RepoGDP

What is GDP?

GDP (Gross Domestic Product) is the total monetary value of all final goods and services produced within a country’s borders during a specific period, usually annually or quarterly. It is the most widely used indicator of a country’s economic size and overall economic health.

What GDP Measures

GDP captures:

• Consumer spending (households)

• Investment (businesses)

• Government spending

• Net exports (exports − imports)

Formally, it is expressed as: GDP = C + I + G + (X − M)

Types of GDP

• Nominal GDP: Measured at current market prices (includes inflation).

• Real GDP: Adjusted for inflation; reflects true growth.

• GDP per capita: GDP divided by population; a proxy for average living standards.

Why GDP Matters

• Used to compare economic performance over time or across countries

• Guides policy decisions (fiscal and monetary)

• Influences investment and credit ratings

Limitations of GDP

GDP does not measure:

• Income inequality

• Quality of life or well-being

• Informal or unpaid work

• Environmental degradation

In short, GDP is a core macroeconomic metric, but it should be interpreted alongside other indicators for a complete picture of economic progress.

---

What is RepoGDP?

Below is a GDP-inspired, repository-level growth scoring engine you can implement as a single composite index, while still preserving interpretability and temporal sensitivity. I will treat a GitHub repository as an “economic system” and explicitly map each variable to a macroeconomic analogue.

---

1. Conceptual Framing: Repo GDP (rGDP)

Repo GDP (rGDP) measures the productive health, momentum, and sustainability of a GitHub repository over time.

Unlike a naïve weighted sum, this design introduces:

• Flow vs Stock separation

• Velocity (growth rate)

• Efficiency and stability modifiers

• Diminishing returns to popularity

This avoids “star-only bias” and rewards active, well-maintained, growing repositories.

---

2. Variable Classification (Economic Analogy)

GitHub Metric	Economic Role	Type
Stars	Consumer confidence / brand value	Stock
Forks	Capital formation / replication	Stock
Watch	Market attention / sentiment	Stock
Open PRs	Work in progress (WIP)	Flow (liability)
Closed PRs	Completed production	Flow
Issues	Operational friction	Flow (liability)
Releases	Output delivery	Flow

---

3. Step 1: Normalize Inputs (Log-Scaled)

Raw GitHub numbers are power-law distributed. Use log normalization to prevent celebrity repos from dominating.

For any metric ( x ):

$$N(x) = \log(1 + x)$$

---

4. Step 2: Compute Sub-Indices

A. Popularity Stock Index (PSI)

(Brand + Reach)

$PSI = 0.5N(\text{Stars}) + 0.3N(\text{Forks}) + 0.2N(\text{Watch})$

Reason:

• Stars indicate approval

• Forks imply deeper engagement

• Watches reflect ongoing interest

---

B. Production Flow Index (PFI)

(Actual engineering output)

$PFI = 0.6N(\text{Closed PRs}) + 0.4N(\text{Releases})$

Reason:

• Closed PRs show contributor throughput

• Releases signal user-visible value

---

C. Operational Debt Index (ODI)

(Friction & backlog — penalizer)

$ODI = 0.6N(\text{Issues}) + 0.4N(\text{Open PRs})$

---

5. Step 3: Efficiency & Velocity Modifiers (Unique Part)

A. Merge Efficiency Ratio (MER)

How well the repo converts work into completion:

$MER = \frac{\text{Closed PRs}}{\text{Closed PRs} + \text{Open PRs} + 1}$

Bounded between 0 and 1.

---

B. Release Productivity Factor (RPF)

Encourages shipping, not just activity:

$RPF = \log(1 + \text{Releases})$

---

C. Operational Drag Coefficient (ODC)

Non-linear penalty for unresolved work:

$ODC = 1 + \sqrt{ODI}$

---

6. Step 4: Core rGDP Formula

$\boxed{ rGDP = \frac{ (PSI \times PFI \times MER \times RPF) }{ ODC } }$

This structure ensures:

• Growth must be popular + productive

• Activity without closure is punished

• Mature repos can still grow through efficiency

---

7. Step 5: Time-Based Growth (GDP Growth Rate)

To rank trending repos:

$rGDP_growth = \frac{rGDP_{t} - rGDP_{t-1}}{rGDP_{t-1} + \epsilon}$

Use weekly or monthly snapshots.

---

8. Interpretation Bands (Like Economic Ratings)

rGDP Score	Interpretation
< 1.0	Stagnant / Abandoned
1.0 – 3.0	Stable
3.0 – 7.0	Growing
7.0 – 15	High-growth
> 15	Breakout / Ecosystem-forming

---

9. Why This Algorithm Is Unique

1. Flow–Stock separation (rare in repo scoring)

2. Non-linear penalties for unresolved work

3. Efficiency-based reward (MER)

4. Release-centric bias (shipping > noise)

5. Time-series compatible (GDP growth analog)

---

10. Optional Extensions (If You Want to Go Deeper)

• Per-Contributor rGDP (productivity normalization)

• Sector-adjusted rGDP (compare only similar tech stacks)

• Recession detection (falling MER + rising ODI)

• Repo Inflation (stars rising but PFI stagnant)

---