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.
Dropback success rate · 2016
Share of dropbacks (incl. sacks & scrambles) with positive EPA.
- Beats raw by
- 15.6%
- lower out-of-sample error
- RMSE raw → shrunk
- 5.5% → 4.6%
- odd vs. even weeks
- Split-half reliability
- 0.47
- how repeatable the raw stat is
- Stabilizes at
- 160
- dropbacks 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.
Dropback success rate · 2016 · full board
| # | Player | Team | Pos | dropbacks | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Matt Ryan | ATL | QB | 575 | 53.4% | 51.6% | 48.5% – 54.6% |
| 2 | Kirk Cousins | WAS | QB | 628 | 52.1% | 50.6% | 47.7% – 53.6% |
| 3 | Drew Brees | NO | QB | 695 | 51.4% | 50.2% | 47.4% – 53.0% |
| 4 | Dak Prescott | DAL | QB | 484 | 51.0% | 49.5% | 46.3% – 52.8% |
| 5 | Derek Anderson◦ provisional | CAR | QB | 54 | 61.1% | 49.1% | 43.5% – 54.7% |
| 6 | Tom Brady | NE | QB | 448 | 50.2% | 48.9% | 45.5% – 52.2% |
| 7 | Matt Barkley | CHI | QB | 222 | 50.9% | 48.5% | 44.3% – 52.7% |
| 8 | Brian Hoyer | CHI | QB | 202 | 50.0% | 47.8% | 43.5% – 52.1% |
| 9 | Andrew Luck | IND | QB | 586 | 48.5% | 47.7% | 44.7% – 50.7% |
| 10 | Matthew Stafford | DET | QB | 630 | 48.1% | 47.5% | 44.6% – 50.4% |
| 11 | Jameis Winston | TB | QB | 607 | 48.1% | 47.5% | 44.5% – 50.4% |
| 12 | Ben Roethlisberger | PIT | QB | 532 | 48.1% | 47.4% | 44.3% – 50.5% |
| 13 | Andy Dalton | CIN | QB | 602 | 48.0% | 47.4% | 44.4% – 50.4% |
| 14 | Aaron Rodgers | GB | QB | 645 | 47.6% | 47.1% | 44.2% – 50.0% |
| 15 | Russell Wilson | SEA | QB | 587 | 47.5% | 47.0% | 44.0% – 50.0% |
| 16 | Jimmy Garoppolo◦ provisional | NE | QB | 66 | 51.5% | 47.0% | 41.5% – 52.4% |
| 17 | Sam Bradford | MIN | QB | 590 | 47.5% | 46.9% | 44.0% – 50.0% |
| 18 | Matt Moore◦ provisional | MIA | QB | 87 | 49.4% | 46.6% | 41.4% – 51.8% |
| 19 | Carson Palmer | ARI | QB | 639 | 46.9% | 46.6% | 43.7% – 49.5% |
| 20 | Alex Smith | KC | QB | 518 | 46.5% | 46.2% | 43.0% – 49.3% |
| 21 | Marcus Mariota | TEN | QB | 475 | 46.1% | 45.9% | 42.6% – 49.1% |
| 22 | Shaun Hill◦ provisional | MIN | QB | 36 | 47.2% | 45.5% | 39.7% – 51.3% |
| 23 | Ryan Tannehill | MIA | QB | 418 | 45.5% | 45.4% | 42.0% – 48.8% |
| 24 | Derek Carr | LV | QB | 580 | 45.3% | 45.3% | 42.3% – 48.3% |
| 25 | Philip Rivers | LAC | QB | 615 | 45.2% | 45.2% | 42.3% – 48.1% |
| 26 | Charlie Whitehurst◦ provisional | CLE | QB | 27 | 44.4% | 45.0% | 39.1% – 51.0% |
| 27 | Brock Osweiler | HOU | QB | 534 | 44.6% | 44.7% | 41.6% – 47.8% |
| 28 | Paxton Lynch◦ provisional | DEN | QB | 91 | 44.0% | 44.7% | 39.5% – 49.9% |
| 29 | Eli Manning | NYG | QB | 619 | 44.1% | 44.3% | 41.4% – 47.2% |
| 30 | EJ Manuel◦ provisional | BUF | QB | 30 | 40.0% | 44.3% | 38.4% – 50.2% |
| 31 | Landry Jones◦ provisional | PIT | QB | 89 | 42.7% | 44.2% | 39.1% – 49.4% |
| 32 | Scott Tolzien◦ provisional | IND | QB | 40 | 40.0% | 44.1% | 38.3% – 49.9% |
| 33 | Trevor Siemian | DEN | QB | 518 | 43.6% | 44.0% | 40.8% – 47.1% |
| 34 | Carson Wentz | PHI | QB | 641 | 43.5% | 43.8% | 41.0% – 46.7% |
| 35 | Cody Kessler | CLE | QB | 217 | 42.9% | 43.8% | 39.6% – 48.0% |
| 36 | Tom Savage◦ provisional | HOU | QB | 78 | 41.0% | 43.8% | 38.5% – 49.1% |
| 37 | Tyrod Taylor | BUF | QB | 478 | 43.1% | 43.6% | 40.4% – 46.8% |
| 38 | Joe Flacco | BAL | QB | 703 | 43.2% | 43.6% | 40.8% – 46.4% |
| 39 | Matt Cassel◦ provisional | TEN | QB | 54 | 38.9% | 43.5% | 38.0% – 49.1% |
| 40 | Kevin Hogan◦ provisional | CLE | QB | 28 | 32.1% | 43.1% | 37.3% – 49.1% |
| 41 | Ryan Fitzpatrick | NYJ | QB | 422 | 42.2% | 43.0% | 39.6% – 46.4% |
| 42 | Nick Foles◦ provisional | KC | QB | 59 | 35.6% | 42.5% | 37.1% – 48.0% |
| 43 | Blake Bortles | JAX | QB | 660 | 41.7% | 42.3% | 39.5% – 45.2% |
| 44 | Cam Newton | CAR | QB | 547 | 41.5% | 42.3% | 39.3% – 45.4% |
| 45 | Jacoby Brissett◦ provisional | NE | QB | 61 | 34.4% | 42.1% | 36.7% – 47.6% |
| 46 | Jay Cutler◦ provisional | CHI | QB | 154 | 39.0% | 42.1% | 37.5% – 46.7% |
| 47 | Colin Kaepernick | SF | QB | 366 | 39.9% | 41.5% | 38.0% – 45.0% |
| 48 | Josh McCown | CLE | QB | 183 | 38.3% | 41.4% | 37.1% – 45.8% |
| 49 | Drew Stanton◦ provisional | ARI | QB | 48 | 29.2% | 41.4% | 35.9% – 47.1% |
| 50 | Bryce Petty◦ provisional | NYJ | QB | 146 | 36.3% | 40.9% | 36.3% – 45.5% |
| 51 | Case Keenum | LA | QB | 345 | 38.6% | 40.6% | 37.0% – 44.2% |
| 52 | Blaine Gabbert | SF | QB | 171 | 36.3% | 40.5% | 36.1% – 45.0% |
| 53 | Robert Griffin III | CLE | QB | 169 | 33.7% | 39.3% | 34.9% – 43.7% |
| 54 | Jared Goff | LA | QB | 230 | 30.4% | 36.4% | 32.5% – 40.5% |
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).