# Misery Index v3 sensitivity

The baseline parameters were fixed before scoring. These sweeps measure dependence; they did not select the baseline.

## One parameter at a time

| Parameter | Tested value | Detroit rank | Detroit score | Tier | First | Spearman vs baseline |
|---|---:|---:|---:|---|---|---:|
| `legacy_share` | 50 | 9 | 70.95 | Severe | ARI | 0.992 |
| `legacy_share` | 60 | 8 | 72.61 | Severe | ARI | 1.000 |
| `legacy_share` | 70 | 7 | 74.26 | Severe | ARI | 0.994 |
| `championship_half_life` | 15 | 7 | 75.19 | Severe | ARI | 0.984 |
| `championship_half_life` | 20 | 8 | 72.61 | Severe | ARI | 1.000 |
| `championship_half_life` | 25 | 9 | 69.59 | Severe | ARI | 0.996 |
| `pre_super_bowl_weight` | 0.25 | 7 | 74.87 | Severe | ARI | 0.993 |
| `pre_super_bowl_weight` | 0.5 | 8 | 72.61 | Severe | ARI | 1.000 |
| `pre_super_bowl_weight` | 0.75 | 9 | 70.35 | Severe | ARI | 0.997 |
| `playoff_win_benchmark` | 0.4 | 7 | 71.90 | Severe | ARI | 0.997 |
| `playoff_win_benchmark` | 0.5 | 8 | 72.61 | Severe | ARI | 1.000 |
| `playoff_win_benchmark` | 0.6 | 8 | 73.08 | Severe | ARI | 0.997 |
| `recent_window` | 3 | 10 | 69.94 | Severe | ARI | 0.987 |
| `recent_window` | 5 | 8 | 72.61 | Severe | ARI | 1.000 |
| `recent_window` | 8 | 7 | 74.28 | Severe | ARI | 0.995 |
| `recent_half_life` | 2 | 8 | 72.48 | Severe | ARI | 0.997 |
| `recent_half_life` | 3 | 8 | 72.61 | Severe | ARI | 1.000 |
| `recent_half_life` | 5 | 8 | 72.82 | Severe | ARI | 0.999 |
| `postseason_berth_relief` | 0.05 | 8 | 73.04 | Severe | ARI | 0.999 |
| `postseason_berth_relief` | 0.1 | 8 | 72.61 | Severe | ARI | 1.000 |
| `postseason_berth_relief` | 0.15 | 8 | 72.18 | Severe | ARI | 1.000 |
| `postseason_win_relief` | 0.2 | 8 | 72.99 | Severe | ARI | 0.999 |
| `postseason_win_relief` | 0.25 | 8 | 72.61 | Severe | ARI | 1.000 |
| `postseason_win_relief` | 0.3 | 8 | 72.23 | Severe | ARI | 1.000 |
| `non_champion_relief_cap` | 0.75 | 8 | 72.61 | Severe | ARI | 1.000 |
| `non_champion_relief_cap` | 0.85 | 8 | 72.61 | Severe | ARI | 1.000 |
| `non_champion_relief_cap` | 0.95 | 8 | 72.61 | Severe | ARI | 1.000 |

## Joint core grid

The joint grid covers 729 combinations (3^6) across the legacy/current split, championship half-life, pre–Super Bowl weight, playoff-win benchmark, recent window, and recent half-life.

- Detroit baseline: rank 8, 72.61, Severe.
- Detroit rank range: 2–12; median 9.0.
- Detroit score range: 60.79–80.77; median 72.50.
- Detroit tier frequency: Historic 3, Severe 726.
- Rank-order correlation range: 0.949–1.000; median 0.981.
- First-place frequency: Arizona Cardinals 729.

## Interpretation

Detroit's exact rank is a comparative output and should be reported with the range above. Its two-layer conclusion is the more stable result: legacy remains exceptionally heavy while the Campbell-era window materially lowers current suffering. No tested variant treats a playoff win or improved regular-season result as added misery.

Machine-readable joint-grid results are in `sensitivity_results_v3.csv`.