Air gaps serve as a fundamental form of external insulation in power transmission lines, rendering the understanding of air discharge mechanisms crucial for engineering applications. The discharge process in long air gaps involves a high degree of complexity and necessitates a comprehensive model incorporating numerous parameters. Traditionally, many of these parameters are derived from fixed theoretical or empirical values, resulting in discrepancies between simulation outcomes and experimental observations. This study presents an advanced numerical model to simulate long gap discharges, considering the streamer region angle, streamer direction, and stochastic leader development, to provide a more accurate representation of electrical discharge characteristics. Additionally, the refined methodology for defining the streamer region enhances the model's applicability to both symmetric and asymmetric geometric configurations. Comprehensive simulations were conducted to analyze the current, velocity, and leader channel path under various voltage conditions, with results benchmarked against experimental data. The incorporation of new physical quantities in the model has significantly enhanced its predictive accuracy for current and velocity. Furthermore, the model's capability to calculate the breakdown voltage of standard engineering gaps was validated, demonstrating a high degree of concordance with empirical data.