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Game quality — opponent-adjusted EPA, 2016–2025
2026-09-14. validate.py → validate_results.json. Shipped as /nfl/game-quality
(scripts/nfl/build_game_quality.py → [redacted]).
The question: the final score hides how a game was won. "59 points" leaves out the 37 allowed; a one-point win leaves out a blown 21-point lead; a close loss leaves out a strip-sack on the last drive. Grade every play by EPAexpected points addedHow much a play changed the number of points its team should expect to score on that drive. A better measure of a play than raw yards. instead, then adjust for the opponent, so players and teams can be compared across different schedules.
Method
- Per game: EPA per scrimmage play on offense and defense, and QB EPA per dropback (passes, sacks, scrambles). Turnover and sack EPA are split out, plus win probability added (WPA).
- Opponent rating: leave-one-out. A defense's rating for game g is its per-game average over its other games that season, so the game being adjusted never rates its own opponent. It is shrunk toward a prior:
rating = (sum over other games + k × prior) / (n_other + k)
prior = league mean + w × (last season's team mean − last season's league mean)
- Adjustment:
adj_off = off − (opp_def_rating − league), and the same for defense and for QB EPA per dropback against pass defense. - Win expectancy: logistic P(win) on EPA margin, no intercept.
1. Shrinkage
Choose k and w by how well the rating predicts the held-out game's value, with each season cut off at week 2, 4, 8 and 18 so early-season behaviour counts equally.
| Unit | Best k | Best w | MSE | No shrinkage |
|---|---|---|---|---|
| Defense EPA/play allowed | 16 | 0.5 | 0.0402 | 0.0539 |
| Offense EPA/play | 12 | 0.5 | 0.0385 | 0.0508 |
| Pass defense EPA/dropback | 24 | 0.5 | 0.0881 | 0.1193 |
- Shrinkage cuts error by about 25% for every unit. The first grid stopped at 12 and the best value sat on its edge, so the grid was widened to 48.
- The curve is flat. k = 12 vs 16 differ in the fifth decimal. Shipped k = 16 for teams and k = 24 for pass defense, which is noisier per game.
- Last season's gap is worth about half. w = 0.5 won in every unit.
2. Does the adjustment help? Odd vs even weeks
If the adjustment removes schedule noise, a team's odd-week and even-week numbers should agree more.
| Measure | Raw r | Adjusted r | n |
|---|---|---|---|
| Offense EPA/play | 0.591 | 0.615 | 320 team-seasons |
| Defense EPA/play | 0.316 | 0.362 | 320 |
| EPA margin | 0.523 | 0.551 | 320 |
| QB EPA/dropback (≥75 dropbacks per half) | 0.469 | 0.486 | 374 QB-seasons |
The adjustment improves all four. The gains are modest but consistent, and largest for defense, the least stable unit.
3. Prediction: weeks 1–9 → weeks 10–18
Opponent ratings here use weeks 1–9 only, so nothing leaks from the future.
| Raw | Adjusted | |
|---|---|---|
| Per-game point margin (2,626 games) | r 0.354 | r 0.359 |
| Season point margin per game | r 0.514 | r 0.526 |
Same direction, small. The adjustment makes a rating slightly more predictive; it does not turn a description into a forecast.
4. Win expectancy
Coefficient 14.24 on EPA margin (5,502 team-games). Brier score 0.094, and it names the winner 86.5% of the time. So about 1 game in 7 is won by the team that lost the play-by-play battle. That is the "fortunate win" the page flags.
Caveats
- Descriptive. One game's grade is what happened, not a rating of the team. The adjusted margin is only somewhat more stable than raw (above).
- Quarterbacks are charged for sacks. Play-by-play puts every sack and dropback on the passer, so a bad offensive line shows up in the QB's numbers; sack EPA is a separate column so you can see how much.
- Early-season adjustments lean on last year. With k = 16, a week-2 rating is about 90% prior.
- Garbage time counts. Plays in decided games are included; the tested adjustment does not filter them.
- The win-expectancy fit includes the seasons it scores (2 parameters on 5,500 games; negligible). The 2026 page uses a fit on completed seasons only.