | TE | 20 | +0.36 | +0.24 | +0.04 – +0.45 |
| 26 | Seth DeValve◦ provisional | CLE | TE | 12 | +0.41 | +0.24 | +0.03 – +0.45 |
| 27 | Zach Ertz◦ provisional | PHI | TE | 106 | +0.25 | +0.24 | +0.08 – +0.40 |
| 28 | Ben Koyack◦ provisional | JAX | TE | 24 | +0.29 | +0.23 | +0.03 – +0.44 |
| 29 | Jeff Heuerman◦ provisional | DEN | TE | 17 | +0.31 | +0.23 | +0.03 – +0.44 |
| 30 | Jason Witten◦ provisional | DAL | TE | 95 | +0.24 | +0.23 | +0.07 – +0.39 |
| 31 | Jordan Matthews◦ provisional | PHI | TE | 119 | +0.24 | +0.23 | +0.07 – +0.39 |
| 32 | Austin Seferian-Jenkins◦ provisional | NYJ | TE | 20 | +0.25 | +0.23 | +0.03 – +0.43 |
| 33 | Ladarius Green◦ provisional | PIT | TE | 35 | +0.24 | +0.23 | +0.04 – +0.42 |
| 34 | Kyle Rudolph | MIN | TE | 133 | +0.23 | +0.23 | +0.08 – +0.38 |
| 35 | Mychal Rivera◦ provisional | LV | TE | 25 | +0.24 | +0.23 | +0.03 – +0.43 |
| 36 | Delanie Walker◦ provisional | TEN | TE | 102 | +0.23 | +0.23 | +0.06 – +0.39 |
| 37 | Jerell Adams◦ provisional | NYG | TE | 21 | +0.23 | +0.23 | +0.02 – +0.43 |
| 38 | Virgil Green◦ provisional | DEN | TE | 37 | +0.22 | +0.22 | +0.03 – +0.42 |
| 39 | Brandon Myers◦ provisional | TB | TE | 15 | +0.20 | +0.22 | +0.02 – +0.43 |
| 40 | Jack Doyle◦ provisional | IND | TE | 75 | +0.22 | +0.22 | +0.05 – +0.39 |
| 41 | A.J. Derby◦ provisional | DEN | TE | 20 | +0.19 | +0.22 | +0.02 – +0.42 |
| 42 | Luke Willson◦ provisional | SEA | TE | 21 | +0.19 | +0.22 | +0.02 – +0.42 |
| 43 | Charles Clay◦ provisional | BUF | TE | 87 | +0.20 | +0.22 | +0.05 – +0.38 |
| 44 | Vernon Davis◦ provisional | WAS | TE | 59 | +0.19 | +0.21 | +0.04 – +0.39 |
| 45 | Clive Walford◦ provisional | LV | TE | 52 | +0.19 | +0.21 | +0.03 – +0.40 |
| 46 | Brent Celek◦ provisional | PHI | TE | 19 | +0.13 | +0.21 | +0.01 – +0.42 |
| 47 | Tyler Kroft◦ provisional | CIN | TE | 12 | +0.05 | +0.21 | +0.00 – +0.42 |
| 48 | Josh Hill◦ provisional | NO | TE | 22 | +0.12 | +0.21 | +0.01 – +0.41 |
| 49 | Jacob Tamme◦ provisional | ATL | TE | 31 | +0.12 | +0.20 | +0.01 – +0.40 |
| 50 | David Johnson◦ provisional | PIT | TE | 12 | -0.01 | +0.20 | -0.01 – +0.41 |
| 51 | Greg Olsen | CAR | TE | 132 | +0.18 | +0.20 | +0.05 – +0.35 |
| 52 | John Phillips◦ provisional | NO | TE | 15 | +0.01 | +0.20 | -0.01 – +0.41 |
| 53 | Jermaine Gresham◦ provisional | ARI | TE | 61 | +0.15 | +0.20 | +0.02 – +0.38 |
| 54 | Garrett Celek◦ provisional | SF | TE | 50 | +0.13 | +0.20 | +0.01 – +0.38 |
| 55 | Crockett Gillmore◦ provisional | BAL | TE | 14 | -0.03 | +0.20 | -0.01 – +0.41 |
| 56 | Richard Rodgers◦ provisional | GB | TE | 47 | +0.11 | +0.19 | +0.01 – +0.38 |
| 57 | Xavier Grimble◦ provisional | PIT | TE | 21 | -0.01 | +0.19 | -0.01 – +0.39 |
| 58 | Coby Fleener◦ provisional | NO | TE | 82 | +0.14 | +0.19 | +0.02 – +0.36 |
| 59 | C.J. Uzomah◦ provisional | CIN | TE | 38 | +0.07 | +0.19 | -0.00 – +0.38 |
| 60 | C.J. Fiedorowicz◦ provisional | HOU | TE | 89 | +0.14 | +0.19 | +0.02 – +0.35 |
| 61 | Antonio Gates◦ provisional | LAC | TE | 94 | +0.13 | +0.18 | +0.02 – +0.35 |
| 62 | Marcedes Lewis◦ provisional | JAX | TE | 30 | -0.01 | +0.18 | -0.02 – +0.37 |
| 63 | Rhett Ellison◦ provisional | MIN | TE | 14 | -0.25 | +0.18 | -0.03 – +0.38 |
| 64 | Ed Dickson◦ provisional | CAR | TE | 19 | -0.16 | +0.17 | -0.03 – +0.38 |
| 65 | Demetrius Harris◦ provisional | KC | TE | 32 | -0.02 | +0.17 | -0.02 – +0.37 |
| 66 | Darren Waller◦ provisional | BAL | TE | 17 | -0.21 | +0.17 | -0.03 – +0.38 |
| 67 | Trey Burton◦ provisional | PHI | TE | 60 | +0.06 | +0.17 | -0.01 – +0.35 |
| 68 | Julius Thomas◦ provisional | JAX | TE | 51 | +0.03 | +0.17 | -0.02 – +0.35 |
| 69 | Ryan Griffin◦ provisional | HOU | TE | 74 | -0.00 | +0.14 | -0.03 – +0.31 |
| 70 | Jesse James◦ provisional | PIT | TE | 61 | -0.06 | +0.13 | -0.05 – +0.31 |
| 71 | Lance Kendricks◦ provisional | LA | TE | 87 | -0.11 | +0.08 | -0.08 – +0.25 |
| 72 | Larry Donnell◦ provisional | NYG | TE | 22 | -0.71 | +0.08 | -0.12 – +0.28 |
| 73 | Will Tye◦ provisional | NYG | TE | 70 | -0.17 | +0.08 | -0.10 – +0.25 |
| 74 | Tyler Higbee◦ provisional | LA | TE | 29 | -0.56 | +0.07 | -0.12 – +0.27 |
| 75 | Dennis Pitta | BAL | TE | 121 | -0.13 | +0.04 | -0.11 – +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).