Comprehensive Multi-Factor Scoring System:

$$ S_{\text{portfolio}} = S_{\text{recency}} + S_{\text{popularity}} + S_{\text{engagement}} + S_{\text{maintenance}} + S_{\text{production}} + S_{\text{quality}} + S_{\text{size}} + S_{\text{docs}} $$

Component Breakdown:

1. Recency Score (Max 50 pts): $$ S_{\text{recency}} = 50 \cdot e^{-\frac{d}{60}} $$ Where $d$ = days since last push (exponential decay with 60-day half-life)

2. Popularity Score (Max 40 pts): $$ S_{\text{popularity}} = \min(40, 5 \cdot \log_2(s + 1)) $$ Where $s$ = stargazers count (logarithmic scaling prevents dominance)

3. Engagement Score (Max 30 pts): $$ S_{\text{engagement}} = \min(15, 3 \cdot \log_2(f + 1)) + \min(15, 3 \cdot \log_2(w + 1)) $$ Where $f$ = forks, $w$ = watchers

4. Maintenance Score (Max 30 pts): $$ S_{\text{maintenance}} = \begin{cases} 30 & \text{if } i = 0 \ 20 & \text{if } i \leq 3 \ 10 & \text{if } i \leq 10 \ 5 & \text{if } i \leq 20 \ 0 & \text{otherwise} \end{cases} $$ Where $i$ = open issues count

5. Impact Score (Community Engagement): $$ I = (s + 1) \times (f + 1) \times \left(1 - \frac{d}{365}\right) \times 10 $$

6. Health Score (Max 100 pts): $$ H = 100 - P_{\text{age}} - P_{\text{docs}} - P_{\text{issues}} + B_{\text{features}} $$

7. Maintainability Index (Max 100 pts): $$ M = 100 - 20 \cdot \delta_{\text{desc}} - 10 \cdot \delta_{\text{homepage}} - \min(30, 10 \cdot \frac{i}{s/1000}) - P_{\text{age}} $$

Total Maximum Score: 225 points