Accurately identifying bleeding sources during minimally invasive surgery (MIS) is crucial for patient safety, faster discharge, and reducing operative time and postoperative complications. Although advances in imaging and bleeding segmentation have improved detection, pinpointing precise hemorrhage origins remains challenging owing to high variability in surgical environments. To address this, Bleeding Alert Maps (BAMs) were initially generated using a fixed Gaussian distribution; however, this static assumption was insufficient to capture the full range of bleeding variability. In this study, we systematically investigate kurtosis as a key factor in BAM construction, evaluating uniform (low kurtosis), Gaussian (moderate kurtosis), and exponential (high kurtosis) ground truth distributions. We apply a generative adversarial network (GAN) to produce BAMs from these distributions, each tested across multiple spread parameters (σ for Gaussian and s for exponential). Our results show that while Gaussian-based BAMs improve up to (σ ≈ 40 and then plateau, exponential-based BAMs continue to yield accuracy gains beyond this threshold, demonstrating a clear distributional advantage. Notably, the best exponential model (s = 50) achieved a ~92% bleeding-point detection rate (137 true positives out of 150), ~85% accuracy, 89% precision, and an F1 score of 0.898. These findings underscore how refining the distribution shape, particularly increasing its kurtosis, significantly enhances the reliability, applicability, and clinical value of automated bleeding source localization in MIS.