The evaluation framework has been updated to prioritize calibrated probabilities and economic weighting over simple threshold-based classification.

Primary Metric: Profit-Weighted Log Loss (PWLL) — 80% Weight
Instead of thresholding, we evaluate the full probability distribution using a cost-sensitive log loss.
Mathematical Definition:
Given $y_i \in \{0,1\}$ as the true label and $p_i$ as the predicted probability:
Weight for Churn ($w_1$): 350
Weight for Active ($w_0$): 15

$$PWLL = -\frac{1}{N} \sum_{i=1}^{n} [w_1 y_i \log(p_i) + w_0 (1 - y_i) \log(1 - p_i)]$$
Normalized Leaderboard Score:
To ensure intuitive tracking, the score is normalized against a baseline:

$$Score_{PWLL} = 1 - \frac{PWLL}{PWLL_{baseline}}$$

Secondary Metrics — 20% Weight
ROC-AUC (10%): Measures ranking quality. (Minimum threshold: 0.65).
Brier Score (10%): Measures probability calibration.
$$Brier = \frac{1}{N} \sum (p_i - y_i)^2$$
$$Score_{Brier} = 1 - Brier$$

Final Scoring Logic
The final leaderboard position is determined by the weighted sum of all metrics:

$$FinalScore = (0.80 \times Score_{PWLL}) + (0.10 \times ROC\_AUC) + (0.10 \times Score_{Brier})$$