A stochastic model for NFL games and point spread assessment.

Area of Science:

• Sports Analytics
• Statistical Modeling
• Probability Distributions

Background:

• Statistical modeling is crucial for sports analytics and strategic decision-making.
• Existing models may not fully capture the nuances of sports outcomes.

Purpose of the Study:

• To introduce a novel stochastic model for analyzing the margin of victory in sports.
• To evaluate the performance and stability of the proposed model.
• To apply the model to real-world sports data for practical insights.

Main Methods:

• Development of a stochastic model based on the difference derived from the Bivariate Affine-Linear Exponential distribution.
• A simulation study to assess parameter stability (bias, standard error, RMSE, confidence intervals).
• Application and comparison of the model using National Football League (NFL) data against existing models.

Main Results:

• The proposed distribution of difference provides an adequate fit for modeling the margin of victory.
• Simulation results demonstrate the stability of the model parameters.
• The model shows competitive performance when applied to real NFL data.

Conclusions:

• The novel stochastic model effectively captures the margin of victory in sports.
• The model's quantile function can be used to assess betting point spreads.
• This approach enhances sports analytics and strategic betting decisions.