Information Theory and Tennis

Abstract

This thesis explores the information theoretic aspects of tennis, and explores the attributes of infinite alphabets and the process of finding optimal codes for them. First, a probabilistic model is constructed to model tennis matches, with games, sets, and tiebreaks modeled as Markov chains. The entropy of a game is then computed and compared to the average length of a optimal prefix-free Huffman code. A modified Golomb code and a combination of Huffman and Golomb codes are also analyzed, in order to provide an encoding for the infinite outcomes of tennis. The expected optimal code length is found for various probabilities of winning. The distribution of the optimal code length for a tennis game is also found, and is used to verify the expected optimal code length. Real match data is used to judge the effectiveness of the model and to compare real code lengths and compression ratios to expected values. Lastly, how the results of this thesis can be applied to other models and alphabets is discussed.