Mathematical and statistical analysis of excitement score in penalty shootouts

Official URL: https://risc01.sabanciuniv.edu/record=b2708499_(Table of contents)

Quantitative measurement of excitement during sports games is a field of study that has not been explored much. In this thesis, our aim was to find the expected excitement score of penalty shootouts mathematically. The excitement score formulations were generated based on the variation in the winning probabilities of teams after each penalty. Probability of success for each penalty originates from a Beta distribution in cases where players’ scoring probabilities are unknown. ExpectationMaximization (EM) algorithm was utilized to find the parameter estimations of Beta distribution. A survey was conducted to understand what makes shootouts exciting for the viewers and participants were asked to choose between two penalty shootout scenarios by examining scenario features at each question. Subsequently, the Bradley-Terry model was used to rank the scenario preferences of the viewers. This ranking was then used to make comparisons with the ranking of the scenarios obtained by using excitement scores. Predictive models were built using machine learning algorithms including Logistic Regression, Random Forest, AdaBoost Classifier and XGBoost to find feature importances. An alternative excitement score calculation was formed by taking the incremental excitement into consideration. Lastly, the excitement score was calculated for cases where scoring probabilities of teams vary at each round for a realistic approach. Discrete-time Markov chain process was used to find winning probabilities of each team. The results demonstrated that our excitement score calculations were successful in determining the least exciting shootouts. Moreover, features deemed as important by the viewers were also crucial mathematically.