title: Quantitative Essays on Mixed Martial Arts A Markov Chain Based Forecasting Model and Analyses of the Judges
Creators: name: Holmes, Benjamin
Publisher: name: University of Liverpool Repository
Year: 2022

description: Whilst Mixed Martial Arts (MMA) has only recently gained mainstream popularity, the rapid rise of it, particularly the Ultimate Fighting Championship (UFC–the most popular MMA promotion), has been unparalleled in sports. Academic research on MMA is still scarce, and the vast majority has focused on the sport’s health implications. This thesis comprises three articles which contribute to the knowledge on MMA, as well as the wider literature regarding sports forecasting and biases. The first article, now published in the International Journal of Forecasting (Holmes et al., 2022), introduces a Markov chain (MC) based model to predict MMA bouts. The states of the MC are associated with key techniques or positions within MMA. Various models based on the athletes’ historical in-fight statistics determine the transition probabilities between states, thus accounting for individual fighting styles. By simulating the chain many times, we obtain probabilities of fight outcomes. These predictions were comparable to the bookmakers, and generated positive returns when used for betting. Compared to other subjectively judges sports, for instance, diving, the performance data available for UFC fights provides an ideal environment to model the judges’ behaviours. Thus, the remaining two papers examined the judges in the UFC. First, we explored the potential of several biases within MMA judging. We find evidence suggesting two biases exist: the judges are influenced by a live audience, thus favouring a home athlete; and the judges favour athletes higher in the official rankings. One issue with previous work was establishing whether the significant effects were due to bias or fighter skill. Under the hypothesis that the betting market is efficient, we address this issue by including the bookmakers’ odds to account for unseen skills. Market efficiency suggests the bias variables don’t add any information on skills beyond what is contained in the odds, and thus significance is indicative of bias, not skill. We demonstrate that the market is efficient, and thus we can be more confident in our conclusions. Second, we use a Bayesian hierarchical model to show that the judges have different preferences towards each action. We identify several actions where judges have a wide range of opinions, even to the extent of actions being valued in opposite directions. Using this model, we demonstrate how the judges’ preferences may themselves determine the winner of a fight, and also develop a “fair”-scoring model that could be used by promotions or athletic commissions for a number of purposes. We apply the concept of variable significance to determine whether a judge’s verdict was mathematically controversial or within reason. Further, we estimate a similar model using scores submitted by fans. This model suggests that fans are more likely to give rarer scores, such as draws. Interestingly, it appears fans are less influenced by bias variables than the judges.