Attack = Defense for Regression, Except Set Pieces (71.9%)
Attack and defense overperformance regress at identical rates (68.3% vs 68.2%). The thesis that defense is 'luckier' is wrong. But set-piece defense regresses at 71.9% — the strongest single regression signal found. Now on gauntlet shadow with 12/12 walk-forward.
The Question
Does defensive overperformance regress more reliably than attacking overperformance? The intuition: finishing is individual skill (persistent), but defensive quality is collective and fragile (one CB injury collapses it). If true, a defense-only variance filter might outperform the combined filter.
What We Found
The thesis is wrong at the aggregate level. Attack and defense regress at identical rates.
| Dimension | Regression Rate | Flags |
|---|---|---|
| Attack overperformance | 68.3% | ~2,200 |
| Defense overperformance | 68.2% | ~2,100 |
| **Delta** | **-0.1pp** | — |
But set-piece defense IS different. The one exception:
| Defense Type | Regression Rate | Delta vs Overall |
|---|---|---|
| Set-piece xGA | **71.9%** | +4.4pp |
| Open-play xGA | 67.6% | -0.6pp |
| Overall defense | 68.2% | baseline |
Teams conceding fewer set-piece goals than their set-piece xGA are getting lucky on headers from corners, free kick walls, and aerial duels. That luck regresses at 71.9% — the strongest single regression signal we've found.
The Nuance
GK PSxG adds a real but sub-threshold signal. When a team's GK is "carrying" the defense (high PSxG+/-) AND the team is a defensive overperformer, regression rate rises to 71.0% (vs 67.2% for normal GK). The +3.8pp delta is real but below our 5pp standalone threshold.
Defense-only filter is WORSE than combined. Combined filter: 69.8% regression rate, 6,975 flags. Defense-only: 68.2%, 4,223 flags. Combined wins on both quality and quantity — it catches more candidates because it includes both attack and defense overperformers.
What Didn't Work
- Attack vs defense split: identical rates, no asymmetry to exploit
- GK PSxG as standalone defense predictor: +3.8pp, below threshold
- Defense-only variance filter: fewer flags AND lower regression rate
- CB absence test: skipped, no historical per-match CB data available
What This Means
The set-piece xGA regression signal (71.9%) was registered and tested through the 10-gate pipeline. Result: 9/10 gates passed (only bootstrap significance fails at p=0.26, marginal +0.6%). It's now on gauntlet shadow with 12/12 walk-forward stability — the strongest temporal consistency of any signal tested. Monitoring for 2-3 weeks.
What's Next
Set-piece xGA regression is accumulating shadow data on /gauntlet. If live P&L confirms, it deploys as an additional enrichment signal alongside the existing variance filter — not replacing it.