variance-strategy-selector

What this skill does

# Variance Strategy Selector

## Table of Contents
- [Example](#example)
- [Workflow](#workflow)
- [Common Patterns](#common-patterns)
- [Guardrails](#guardrails)
- [Quick Reference](#quick-reference)

## Example

**Scenario**: A fantasy manager is 15% behind their opponent with 3 lineup slots left to decide this week. Losing this week eliminates them from playoff contention.

**Inputs**:
- `current_win_probability` = 0.32 (heavy underdog)
- `downside_asymmetry` = 0.90 (must-win, catastrophic if lost)
- `slots_to_decide` = 3

**Band classification**: `win_probability < 0.40` -> posture = "seek", base multiplier range 1.15-1.30.

**Asymmetry amplification**: `downside_asymmetry > 0.8` -> shift multiplier further from 1.0 by +0.10 on the seek side. Base 1.20 + 0.10 = **1.30**.

**Slot-count dampening**: `slots_to_decide = 3`, below the 5-slot threshold -> no dampening applied.

**Outputs**:
- `variance_posture`: "seek"
- `variance_multiplier`: 1.30
- `confidence_band`: "high-variance (seek aggressively)"
- `rationale`: "Pre-move win probability is 0.32 (heavy underdog) and the downside is catastrophic (must-win, asymmetry 0.90). Maximizing variance raises the probability of a right-tail outcome. Consumer should boost high-variance options (boom-bust players, concentrated positions, longshot bets) by 30%."

**Consumer application** (downstream skill applies the multiplier):
```
adjusted_player_score = base_score x (1 + (boom_bust_score - 0.5) x (variance_multiplier - 1))
```
A boom-bust score of 0.8 (high-variance player) with multiplier 1.30 gets a +9% boost relative to a steady player.

## Workflow

Copy this checklist and track progress:

```
Variance Strategy Selection Progress:
- [ ] Step 1: Collect inputs (win_probability, downside_asymmetry, slots_to_decide)
- [ ] Step 2: Classify win-probability band (seek / neutral / minimize)
- [ ] Step 3: Apply downside-asymmetry amplification
- [ ] Step 4: Apply slot-count dampening
- [ ] Step 5: Clamp multiplier to valid range and validate monotonicity
- [ ] Step 6: Emit structured output with rationale
```

**Step 1: Collect inputs**

- [ ] `current_win_probability` is a float in [0, 1]. Reject values outside this range.
- [ ] `downside_asymmetry` is a float in [0, 1] where 1.0 = losing is catastrophic (must-win for playoffs, elimination game, bankroll ruin).
- [ ] `slots_to_decide` is a non-negative integer representing how many independent decisions this posture covers (lineup slots, portfolio positions, bet sequence length).

See [resources/template.md](resources/template.md#input-validation-checklist) for input validation rules.

**Step 2: Classify win-probability band**

Apply the three-band rule:

- [ ] `win_probability < 0.40` -> posture = "seek", base multiplier 1.15-1.30
- [ ] `0.40 <= win_probability <= 0.60` -> posture = "neutral", base multiplier 1.00
- [ ] `win_probability > 0.60` -> posture = "minimize", base multiplier 0.80-0.90

Within the "seek" band, pick the base multiplier proportional to how far below 0.40 the probability is: `base = 1.15 + (0.40 - win_probability) x 0.375`, clamped to 1.30. Within "minimize", mirror: `base = 0.90 - (win_probability - 0.60) x 0.25`, clamped to 0.80.

See [resources/methodology.md](resources/methodology.md#why-underdogs-want-variance) for the underlying right-tail / left-tail logic.

**Step 3: Apply downside-asymmetry amplification**

If the loss is catastrophic, the underdog must swing harder and the favorite must protect harder. The adjustment is symmetric around 1.0.

- [ ] If `downside_asymmetry > 0.8` and posture = "seek": shift multiplier +0.10 (further above 1.0)
- [ ] If `downside_asymmetry > 0.8` and posture = "minimize": shift multiplier -0.10 (further below 1.0)
- [ ] If `downside_asymmetry > 0.8` and posture = "neutral": no shift (neutral remains neutral by definition)
- [ ] If `downside_asymmetry <= 0.8`: no shift

**Step 4: Apply slot-count dampening**

With many independent decisions, the Central Limit Theorem diversifies variance on its own. Pushing the multiplier hard across many slots is redundant.

- [ ] If `slots_to_decide > 5`: dampen the distance from 1.0 by a factor of `5 / slots_to_decide` (bounded below at 0.5). E.g. with 10 slots, reduce the gap by half.
- [ ] If `slots_to_decide <= 5`: no dampening.

See [resources/methodology.md](resources/methodology.md#central-limit-dampening) for the math.

**Step 5: Clamp and validate monotonicity**

- [ ] Clamp the final multiplier to the range [0.70, 1.40]. Values outside this range indicate an input or computation error.
- [ ] Confirm monotonicity: as `win_probability` decreases, multiplier must weakly increase. As `downside_asymmetry` increases, |multiplier - 1.0| must weakly increase.

**Step 6: Emit structured output**

Return the four required fields:

- [ ] `variance_posture` -- "seek" | "neutral" | "minimize"
- [ ] `variance_multiplier` -- final number in [0.70, 1.40]
- [ ] `confidence_band` -- short human-readable descriptor (e.g. "high-variance (seek aggressively)", "low-variance (protect the lead)")
- [ ] `rationale` -- 2-3 sentences citing win probability band, asymmetry flag, slot count effect, and how the consumer should interpret the multiplier

Validate using [resources/evaluators/rubric_variance_strategy_selector.json](resources/evaluators/rubric_variance_strategy_selector.json). Minimum standard: average score of 3.5 or above.

## Common Patterns

**Pattern 1: Heavy underdog, must-win (fantasy sports)**
- Inputs: win_prob ~0.30, asymmetry ~0.90, slots 1-3
- Output: posture "seek", multiplier ~1.30
- Rationale: Swing for the fences. Prefer a high-K / high-HR boom-bust hitter over a high-contact singles hitter; prefer a volatile SP with upside over a stable #4 starter. Consumer skill (e.g. `mlb-lineup-optimizer`) multiplies boom-bust weight by 1.30.

**Pattern 2: Heavy favorite, large portfolio / many slots**
- Inputs: win_prob ~0.75, asymmetry ~0.50, slots ~12 (full lineup / diversified portfolio)
- Output: posture "minimize", multiplier ~0.92 (after slot dampening from 0.85)
- Rationale: Protect the lead, but don't over-engineer -- with 12 slots the portfolio is already diversified by the Central Limit effect. Small damp on the variance knob is enough. Consumer reduces concentration / boom-bust weight by 8%.

**Pattern 3: Even matchup (poker mid-stack)**
- Inputs: win_prob ~0.50, asymmetry ~0.40, slots ~5 (next 5 hands)
- Output: posture "neutral", multiplier 1.00
- Rationale: Play close to GTO. No variance tilt either way. Consumer applies no adjustment to bet sizing.

**Pattern 4: Mild favorite, one decisive decision (racing / options expiry)**
- Inputs: win_prob ~0.65, asymmetry ~0.85, slots 1
- Output: posture "minimize", multiplier ~0.75 (base 0.85 - 0.10 asymmetry shift, no slot dampening)
- Rationale: One shot, lead to protect, catastrophic if squandered. The race leader does not take the high-risk inside line; the hedged call writer does not lift the hedge on expiry day. Consumer hard-damps variance.

## Guardrails

1. **Bands are hard, not fuzzy.** Do not interpolate the posture label across 0.40 and 0.60 thresholds. Posture is categorical (seek / neutral / minimize); the multiplier is continuous within each band. Consumers rely on the categorical label for branching logic.

2. **Asymmetry amplifies, never reverses.** A catastrophic downside makes a favorite more conservative and an underdog more aggressive. It never flips the direction. If the computed multiplier would cross 1.0 because of an asymmetry shift, clamp at 1.0 and recheck inputs.

3. **Slot dampening applies to the distance from 1.0, not to the multiplier itself.** Implementation: `final = 1.0 + (pre_dampening - 1.0) x min(1.0, 5 / slots)`. Dampening 1.30 across 10 slots gives 1.15, not 0.65.

4. **Edge cases at probability 0 and 1.** If `win_probability = 0`, posture is "seek" with maximum multiplier (1.30 pre-asymmetry, 1.40 post); the analogy is a lottery ticket -- variance is the only path to