Modeling Stoppage Time as a Convolution of Negative Binomials

Sammanfattning: This thesis develops and evaluates a probabilistic model that estimates the stoppage time in football. Stoppage time represents the additional minutes of play given after the original matchtime is over. It is crucial in determining the course of events during the remainder of a match, thereby affecting the odds of live sports betting. The proposed approach uses the negative binomial distribution to model events in football and stoppage time is viewed as a convolution of these distributions. The parameters of the negative binomials are estimated using machine learning methods in Python, with TensorFlow as the underlying framework. The data used for the analysis consists of event data for thousands of football matches with corresponding stoppage time, as well as the duration of pauses that have occurred in these games. The negative binomial distribution is shown to be a good fit and can be adapted to the data using scaling and resolution techniques. The model allows us to see how different events contribute to the stoppage time, and the results indicate that injuries, VAR checks, and red cards have the most significant impact on stoppage time. The model has potential for use in live sports betting and can enhance the accuracy of odds calculation. This work was conducted in collaboration with xAlgo which is a department of Kambi, a business-to-business provider of sports betting services.