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Get Started Free →Sobol variance decomposition — compute first-order and total-order sensitivity indices to quantify each parameter's contribution to output variance.
.claude/skills/yogsoth-ai-variance-decomposition/SKILL.md| Test case | Without → With | Effect | Δ tokens | Δ turns |
|---|---|---|---|---|
| case-02 | ✗→✓ | ▲ Improved | 118% | 0% |
| case-03 | ✗→✓ | ▲ Improved | 6% | 0% |
| case-05 | ✗→✓ | ▲ Improved | 165% | 0% |
| case-07 | ✗→✓ | ▲ Improved | -2% | 0% |
| case-08 | ✗→✓ | ▲ Improved | -35% | 0% |
Quantify each parameter's contribution to output variance.
| Base SOP | Target | ±10% Range | |----------|--------|------------| | web-search | 20 | 18–22 | | web-research | 10 | 9–11 | | paper-overview | 30 | 27–33 | | paper-search | 25 | 22–28 | | paper-research | 15 | 13–17 |
<HARD-GATE>
| SOP | Done | Target | % |
|-----|------|--------|---|
| web-search | ? | 20 | ? |
| web-research | ? | 10 | ? |
| paper-overview | ? | 30 | ? |
| paper-search | ? | 25 | ? |
| paper-research | ? | 15 | ? |
Budget Gate: OPEN/CLOSED (>=80% required to exit)
</HARD-GATE>Import: web-search, web-research, paper-overview, paper-search, paper-research Subagent: sobol-decomposition, interaction-detection
For parameters surviving screening, compute Sobol first-order (Si) and total-order (STi) indices. Si measures direct effect, STi-Si measures interaction contribution. Focus on parameters with high STi.
<!-- BEGIN available-tables (generated) -->
Optional, no fixed order; the final leaf is always a sop.
| Tactic | When to use | | --- | --- | | screening-then-decomposition | Two-phase sensitivity — Morris quick screening to eliminate unimportant factors, then Sobol precise decomposition on survivors. Efficient allocation of analytical effort. |
Optional, no fixed order; the final leaf is always a sop.
| SOP | When to use | | --- | --- | | interaction-detection | Detect and characterize significant parameter interactions from Sobol decomposition results. | | sobol-decomposition | Sobol variance decomposition — compute first-order and total-order sensitivity indices for precise variance attribution. |
<!-- END available-tables (generated) -->
| Case | Status | Duration (ms) | Turns | Tokens | Tool calls | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Without | With | Δ | Without | With | Δ | Without | With | Δ | Without | With | Δ | ||
case-01 | fail→fail | 33,089 | 45,935 | +39% | 1 | 1 | 0% | 5,629 | 8,794 | +56% | 0 | 0 | — |
case-02 | fail→pass | 27,302 | 44,678 | +64% | 1 | 1 | 0% | 3,933 | 8,555 | +118% | 0 | 0 | — |
case-03 | fail→pass | 43,499 | 50,386 | +16% | 1 | 1 | 0% | 8,264 | 8,786 | +6% | 0 | 0 | — |
case-04 | fail→fail | 21,078 | 47,000 | +123% | 1 | 1 | 0% | 2,904 | 8,778 | +202% | 0 | 0 | — |
case-05 | fail→pass | 22,447 | 41,474 | +85% | 1 | 1 | 0% | 3,115 | 8,243 | +165% | 0 | 0 | — |
case-06 | fail→fail | 19,333 | 12,569 | -35% | 1 | 1 | 0% | 2,220 | 2,084 | -6% | 0 | 0 | — |
case-07 | fail→pass | 33,800 | 12,025 | -64% | 1 | 1 | 0% | 1,732 | 1,691 | -2% | 0 | 0 | — |
case-08 | fail→pass | 15,768 | 7,948 | -50% | 1 | 1 | 0% | 1,587 | 1,039 | -35% | 0 | 0 | — |
case-09 | fail→fail | 35,143 | 16,060 | -54% | 1 | 1 | 0% | 2,328 | 2,433 | +5% | 0 | 0 | — |
case-10 | fail→fail | 15,011 | 19,488 | +30% | 1 | 1 | 0% | 1,761 | 3,382 | +92% | 0 | 0 | — |
case-11 | pass→pass | 17,228 | 14,461 | -16% | 1 | 1 | 0% | 2,115 | 2,166 | +2% | 0 | 0 | — |
case-12 | fail→fail | 19,059 | 7,865 | -59% | 1 | 1 | 0% | 2,266 | 993 | -56% | 0 | 0 | — |
case-13 | fail→pass | 54,771 | 43,867 | -20% | 1 | 1 | 0% | 4,309 | 8,758 | +103% | 0 | 0 | — |
case-14 | fail→fail | 27,805 | 7,263 | -74% | 1 | 1 | 0% | 1,303 | 901 | -31% | 0 | 0 | — |
case-15 | pass→pass | 19,647 | 38,542 | +96% | 1 | 1 | 0% | 2,317 | 6,861 | +196% | 0 | 0 | — |
case-16 | fail→fail | 17,072 | 7,434 | -56% | 1 | 1 | 0% | 2,676 | 980 | -63% | 0 | 0 | — |
case-17 | fail→fail | 19,028 | 34,409 | +81% | 1 | 1 | 0% | 2,769 | 6,531 | +136% | 0 | 0 | — |
case-18 | fail→fail | 41,504 | 10,909 | -74% | 1 | 1 | 0% | 1,979 | 1,765 | -11% | 0 | 0 | — |
case-19 | fail→fail | 27,026 | 8,160 | -70% | 1 | 1 | 0% | 1,043 | 1,093 | +5% | 0 | 0 | — |
case-20 | pass→pass | 20,412 | 27,183 | +33% | 1 | 1 | 0% | 2,975 | 4,853 | +63% | 0 | 0 | — |
case-21 | pass→pass | 23,023 | 41,836 | +82% | 1 | 1 | 0% | 3,631 | 8,209 | +126% | 0 | 0 | — |
case-22 | pass→fail | 22,158 | 41,674 | +88% | 1 | 1 | 0% | 3,750 | 8,792 | +134% | 0 | 0 | — |
case-23 | fail→pass | 41,949 | 8,847 | -79% | 1 | 1 | 0% | 1,327 | 1,240 | -7% | 0 | 0 | — |
DecimalAI ran this skill against gemini-3.6-flash twice over the same eval suite — once with the skill loaded and once without — and compared the two runs case by case. 23 cases were attempted, and 18 counted toward the lift figure. The other 5 produced results that are not comparable between the two arms, so they are excluded from the headline rather than averaged into it. The headline lift of +26 percentage points is the difference between those two pass rates over the 18 comparable cases. 2 cases got worse with the skill loaded, and they are included in that figure.
Without the skill loaded, the model failed this case. With it loaded, the same prompt on the same model passed. This is one improved case from the latest verified run; every case, including any that regressed, is in the table above.
Other measured skills in the registry, with their headline benchmark lift.