Best of N contests: Implications of Simpson's Paradox in tennis

Statistical theories have long been the impetus for research within studies of sport. This is likely due to the abundance of data in sport. This thesis introduces a statistical theory known as Simpson's Paradox wherein an apparent correlation of variables is reversed when the variables are combined. Simpson's Paradox has been the focus of studies involving sports such as basketball and baseball due to the strong presence of statistics in each respective sport. Building on the previous research, this thesis examines the prevalence of Simpson's Paradox in professional tennis. Overtly, this thesis attempts to identify tennis matches from specified tournaments where cases of Simpson's Paradox are present.;A match is considered an instance of Simpson's Paradox when a player wins more points than his opponent but loses the overall match. Data from sanctioned tennis tournaments over the course of 21 years will be used to investigate cases of Simpson's Paradox on the point level. Finding instances of Simpson's Paradox within the data set may provide insight to incentives and strategy in tennis. Specifically, a player may exert less effort in select situations such as returning serve if he believes he will have a better chance of winning the overall set or match.;Analyzing a data set of over 55,000 individual tennis matches, I find that roughly 5% of matches exhibit Simpson's Paradox. The results provide an opportunity for gambling related activity to profit from the unique scoring system utilized in tennis. Governing bodies need to be aware of betting-related corruption that has become increasingly popular in sports in order to protect and maintain the integrity of tennis. While (sub)-conscious incentive effects may explain instances of Simpson's Paradox, the unique best of N nature of tennis' scoring system primarily drives my results.