Core Methods

Core Methods — Theory & Derivation

Textbook: Chapter 3 | Module: startup_valuation.core | Last verified: 2026-08-11

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Contents

1. Scorecard Method ⬅ Complete 13-step derivation
2. Berkus Method
3. Risk Factor Summation
4. VC Method

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Scorecard Method

1. Learning Objective

Derive the Scorecard Valuation Method for pre-revenue startups. By the end of this section, you will be able to:

• Compute a target valuation from an average regional valuation
• Apply factor weights and scores to adjust for startup-specific strengths and weaknesses
• Understand the assumptions behind the method
• Implement the calculation in Python

2. Prerequisites

• Understanding of pre-money vs post-money valuation
• Basic algebra (weighted averages)
• Familiarity with the Glossary notation

3. Definitions

Symbol	Meaning	Units	Code Variable
$$V_{avg}$$	Average pre-money valuation for comparable startups in the region	USD	average_valuation
$$w_i$$	Weight assigned to factor $$i$$ (importance of each factor)	Dimensionless (sum = 1.0)	weights[i]
$$s_i$$	Score for factor $$i$$ relative to average (1.0 = average)	Dimensionless	scores[i]
$$n$$	Number of factors (typically 7)	Count	len(weights)
$$V$$	Target valuation (output)	USD	result.value

4. Assumptions

1. Average valuation is from comparable regional deals — The $$V_{avg}$$ baseline is derived from actual funding rounds of similar-stage startups in the same geography and industry.
2. Scores are relative to average (1.0 = average): A score of 1.0 means the startup is average on that factor. Scores > 1.0 indicate above-average strength. Scores < 1.0 indicate below-average.
3. Weights reflect factor importance for this stage: The seven standard factors (Team, Product, Market, etc.) are weighted according to their importance at the startup's current stage.
4. Factors are independent: The method assumes additive independence — each factor contributes independently to the adjustment.
5. Linear scaling: The valuation adjustment is linear with respect to the weighted score. No diminishing returns or interaction effects.

5. Starting Equation

The Scorecard Method adjusts the average regional valuation by a weighted sum of factor scores:

$$V = V_{avg} \times \sum_{i=1}^{n} w_i \times s_i$$

Where $$\sum w_i = 1$$ and $$s_i &gt; 0$$.

Source: Startup Valuation textbook, Chapter 3, Section 3.1, Formula 3.1.

6. Derivation

Step 1 — Baseline. Start with the average pre-money valuation $$V_{avg}$$ for comparable startups in the same region and industry.

Step 2 — Factor identification. Identify $$n$$ factors that influence startup valuation. Typical factors (Bill Payne's framework):

Factor	Typical Weight	Rationale
Team	30%	The team's experience and track record are the strongest predictors of startup success
Product/Technology	25%	Product maturity, IP protection, and technical differentiation
Market Size & Growth	15%	Addressable market size and growth rate
Competitive Environment	10%	Number and strength of competitors
Marketing/Sales	10%	Go-to-market strategy and sales channels
Need for Additional Investment	5%	Future capital requirements
Other Factors	5%	Legal, regulatory, or other considerations

Step 3 — Scoring. For each factor, assign a score $$s_i$$ relative to the average comparable startup:

$$s_i = \begin{cases} > 1.0 & \text{Above average} \ 1.0 & \text{Average} \ < 1.0 & \text{Below average} \end{cases}$$

Scores typically range from 0.5 (significantly below average) to 2.0 (significantly above average).

Step 4 — Weighted score. Compute the weighted sum of scores:

$$\text{Weighted Score} = \sum_{i=1}^{n} w_i \times s_i$$

This produces a single multiplier. A result of 1.0 means the startup is average across all factors (valuation = $$V_{avg}$$).

Step 5 — Apply multiplier. Multiply the average valuation by the weighted score:

$$V = V_{avg} \times \text{Weighted Score}$$

7. Intermediate Checks

Check 1 — Weight normalization: $$\sum w_i = 1.0$$ (within tolerance of 0.01).

Check 2 — Score bounds: All $$s_i &gt; 0$$. Negative scores are undefined (you can't have negative strength).

Check 3 — Multiplier range: For typical scores (0.5 to 2.0), the weighted score ranges from 0.5 to 2.0, meaning the valuation ranges from $$0.5 \times V_{avg}$$ to $$2.0 \times V_{avg}$$.

8. Final Computational Form

The library implements this directly:

weighted_score = sum(w * s for w, s in zip(weights, scores))
valuation = average_valuation * weighted_score

This is the stable computational form — no numerical issues for typical inputs.

9. Algorithm Mapping

Mathematical Step	Python Call	Source
Weight normalization check	abs(sum(weights) - 1.0) > 0.01	core.py:37
Score-weights length check	len(weights) != len(scores)	core.py:39
Weighted sum	sum(w * s for w, s in zip(weights, scores))	core.py:42
Final valuation	average_valuation * weighted_score	core.py:43

10. Worked Numerical Example

Scenario: A pre-revenue SaaS startup in the Bay Area. Comparable startups in the region raise at an average pre-money valuation of $1,500,000.

Factor	Weight	Score	Weighted Score
Team	0.30	1.25	0.375
Product	0.25	1.50	0.375
Market	0.15	1.20	0.180
Competition	0.10	0.75	0.075
Marketing	0.10	1.00	0.100
Funding Need	0.05	0.90	0.045
Other	0.05	1.00	0.050
Total	1.00		1.200

$$V = $1{,}500{,}000 \times 1.200 = $1{,}800{,}000$$

The startup's target pre-money valuation is $1,800,000 — 20% above the regional average, driven primarily by a strong team (1.25) and superior product (1.50), partially offset by a weak competitive position (0.75).

Python verification:

from startup_valuation.core import scorecard_valuation

result = scorecard_valuation(
    average_valuation=1_500_000,
    weights=[0.30, 0.25, 0.15, 0.10, 0.10, 0.05, 0.05],
    scores=[1.25, 1.50, 1.20, 0.75, 1.00, 0.90, 1.00],
)
print(f"${result.value:,.0f}")  # $1,800,000

11. Numerical Limitations

• Weight precision: Weights must sum to 1.0. A tolerance of ±0.01 is enforced. Inputs with sum outside this range raise ValueError.
• Score domain: Scores must be strictly positive. Zero or negative scores are undefined.
• No confidence interval: The method produces a point estimate. For probabilistic output, use Scenario Analysis or Monte Carlo simulation.
• Stage sensitivity: Factor weights change by startup stage (pre-seed weights differ from Series A weights). The method does not auto-adjust weights.

12. Validation

The textbook reports a target valuation of $1,800,000 for the example above. The library produces:

assert result.value == pytest.approx(1_800_000)  # Exact match within tolerance

The library's test suite validates this against the textbook example (see tests/test_core.py:15-21).

13. References and Related Pages

• Textbook: Startup Valuation, Chapter 3, Section 3.1 — Scorecard Method
• API: scorecard_valuation()
• Source: core.py:11-59
• Test: tests/test_core.py:15-21
• Next: Berkus Method | Advanced Methods

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Berkus Method

Full derivation coming in Phase 2. See API docs for the Python interface.

The Berkus Method assigns dollar values to five key risk-reduction milestones: Sound Idea, Prototype, Quality Management Team, Strategic Relationships, and Product Rollout/Sales. The valuation is the sum of the values achieved.

$$V = \sum_{i=1}^{5} \text{Value}_i$$

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Risk Factor Summation

Full derivation coming in Phase 2. See API docs for the Python interface.

The Risk Factor Summation method starts with a baseline valuation and adjusts up or down for each of 12 risk factors.

$$V = V_{base} \times \left(1 + \sum_{i=1}^{12} \Delta_i\right)$$

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VC Method

Full derivation coming in Phase 2. See API docs for the Python interface.

The Venture Capital Method works backward from an expected exit value, discounting for the target return rate and accounting for dilution.

$$V_{post} = \frac{\text{Exit Value}}{(1 + \text{Target Return})^{\text{Years}}}$$

$$V_{pre} = V_{post} - \text{Investment}$$