gh-lyndonkl-claude/skills/expected-value/resources/template.md

Expected Value Templates

Quick-start templates for decision framing, outcome identification, probability estimation, payoff quantification, EV calculation, and sensitivity analysis.

Workflow

Expected Value Analysis Progress:
- [ ] Step 1: Define decision and alternatives
- [ ] Step 2: Identify possible outcomes
- [ ] Step 3: Estimate probabilities
- [ ] Step 4: Estimate payoffs (values)
- [ ] Step 5: Calculate expected values
- [ ] Step 6: Interpret and adjust for risk preferences

Step 1: Define decision and alternatives → Use Decision Framing Template

Step 2: Identify possible outcomes → Use Outcome Identification Template

Step 3: Estimate probabilities → Use Probability Estimation Template

Step 4: Estimate payoffs → Use Payoff Quantification Template

Step 5: Calculate expected values → Use EV Calculation Template

Step 6: Interpret and adjust for risk → Use Risk Adjustment Template and Sensitivity Analysis Template

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Decision Framing Template

Decision to be made: [Clear statement of the choice]

Context: [Why are you making this decision? What's the deadline? What constraints exist?]

Alternatives (mutually exclusive options):

1. [Alternative 1]: [Brief description]
2. [Alternative 2]: [Brief description]
3. [Alternative 3]: [Brief description, if applicable]
4. Do nothing / status quo: [Always consider baseline]

Success criteria: [How will you know if this was a good decision? What are you optimizing for?]

Assumptions:

• [Key assumption 1]
• [Key assumption 2]
• [Key assumption 3]

Out of scope (not considering):

• [Factor 1 you're explicitly not modeling]
• [Factor 2]

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Outcome Identification Template

For each alternative, identify 3-5 possible outcomes (scenarios).

Alternative: [Name]

Outcome 1: Best case

• Description: [What happens in optimistic scenario?]
• Key drivers: [What needs to go right?]
• Likelihood indicator: [Rough sense: common, uncommon, rare?]

Outcome 2: Base case

• Description: [What happens in most likely scenario?]
• Key drivers: [What's the typical path?]
• Likelihood indicator: [Should be most probable]

Outcome 3: Worst case

• Description: [What happens in pessimistic scenario?]
• Key drivers: [What needs to go wrong?]
• Likelihood indicator: [How bad could it get?]

Outcome 4: [Other scenario, if needed]

• Description:
• Key drivers:
• Likelihood indicator:

Check: Do these outcomes cover the full range of possibilities? Are they mutually exclusive (no overlap)?

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Probability Estimation Template

Estimate probability for each outcome using multiple methods, then reconcile.

Outcome: [Name]

Method	Estimate	Notes
Base rates (reference class)	[X%]	[Similar situations: N cases, frequency]
Inside view (causal model)	[Y%]	[Key factors: p_A × p_B × p_C]
Expert judgment	[Z%]	[Average of expert estimates]
Data/model	[W%]	[Forecast, confidence interval]

Final estimate: [Weighted average] Confidence: [Range if uncertain]

All outcomes (must sum to 1.0):

• Outcome 1: [p₁], Outcome 2: [p₂], Outcome 3: [p₃]. Total: [p₁+p₂+p₃ = 1.0 ✓]

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Payoff Quantification Template

Outcome: [Name]

Monetary: Revenue [+$X], Cost [-$Y], Savings [+$Z], Opp. cost [-$W]. Net: [Sum]

Non-monetary (convert to $ or utility): Time [X hrs × $rate], Reputation [$Z], Learning [$W], Strategic [qualitative or $], Morale [qualitative or $]

Time horizon: [When?] Discount rate: [r%/yr if multi-period]

NPV (if multi-period): Yr0 [$X/(1+r)⁰], Yr1 [$Y/(1+r)¹], Yr2 [$Z/(1+r)²]. Total NPV: [Sum]

Total Payoff: [$ or utility] Uncertainty: [Point estimate or range: low-high]

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EV Calculation Template

Calculate expected value for each alternative.

Alternative: [Name]

Outcome	Probability (p)	Payoff (v)	p × v
[Outcome 1]	[p₁]	[v₁]	[p₁ × v₁]
[Outcome 2]	[p₂]	[v₂]	[p₂ × v₂]
[Outcome 3]	[p₃]	[v₃]	[p₃ × v₃]
Total	1.0		EV = Σ (p × v)

Expected Value: [EV = p₁×v₁ + p₂×v₂ + p₃×v₃]

Variance: Var = Σ (pᵢ × (vᵢ - EV)²)

• (v₁ - EV)² × p₁ = [X]
• (v₂ - EV)² × p₂ = [Y]
• (v₃ - EV)² × p₃ = [Z]
• Variance = [X + Y + Z]

Standard Deviation: σ = √Var = [σ]

Coefficient of Variation: CV = σ / EV = [CV] (lower = better risk-adjusted return)

Comparison Across Alternatives

Alternative	EV	σ (risk)	CV	Rank by EV
[Alt 1]	[EV₁]	[σ₁]	[CV₁]	[1]
[Alt 2]	[EV₂]	[σ₂]	[CV₂]	[2]
[Alt 3]	[EV₃]	[σ₃]	[CV₃]	[3]

Preliminary recommendation (based on EV): [Highest EV alternative]

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Sensitivity Analysis Template

Test how sensitive the decision is to changes in key assumptions.

One-Way Sensitivity (vary one variable at a time)

Variable: Probability of [Outcome X]

p(Outcome X)	EV(Alt 1)	EV(Alt 2)	Best choice
[Low: p-20%]	[EV]	[EV]	[Alt]
[Base: p]	[EV]	[EV]	[Alt]
[High: p+20%]	[EV]	[EV]	[Alt]

Breakeven: At what probability does decision flip? Solve: EV(Alt 1) = EV(Alt 2).

Variable: Payoff of [Outcome Y]

v(Outcome Y)	EV(Alt 1)	EV(Alt 2)	Best choice
[Low: v-30%]	[EV]	[EV]	[Alt]
[Base: v]	[EV]	[EV]	[Alt]
[High: v+30%]	[EV]	[EV]	[Alt]

Tornado Diagram (which variables have most impact on EV?)

Variable	Range tested	Impact on EV (swing)	Rank
[Var 1]	[low-high]	[±$X]	[1 (highest impact)]
[Var 2]	[low-high]	[±$Y]	[2]
[Var 3]	[low-high]	[±$Z]	[3]

Interpretation: Focus on high-impact variables. Get better estimates for top 2-3.

Scenario Analysis (vary multiple variables together)

Scenario	Assumptions	EV(Alt 1)	EV(Alt 2)	Best
Optimistic	[High demand, low cost, no delays]	[EV]	[EV]	[Alt]
Base	[Expected values]	[EV]	[EV]	[Alt]
Pessimistic	[Low demand, high cost, delays]	[EV]	[EV]	[Alt]

Robustness: Does the decision hold across scenarios? If different winners in different scenarios → decision is fragile, more info needed.

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Risk Adjustment Template

Risk profile: Risk-neutral / Risk-averse / Risk-seeking? One-shot or repeated decision?

Utility function (if risk-averse): U(x) = x (neutral), √x (moderate aversion), log(x) (strong aversion)

Expected Utility (if risk-averse)

Outcome	p	v	U(v)	p × U(v)
[Out 1]	[p₁]	[v₁]	[U(v₁)]	[p₁ × U(v₁)]
[Out 2]	[p₂]	[v₂]	[U(v₂)]	[p₂ × U(v₂)]
Total	1.0			EU = Σ

Certainty Equivalent: CE = U⁻¹(EU). Risk Premium: EV - CE.

Non-monetary factors: Strategic value [$/qualitative], Alignment with mission [score 1-5], Regret [low/med/high]

Recommendation: Highest EV [Alt X], Highest EU [Alt Y], Final choice: [Alt Z with rationale]

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Decision Tree Template

For sequential decisions (make choice, observe outcome, make another choice).

Tree Structure

[Decision 1] → [Outcome A] → [Decision 2a] → [Outcome C]
                                           → [Outcome D]
             → [Outcome B] → [Decision 2b] → [Outcome E]
                                           → [Outcome F]

Fold-Back Induction (work backwards from end)

Step 1: Calculate EV at terminal nodes (final outcomes)

• Outcome C: [payoff = $X]
• Outcome D: [payoff = $Y]
• Outcome E: [payoff = $Z]
• Outcome F: [payoff = $W]

Step 2: Calculate EV at Decision 2a

• If choose path to C: [p(C) × $X]
• If choose path to D: [p(D) × $Y]
• Optimal Decision 2a: [Choose whichever has higher EV]
• EV(Decision 2a): [max of the two]

Step 3: Calculate EV at Decision 2b

• If choose path to E: [p(E) × $Z]
• If choose path to F: [p(F) × $W]
• Optimal Decision 2b: [Choose whichever has higher EV]
• EV(Decision 2b): [max of the two]

Step 4: Calculate EV at Decision 1

• If choose path to A: [p(A) × EV(Decision 2a)]
• If choose path to B: [p(B) × EV(Decision 2b)]
• Optimal Decision 1: [Choose whichever has higher EV]
• Overall EV: [max of the two]

Optimal Strategy:

1. At Decision 1: [Choose A or B]
2. If A occurs, at Decision 2a: [Choose path to C or D]
3. If B occurs, at Decision 2b: [Choose path to E or F]

Value of Information: If you could know outcome before Decision 1, how much would that be worth?

• EVPI = EV(with perfect info) - EV(current decision)

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Complete EV Analysis Template

Decision: [Name]

Date: [Date]

Decision maker: [Name/Team]

1. Decision Framing

Alternatives:

1. [Alt 1]
2. [Alt 2]
3. [Alt 3]

Success criteria: [What are you optimizing for?]

2. Outcomes and Probabilities

Alternative	Outcome	Probability	Payoff	p × v
[Alt 1]	[Outcome 1]	[p₁]	[v₁]	[p₁ × v₁]
	[Outcome 2]	[p₂]	[v₂]	[p₂ × v₂]
	[Outcome 3]	[p₃]	[v₃]	[p₃ × v₃]
	EV(Alt 1)			[EV₁]
[Alt 2]	[Outcome 1]	[p₁]	[v₁]	[p₁ × v₁]
	[Outcome 2]	[p₂]	[v₂]	[p₂ × v₂]
	[Outcome 3]	[p₃]	[v₃]	[p₃ × v₃]
	EV(Alt 2)			[EV₂]

3. Comparison

Alternative	EV	σ (risk)	CV
[Alt 1]	[EV₁]	[σ₁]	[CV₁]
[Alt 2]	[EV₂]	[σ₂]	[CV₂]

Highest EV: [Alt X with EV = $Y]

4. Sensitivity Analysis

Key assumptions:

• [Assumption 1]: [If this changes by X%, decision flips? Yes/No]
• [Assumption 2]: [Breakeven value = ?]

Robustness: [Is decision robust across scenarios?]

5. Risk Adjustment

Risk profile: [One-shot or repeated? Risk-averse or neutral?]

Recommendation: [Alt X]

Rationale: [Why this choice given EV, risk, strategic factors?]

6. Action Plan

Next steps:

1. [Immediate action]
2. [Follow-up in X days/weeks]
3. [Decision review date]

Contingencies: [If Outcome Y occurs, we will...]