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.
Completion % · 2021
Completions per pass attempt. Depth-of-target confound: a checkdown offense completes more. Pair with CPOE.
- Beats raw by
- 15.6%
- lower out-of-sample error
- RMSE raw → shrunk
- 5.2% → 4.4%
- odd vs. even weeks
- Split-half reliability
- 0.42
- how repeatable the raw stat is
- Stabilizes at
- 216
- attempts 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.
Completion % · 2021 · full board
| # | Player | Team | Pos | attempts | Raw | Shrunk | 90% interval |
|---|---|---|---|---|---|---|---|
| 1 | Tom Brady | TB | QB | 742 | 65.4% | 64.2% | 61.6% – 66.7% |
| 2 | Aaron Rodgers | GB | QB | 562 | 65.1% | 63.8% | 60.9% – 66.6% |
| 3 | Dak Prescott | DAL | QB | 631 | 65.0% | 63.8% | 61.0% – 66.5% |
| 4 | Colt McCoy◦ provisional | ARI | QB | 105 | 70.5% | 63.6% | 59.1% – 67.9% |
| 5 | Kyler Murray | ARI | QB | 514 | 64.8% | 63.4% | 60.5% – 66.3% |
| 6 | Derek Carr | LV | QB | 669 | 64.0% | 63.0% | 60.4% – 65.7% |
| 7 | Joe Burrow | CIN | QB | 573 | 63.9% | 62.9% | 60.0% – 65.7% |
| 8 | Mac Jones | NE | QB | 551 | 63.9% | 62.8% | 60.0% – 65.7% |
| 9 | Matthew Stafford | LA | QB | 634 | 63.7% | 62.8% | 60.1% – 65.5% |
| 10 | Tua Tagovailoa | MIA | QB | 410 | 64.1% | 62.8% | 59.6% – 65.9% |
| 11 | Jimmy Garoppolo | SF | QB | 472 | 63.8% | 62.6% | 59.6% – 65.7% |
| 12 | Patrick Mahomes | KC | QB | 688 | 63.4% | 62.6% | 60.0% – 65.2% |
| 13 | Kirk Cousins | MIN | QB | 592 | 62.8% | 62.1% | 59.3% – 64.9% |
| 14 | Justin Herbert | LAC | QB | 710 | 62.4% | 61.9% | 59.2% – 64.5% |
| 15 | Mike White◦ provisional | NYJ | QB | 137 | 64.2% | 61.8% | 57.5% – 66.0% |
| 16 | Matt Ryan | ATL | QB | 602 | 62.3% | 61.7% | 58.9% – 64.5% |
| 17 | Jared Goff | DET | QB | 534 | 62.2% | 61.6% | 58.7% – 64.5% |
| 18 | Josh Johnson◦ provisional | BAL | QB | 88 | 64.8% | 61.5% | 56.9% – 66.1% |
| 19 | Tim Boyle◦ provisional | DET | QB | 95 | 64.2% | 61.4% | 56.9% – 65.9% |
| 20 | Teddy Bridgewater | DEN | QB | 460 | 62.0% | 61.4% | 58.3% – 64.5% |
| 21 | Ryan Tannehill | TEN | QB | 579 | 61.7% | 61.3% | 58.4% – 64.1% |
| 22 | Davis Mills | HOU | QB | 426 | 61.7% | 61.2% | 58.0% – 64.4% |
| 23 | Nick Mullens◦ provisional | CLE | QB | 30 | 66.7% | 61.0% | 55.8% – 66.0% |
| 24 | Gardner Minshew◦ provisional | PHI | QB | 66 | 62.1% | 60.7% | 55.8% – 65.4% |
| 25 | Josh Allen | BUF | QB | 675 | 60.6% | 60.5% | 57.8% – 63.2% |
| 26 | Case Keenum◦ provisional | CLE | QB | 77 | 61.0% | 60.4% | 55.7% – 65.1% |
| 27 | Joe Flacco◦ provisional | NYJ | QB | 44 | 61.4% | 60.4% | 55.4% – 65.3% |
| 28 | Daniel Jones | NYG | QB | 384 | 60.4% | 60.3% | 57.0% – 63.6% |
| 29 | Garrett Gilbert◦ provisional | WAS | QB | 33 | 60.6% | 60.3% | 55.1% – 65.3% |
| 30 | Mason Rudolph◦ provisional | PIT | QB | 58 | 60.3% | 60.2% | 55.3% – 65.0% |
| 31 | Ben Roethlisberger | PIT | QB | 648 | 60.2% | 60.2% | 57.4% – 62.9% |
| 32 | Geno Smith◦ provisional | SEA | QB | 108 | 60.2% | 60.2% | 55.7% – 64.6% |
| 33 | Nick Foles◦ provisional | CHI | QB | 40 | 60.0% | 60.2% | 55.1% – 65.1% |
| 34 | Cooper Rush◦ provisional | DAL | QB | 50 | 60.0% | 60.2% | 55.2% – 65.0% |
| 35 | Taylor Heinicke | WAS | QB | 535 | 60.0% | 60.1% | 57.1% – 63.0% |
| 36 | Sean Mannion◦ provisional | MIN | QB | 38 | 57.9% | 59.9% | 54.8% – 64.9% |
| 37 | Russell Wilson | SEA | QB | 435 | 59.5% | 59.8% | 56.6% – 62.9% |
| 38 | Tyler Huntley◦ provisional | BAL | QB | 208 | 58.7% | 59.4% | 55.5% – 63.3% |
| 39 | Andy Dalton | CHI | QB | 257 | 58.0% | 59.0% | 55.3% – 62.7% |
| 40 | Jordan Love◦ provisional | GB | QB | 66 | 54.5% | 58.9% | 54.0% – 63.6% |
| 41 | Carson Wentz | IND | QB | 552 | 58.3% | 58.9% | 55.9% – 61.8% |
| 42 | Jacoby Brissett | MIA | QB | 245 | 57.6% | 58.8% | 55.0% – 62.5% |
| 43 | Trey Lance◦ provisional | SF | QB | 75 | 54.7% | 58.8% | 54.0% – 63.5% |
| 44 | Lamar Jackson | BAL | QB | 425 | 57.9% | 58.7% | 55.5% – 61.8% |
| 45 | Drew Lock◦ provisional | DEN | QB | 120 | 55.8% | 58.6% | 54.2% – 63.0% |
| 46 | Jalen Hurts | PHI | QB | 461 | 57.5% | 58.4% | 55.2% – 61.5% |
| 47 | Tyrod Taylor◦ provisional | HOU | QB | 163 | 55.8% | 58.3% | 54.1% – 62.5% |
| 48 | Ian Book◦ provisional | NO | QB | 28 | 42.9% | 58.2% | 53.0% – 63.3% |
| 49 | Jameis Winston◦ provisional | NO | QB | 172 | 55.2% | 58.0% | 53.8% – 62.1% |
| 50 | Brandon Allen◦ provisional | CIN | QB | 39 | 43.6% | 57.6% | 52.5% – 62.7% |
| 51 | PJ Walker◦ provisional | CAR | QB | 74 | 48.6% | 57.3% | 52.4% – 62.0% |
| 52 | Trevor Lawrence | JAX | QB | 639 | 56.2% | 57.2% | 54.4% – 60.0% |
| 53 | Trevor Siemian◦ provisional | NO | QB | 201 | 53.7% | 57.1% | 53.1% – 61.0% |
| 54 | Sam Darnold | CAR | QB | 442 | 55.0% | 56.7% | 53.5% – 59.9% |
| 55 | Cam Newton◦ provisional | CAR | QB | 137 | 50.4% | 56.4% | 52.0% – 60.7% |
| 56 | Baker Mayfield | CLE | QB | 464 | 54.5% | 56.3% | 53.2% – 59.4% |
| 57 | Mike Glennon◦ provisional | NYG | QB | 177 | 50.8% | 56.0% | 51.8% – 60.1% |
| 58 | Jake Fromm◦ provisional | NYG | QB | 66 | 40.9% | 55.7% | 50.8% – 60.5% |
| 59 | Justin Fields | CHI | QB | 306 | 52.0% | 55.4% | 51.8% – 58.9% |
| 60 | Zach Wilson | NYJ | QB | 430 | 49.5% | 53.1% | 49.9% – 56.3% |
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).