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Zhongwei Li
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# Advanced Chain Estimation → Decision → Storytelling Methodology
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## Workflow
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Copy this checklist and track your progress:
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```
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Advanced Analysis Progress:
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- [ ] Step 1: Select appropriate advanced technique for complexity
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- [ ] Step 2: Build model (decision tree, Monte Carlo, real options)
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- [ ] Step 3: Run analysis and interpret results
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- [ ] Step 4: Validate robustness across scenarios
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- [ ] Step 5: Translate technical findings into narrative
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```
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**Step 1: Select appropriate advanced technique for complexity**
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Choose technique based on decision characteristics: decision trees for sequential choices, Monte Carlo for multiple interacting uncertainties, real options for flexibility value, multi-criteria analysis for qualitative + quantitative factors. See [Technique Selection Guide](#technique-selection-guide) for decision flowchart.
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**Step 2: Build model**
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Structure problem using chosen technique: define states and branches for decision trees, specify probability distributions for Monte Carlo, identify options and decision points for real options analysis, establish criteria and weights for multi-criteria. See technique-specific sections below for modeling guidance.
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**Step 3: Run analysis and interpret results**
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Execute calculations (manually for small trees, with tools for complex simulations), interpret output distributions or decision paths, identify dominant strategies or highest-value options, and quantify value of information or flexibility where applicable.
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**Step 4: Validate robustness across scenarios**
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Test assumptions with stress testing, vary key parameters to check sensitivity, compare results across different modeling approaches, and identify conditions where conclusion changes. See [Sensitivity and Robustness Testing](#sensitivity-and-robustness-testing).
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**Step 5: Translate technical findings into narrative**
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Convert technical analysis into business language, highlight key insights without overwhelming with methodology, explain "so what" for decision-makers, and provide clear recommendation with confidence bounds. See [Communicating Complex Analysis](#communicating-complex-analysis).
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---
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## Technique Selection Guide
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**Decision Trees** → Sequential decisions with discrete outcomes and known probabilities
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- Use when: Clear sequence of choices, branching scenarios, need optimal path
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- Example: Build vs buy with adoption uncertainty
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**Monte Carlo Simulation** → Multiple interacting uncertainties with continuous distributions
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- Use when: Many uncertain variables, complex interactions, need probability distributions
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- Example: Project NPV with uncertain cost, revenue, timeline
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**Real Options Analysis** → Decisions with flexibility value (defer, expand, abandon)
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- Use when: Uncertainty resolves over time, value of waiting, staged commitments
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- Example: Pilot before full launch, expand if successful
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**Multi-Criteria Decision Analysis (MCDA)** → Mix of quantitative and qualitative factors
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- Use when: Multiple objectives, stakeholder tradeoffs, subjective criteria
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- Example: Vendor selection (cost + quality + relationship)
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---
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## Decision Trees
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### Structure
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- **Decision node (□)**: Your choice
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- **Chance node (○)**: Uncertain outcome with probabilities
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- **Terminal node**: Final payoff
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### Method
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1. Map all decisions and chance events
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2. Assign probabilities to chance events
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3. Work backward: calculate EV at chance nodes, choose best at decision nodes
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4. Identify optimal path
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### Example
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```
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□ Build vs Buy
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├─ Build → ○ Success (60%) → $500k
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│ └─ Fail (40%) → $100k
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└─ Buy → ○ Fits (70%) → $400k
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└─ Doesn't (30%) → $150k
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Build EV = (500 × 0.6) + (100 × 0.4) = $340k
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Buy EV = (400 × 0.7) + (150 × 0.3) = $325k
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Decision: Build (higher EV)
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```
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### Value of Information
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- EVPI = EV with perfect info - EV without info
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- Tells you how much to spend on reducing uncertainty
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---
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## Monte Carlo Simulation
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### When to Use
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- Multiple uncertain variables (>3)
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- Complex interactions between variables
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- Need full probability distribution of outcomes
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- Continuous ranges (not discrete scenarios)
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### Method
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1. **Identify uncertain variables**: cost, revenue, timeline, adoption rate, etc.
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2. **Define distributions**: normal, log-normal, triangular, uniform
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3. **Specify correlations**: if variables move together
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4. **Run simulation**: 10,000+ iterations
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5. **Analyze output**: mean, median, percentiles, probability of success
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### Distribution Types
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- **Normal**: μ ± σ (height, measurement error)
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- **Log-normal**: positively skewed (project duration, costs)
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- **Triangular**: min/most likely/max (quick estimation)
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- **Uniform**: all values equally likely (no information)
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### Interpretation
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- **P50 (median)**: 50% chance of exceeding
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- **P10/P90**: 80% confidence interval
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- **Probability of target**: P(NPV > $0), P(ROI > 20%)
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### Tools
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- Excel: =NORM.INV(RAND(), mean, stdev)
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- Python: `numpy.random.normal(mean, stdev, size=10000)`
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- @RISK, Crystal Ball: Monte Carlo add-ins
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---
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## Real Options Analysis
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### Concept
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Flexibility has value. Option to defer, expand, contract, or abandon is worth more than committing upfront.
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### When to Use
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- Uncertainty resolves over time (can learn before committing)
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- Irreversible investments (can't easily reverse)
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- Staged decisions (pilot → scale)
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### Types of Options
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- **Defer**: Wait for more information before committing
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- **Expand**: Scale up if successful
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- **Contract/Abandon**: Scale down or exit if unsuccessful
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- **Switch**: Change approach mid-course
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### Valuation Approach
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**Simple NPV (no flexibility):**
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- Commit now: EV = Σ(outcome × probability)
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**With real option:**
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- Value = NPV of commitment + Value of flexibility
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- Flexibility value = Expected payoff from optimal future decision - Expected payoff from committing now
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### Example
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- **Commit to full launch now**: $1M investment, 60% success → $3M, 40% fail → $0
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- EV = (3M × 0.6) + (0 × 0.4) - 1M = $800K
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- **Pilot first ($200K), then decide**:
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- Good pilot (60%) → full launch → EV $1.8M (0.6 × 3M - 1M)
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- Bad pilot (40%) → abandon → lose $200K
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- EV = (1.8M × 0.6) + (-0.2M × 0.4) = $1.0M
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- **Real option value** = $1.0M - $800K = $200K (value of flexibility to learn first)
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---
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## Multi-Criteria Decision Analysis (MCDA)
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### When to Use
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- Multiple objectives that can't be reduced to single metric (not just NPV)
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- Qualitative + quantitative factors
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- Stakeholder tradeoffs (different groups value different things)
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### Method
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**1. Identify criteria** (from stakeholder perspectives)
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- Cost, speed, quality, risk, strategic fit, customer impact, etc.
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**2. Weight criteria** (based on priorities)
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- Sum to 100%
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- Finance might weight cost 40%, Product weights customer impact 30%
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**3. Score alternatives** (1-5 or 1-10 scale on each criterion)
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- Alternative A: Cost=4, Speed=2, Quality=5
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- Alternative B: Cost=2, Speed=5, Quality=3
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**4. Calculate weighted scores**
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- A = (4 × 0.3) + (2 × 0.4) + (5 × 0.3) = 3.5
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- B = (2 × 0.3) + (5 × 0.4) + (3 × 0.3) = 3.5
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**5. Sensitivity analysis** on weights
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- How much would weights need to change to flip the decision?
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### Handling Qualitative Criteria
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- **Scoring rubric**: Define what 1, 3, 5 means for "strategic fit"
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- **Pairwise comparison**: Compare alternatives head-to-head on each criterion
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- **Range**: Use min-max scaling to normalize disparate units
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---
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## Sensitivity and Robustness Testing
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### One-Way Sensitivity
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- Vary one parameter at a time (e.g., cost ±20%)
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- Check if conclusion changes
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- Identify which parameters matter most
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### Two-Way Sensitivity
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- Vary two parameters simultaneously
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- Create sensitivity matrix or contour plot
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- Example: Cost (rows) × Revenue (columns) → NPV
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### Tornado Diagram
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- Bar chart showing impact of each parameter
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- Longest bars = most sensitive parameters
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- Focus analysis on top 2-3 drivers
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### Scenario Analysis
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- Define coherent scenarios (pessimistic, base, optimistic)
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- Not just parameter ranges, but plausible futures
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- Calculate outcome for each complete scenario
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### Break-Even Analysis
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- At what value does conclusion change?
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- "Need revenue >$500K to beat alternative"
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- "If cost exceeds $300K, pivot to Plan B"
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### Stress Testing
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- Extreme scenarios (worst case everything goes wrong)
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- Identify fragility: "Works unless X and Y both fail"
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- Build contingency plans for stress scenarios
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---
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## Communicating Complex Analysis
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### For Executives
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**Focus**: Bottom line, confidence, risks
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- Recommendation (1 sentence)
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- Key numbers (EV, NPV, ROI)
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- Confidence level (P10-P90 range)
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- Top 2 risks + mitigations
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- Decision criteria: "Proceed if X, pivot if Y"
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### For Technical Teams
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**Focus**: Methodology, assumptions, sensitivity
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- Modeling approach and rationale
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- Key assumptions with justification
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- Sensitivity analysis results
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- Robustness checks performed
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- Limitations of analysis
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### For Finance
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**Focus**: Numbers, assumptions, financial metrics
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- Cash flow timing
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- Discount rate and rationale
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- NPV, IRR, payback period
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- Risk-adjusted returns
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- Comparison to hurdle rate
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### General Principles
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- **Lead with conclusion**, then support with analysis
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- **Show confidence bounds**, not just point estimates
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- **Explain "so what"**, not just "what"
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- **Use visuals**: probability distributions, decision trees, tornado charts
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- **Be honest about limitations**: "Assumes X, sensitive to Y"
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---
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## Common Pitfalls in Advanced Analysis
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### False Precision
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- **Problem**: Reporting $1,234,567 when uncertainty is ±50%
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- **Fix**: Round appropriately. Use ranges, not points.
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### Ignoring Correlations
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- **Problem**: Modeling all uncertainties as independent when they're linked
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- **Fix**: Specify correlations in Monte Carlo (costs move together, revenue and volume linked)
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### Overfit ting Models
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- **Problem**: Building complex models with 20 parameters when data is thin
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- **Fix**: Keep models simple. Complexity doesn't equal accuracy.
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### Anchoring on Base Case
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- **Problem**: Treating "most likely" as "expected value"
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- **Fix**: Calculate probability-weighted EV. Assymetric distributions matter.
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### Analysis Paralysis
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- **Problem**: Endless modeling instead of deciding
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- **Fix**: Set time limits. "Good enough" threshold. Decide with available info.
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### Confirmation Bias
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- **Problem**: Modeling to justify predetermined conclusion
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- **Fix**: Model alternatives fairly. Seek disconfirming evidence. External review.
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### Ignoring Soft Factors
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- **Problem**: Optimizing NPV while ignoring strategic fit, team morale, brand impact
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- **Fix**: Use MCDA for mixed quantitative + qualitative. Make tradeoffs explicit.
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---
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## Advanced Tools and Resources
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### Spreadsheet Tools
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- **Excel**: Data tables, Scenario Manager, Goal Seek
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- **Google Sheets**: Same capabilities, collaborative
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### Specialized Software
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- **@RISK** (Palisade): Monte Carlo simulation add-in for Excel
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- **Crystal Ball** (Oracle): Similar Monte Carlo tool
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- **Python**: `numpy`, `scipy`, `simpy` for custom simulations
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- **R**: Statistical analysis and simulation
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### When to Use Tools vs. Manual
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- **Manual** (small decision trees): < 10 branches, quick calculation
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- **Spreadsheet** (medium complexity): Decision trees, simple Monte Carlo (< 5 variables)
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- **Specialized tools** (high complexity): 10+ uncertain variables, complex correlations, sensitivity analysis
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### Learning Resources
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- Decision analysis: "Decision Analysis for the Professional" - Skinner
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- Monte Carlo: "Risk Analysis in Engineering" - Modarres
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- Real options: "Real Options" - Copeland & Antikarov
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- MCDA: "Multi-Criteria Decision Analysis" - Belton & Stewart
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---
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## Summary
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**Choose technique based on problem structure:**
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- Sequential choices → Decision trees
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- Multiple uncertainties → Monte Carlo
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- Flexibility value → Real options
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- Mixed criteria → MCDA
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**Focus on:**
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- Robust conclusions (stress test assumptions)
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- Clear communication (translate technical to business language)
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- Actionable insights (not just numbers)
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- Honest limits (acknowledge what analysis can't tell you)
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**Remember:**
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- Models inform decisions, don't make them
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- Simple model well-executed beats complex model poorly-executed
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- Transparency about assumptions matters more than sophistication
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- "All models are wrong, some are useful" - George Box
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