This paper develops a mathematical framework for forecasting FIFA World Cup match outcomes, extending the classical Poisson distribution to account for the structural complexities of international football. This paper first derives the Poisson distribution as the limiting case of the Binomial distribution, then applies a baseline model to the Iraq-Norway fixture using qualification data to construct a full scoreline probability matrix. The eventual 4-1 result– a low-probability tail outcome– motivates two structural extensions: a Home Advantage multiplier, with a Dixon-Coles-style low-score correction, τ, and a transition from a static Poisson process to a Non-Homogeneous Poisson Process (NHPP) that lets scoring intensity vary across regulation time, stoppage time, and extra time. The analysis then moves beyond static pre-match estimation entirely. A Bayesian updating engine is introduced to revise scoring intensity in real time as live match events unfold and a Poisson-Gamma conjugate framework is developed to recursively update team strength across tournament rounds without intractable numerical integration, validated against Norway's Round of 32 and 16 fixtures. Finally, the Norway-England quarter-final is used to expose the model's structural limits: its inability to natively represent extra time and its blindness to unmeasured "Chaos Variance" from latent match states. This motivates future extensions via copulas, time-varying intensity functions, and hidden Markov models. Together, these extensions turn a static pre-match estimate into a recursive, self-updating framework for football forecasting.