339 lines
11 KiB
Markdown
339 lines
11 KiB
Markdown
# Expected Value Templates
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Quick-start templates for decision framing, outcome identification, probability estimation, payoff quantification, EV calculation, and sensitivity analysis.
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## Workflow
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```
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Expected Value Analysis Progress:
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- [ ] Step 1: Define decision and alternatives
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- [ ] Step 2: Identify possible outcomes
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- [ ] Step 3: Estimate probabilities
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- [ ] Step 4: Estimate payoffs (values)
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- [ ] Step 5: Calculate expected values
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- [ ] Step 6: Interpret and adjust for risk preferences
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```
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**Step 1: Define decision and alternatives** → Use [Decision Framing Template](#decision-framing-template)
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**Step 2: Identify possible outcomes** → Use [Outcome Identification Template](#outcome-identification-template)
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**Step 3: Estimate probabilities** → Use [Probability Estimation Template](#probability-estimation-template)
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**Step 4: Estimate payoffs** → Use [Payoff Quantification Template](#payoff-quantification-template)
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**Step 5: Calculate expected values** → Use [EV Calculation Template](#ev-calculation-template)
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**Step 6: Interpret and adjust for risk** → Use [Risk Adjustment Template](#risk-adjustment-template) and [Sensitivity Analysis Template](#sensitivity-analysis-template)
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---
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## Decision Framing Template
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**Decision to be made**: [Clear statement of the choice]
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**Context**: [Why are you making this decision? What's the deadline? What constraints exist?]
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**Alternatives** (mutually exclusive options):
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1. **[Alternative 1]**: [Brief description]
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2. **[Alternative 2]**: [Brief description]
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3. **[Alternative 3]**: [Brief description, if applicable]
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4. **Do nothing / status quo**: [Always consider baseline]
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**Success criteria**: [How will you know if this was a good decision? What are you optimizing for?]
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**Assumptions**:
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- [Key assumption 1]
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- [Key assumption 2]
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- [Key assumption 3]
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**Out of scope** (not considering):
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- [Factor 1 you're explicitly not modeling]
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- [Factor 2]
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---
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## Outcome Identification Template
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For each alternative, identify 3-5 possible outcomes (scenarios).
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### Alternative: [Name]
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**Outcome 1: Best case**
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- **Description**: [What happens in optimistic scenario?]
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- **Key drivers**: [What needs to go right?]
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- **Likelihood indicator**: [Rough sense: common, uncommon, rare?]
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**Outcome 2: Base case**
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- **Description**: [What happens in most likely scenario?]
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- **Key drivers**: [What's the typical path?]
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- **Likelihood indicator**: [Should be most probable]
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**Outcome 3: Worst case**
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- **Description**: [What happens in pessimistic scenario?]
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- **Key drivers**: [What needs to go wrong?]
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- **Likelihood indicator**: [How bad could it get?]
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**Outcome 4: [Other scenario, if needed]**
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- **Description**:
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- **Key drivers**:
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- **Likelihood indicator**:
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**Check**: Do these outcomes cover the full range of possibilities? Are they mutually exclusive (no overlap)?
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---
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## Probability Estimation Template
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Estimate probability for each outcome using multiple methods, then reconcile.
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### Outcome: [Name]
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| Method | Estimate | Notes |
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|--------|----------|-------|
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| **Base rates** (reference class) | [X%] | [Similar situations: N cases, frequency] |
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| **Inside view** (causal model) | [Y%] | [Key factors: p_A × p_B × p_C] |
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| **Expert judgment** | [Z%] | [Average of expert estimates] |
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| **Data/model** | [W%] | [Forecast, confidence interval] |
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**Final estimate**: [Weighted average] **Confidence**: [Range if uncertain]
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**All outcomes** (must sum to 1.0):
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- Outcome 1: [p₁], Outcome 2: [p₂], Outcome 3: [p₃]. **Total**: [p₁+p₂+p₃ = 1.0 ✓]
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---
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## Payoff Quantification Template
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### Outcome: [Name]
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**Monetary**: Revenue [+$X], Cost [-$Y], Savings [+$Z], Opp. cost [-$W]. **Net**: [Sum]
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**Non-monetary** (convert to $ or utility): Time [X hrs × $rate], Reputation [$Z], Learning [$W], Strategic [qualitative or $], Morale [qualitative or $]
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**Time horizon**: [When?] **Discount rate**: [r%/yr if multi-period]
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**NPV** (if multi-period): Yr0 [$X/(1+r)⁰], Yr1 [$Y/(1+r)¹], Yr2 [$Z/(1+r)²]. **Total NPV**: [Sum]
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**Total Payoff**: [$ or utility] **Uncertainty**: [Point estimate or range: low-high]
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---
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## EV Calculation Template
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Calculate expected value for each alternative.
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### Alternative: [Name]
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| Outcome | Probability (p) | Payoff (v) | p × v |
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|---------|----------------|-----------|-------|
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| [Outcome 1] | [p₁] | [v₁] | [p₁ × v₁] |
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| [Outcome 2] | [p₂] | [v₂] | [p₂ × v₂] |
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| [Outcome 3] | [p₃] | [v₃] | [p₃ × v₃] |
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| **Total** | **1.0** | | **EV = Σ (p × v)** |
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**Expected Value**: [EV = p₁×v₁ + p₂×v₂ + p₃×v₃]
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**Variance**: Var = Σ (pᵢ × (vᵢ - EV)²)
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- (v₁ - EV)² × p₁ = [X]
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- (v₂ - EV)² × p₂ = [Y]
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- (v₃ - EV)² × p₃ = [Z]
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- **Variance** = [X + Y + Z]
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**Standard Deviation**: σ = √Var = [σ]
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**Coefficient of Variation**: CV = σ / EV = [CV] (lower = better risk-adjusted return)
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### Comparison Across Alternatives
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| Alternative | EV | σ (risk) | CV | Rank by EV |
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|-------------|-------|----------|-----|------------|
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| [Alt 1] | [EV₁] | [σ₁] | [CV₁] | [1] |
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| [Alt 2] | [EV₂] | [σ₂] | [CV₂] | [2] |
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| [Alt 3] | [EV₃] | [σ₃] | [CV₃] | [3] |
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**Preliminary recommendation** (based on EV): [Highest EV alternative]
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---
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## Sensitivity Analysis Template
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Test how sensitive the decision is to changes in key assumptions.
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### One-Way Sensitivity (vary one variable at a time)
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**Variable**: Probability of [Outcome X]
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| p(Outcome X) | EV(Alt 1) | EV(Alt 2) | Best choice |
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|-------------|-----------|-----------|-------------|
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| [Low: p-20%] | [EV] | [EV] | [Alt] |
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| [Base: p] | [EV] | [EV] | [Alt] |
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| [High: p+20%] | [EV] | [EV] | [Alt] |
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**Breakeven**: At what probability does decision flip? Solve: EV(Alt 1) = EV(Alt 2).
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**Variable**: Payoff of [Outcome Y]
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| v(Outcome Y) | EV(Alt 1) | EV(Alt 2) | Best choice |
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|-------------|-----------|-----------|-------------|
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| [Low: v-30%] | [EV] | [EV] | [Alt] |
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| [Base: v] | [EV] | [EV] | [Alt] |
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| [High: v+30%] | [EV] | [EV] | [Alt] |
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### Tornado Diagram (which variables have most impact on EV?)
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| Variable | Range tested | Impact on EV (swing) | Rank |
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|----------|-------------|---------------------|------|
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| [Var 1] | [low-high] | [±$X] | [1 (highest impact)] |
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| [Var 2] | [low-high] | [±$Y] | [2] |
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| [Var 3] | [low-high] | [±$Z] | [3] |
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**Interpretation**: Focus on high-impact variables. Get better estimates for top 2-3.
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### Scenario Analysis (vary multiple variables together)
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| Scenario | Assumptions | EV(Alt 1) | EV(Alt 2) | Best |
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|----------|------------|-----------|-----------|------|
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| **Optimistic** | [High demand, low cost, no delays] | [EV] | [EV] | [Alt] |
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| **Base** | [Expected values] | [EV] | [EV] | [Alt] |
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| **Pessimistic** | [Low demand, high cost, delays] | [EV] | [EV] | [Alt] |
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**Robustness**: Does the decision hold across scenarios? If different winners in different scenarios → decision is fragile, more info needed.
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---
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## Risk Adjustment Template
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**Risk profile**: Risk-neutral / Risk-averse / Risk-seeking? One-shot or repeated decision?
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**Utility function** (if risk-averse): U(x) = x (neutral), √x (moderate aversion), log(x) (strong aversion)
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### Expected Utility (if risk-averse)
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| Outcome | p | v | U(v) | p × U(v) |
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|---------|---|---|------|----------|
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| [Out 1] | [p₁] | [v₁] | [U(v₁)] | [p₁ × U(v₁)] |
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| [Out 2] | [p₂] | [v₂] | [U(v₂)] | [p₂ × U(v₂)] |
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| **Total** | **1.0** | | | **EU = Σ** |
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**Certainty Equivalent**: CE = U⁻¹(EU). **Risk Premium**: EV - CE.
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**Non-monetary factors**: Strategic value [$/qualitative], Alignment with mission [score 1-5], Regret [low/med/high]
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**Recommendation**: Highest EV [Alt X], Highest EU [Alt Y], **Final choice**: [Alt Z with rationale]
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---
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## Decision Tree Template
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For sequential decisions (make choice, observe outcome, make another choice).
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### Tree Structure
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```
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[Decision 1] → [Outcome A] → [Decision 2a] → [Outcome C]
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→ [Outcome D]
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→ [Outcome B] → [Decision 2b] → [Outcome E]
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→ [Outcome F]
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```
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### Fold-Back Induction (work backwards from end)
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**Step 1: Calculate EV at terminal nodes** (final outcomes)
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- Outcome C: [payoff = $X]
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- Outcome D: [payoff = $Y]
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- Outcome E: [payoff = $Z]
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- Outcome F: [payoff = $W]
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**Step 2: Calculate EV at Decision 2a**
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- If choose path to C: [p(C) × $X]
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- If choose path to D: [p(D) × $Y]
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- **Optimal Decision 2a**: [Choose whichever has higher EV]
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- **EV(Decision 2a)**: [max of the two]
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**Step 3: Calculate EV at Decision 2b**
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- If choose path to E: [p(E) × $Z]
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- If choose path to F: [p(F) × $W]
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- **Optimal Decision 2b**: [Choose whichever has higher EV]
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- **EV(Decision 2b)**: [max of the two]
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**Step 4: Calculate EV at Decision 1**
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- If choose path to A: [p(A) × EV(Decision 2a)]
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- If choose path to B: [p(B) × EV(Decision 2b)]
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- **Optimal Decision 1**: [Choose whichever has higher EV]
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- **Overall EV**: [max of the two]
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**Optimal Strategy**:
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1. At Decision 1: [Choose A or B]
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2. If A occurs, at Decision 2a: [Choose path to C or D]
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3. If B occurs, at Decision 2b: [Choose path to E or F]
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**Value of Information**: If you could know outcome before Decision 1, how much would that be worth?
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- EVPI = EV(with perfect info) - EV(current decision)
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---
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## Complete EV Analysis Template
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**Decision**: [Name]
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**Date**: [Date]
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**Decision maker**: [Name/Team]
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### 1. Decision Framing
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**Alternatives**:
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1. [Alt 1]
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2. [Alt 2]
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3. [Alt 3]
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**Success criteria**: [What are you optimizing for?]
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### 2. Outcomes and Probabilities
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| Alternative | Outcome | Probability | Payoff | p × v |
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|-------------|---------|------------|--------|-------|
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| **[Alt 1]** | [Outcome 1] | [p₁] | [v₁] | [p₁ × v₁] |
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| | [Outcome 2] | [p₂] | [v₂] | [p₂ × v₂] |
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| | [Outcome 3] | [p₃] | [v₃] | [p₃ × v₃] |
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| | **EV(Alt 1)** | | | **[EV₁]** |
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| **[Alt 2]** | [Outcome 1] | [p₁] | [v₁] | [p₁ × v₁] |
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| | [Outcome 2] | [p₂] | [v₂] | [p₂ × v₂] |
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| | [Outcome 3] | [p₃] | [v₃] | [p₃ × v₃] |
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| | **EV(Alt 2)** | | | **[EV₂]** |
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### 3. Comparison
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| Alternative | EV | σ (risk) | CV |
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|-------------|-------|----------|-----|
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| [Alt 1] | [EV₁] | [σ₁] | [CV₁] |
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| [Alt 2] | [EV₂] | [σ₂] | [CV₂] |
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**Highest EV**: [Alt X with EV = $Y]
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### 4. Sensitivity Analysis
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**Key assumptions**:
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- [Assumption 1]: [If this changes by X%, decision flips? Yes/No]
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- [Assumption 2]: [Breakeven value = ?]
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**Robustness**: [Is decision robust across scenarios?]
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### 5. Risk Adjustment
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**Risk profile**: [One-shot or repeated? Risk-averse or neutral?]
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**Recommendation**: [Alt X]
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**Rationale**: [Why this choice given EV, risk, strategic factors?]
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### 6. Action Plan
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**Next steps**:
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1. [Immediate action]
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2. [Follow-up in X days/weeks]
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3. [Decision review date]
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**Contingencies**: [If Outcome Y occurs, we will...]
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