Hierarchical Models for Estimating Individual Ratings from Group Competitions

Providing direct and indirect contributions of more than $18 billion to the nation’s gross output in 2004, the computer and video gaming industry is one of the fastest-growing sectors of entertainment. A large part of that market includes team-oriented online games. In fact, according a recent study online gaming is the most popular online entertainment activity in the United States. Players in these games often have a high-level of interest in statistics that help them assess their ability compared to other players. However few models exist that estimate individual player ratings from team competitions. There are models that can be used at the team-level, however the dynamic nature of the teams in the more popular public-style play of these games makes it necessary to build team strengths from player abilities. The following presents a model that describe team abilities in terms of how well the individual players on the teams contribute to their team’s winning. In addition, the model presented includes parameters that estimate other characteristics of the games themselves. The model is posed in a hierarchical Bayesian framework. In addition to giving players a better estimate of their skill, this model can also be used to improve current gameplay, and create more enjoyable games in the future. Companies and servers that apply well-developed statistics for assessing their players’ abilities are more likely to attract and retain players, leading to greater success in the industry. The model is fit using both Markov-Chain Monte Carlo (MCMC) and a recursive updating method. As measured on 4,675 matches, the recursive method results in an accuracy of 73% when used to predict the outcomes of the matches used to estimate player ratings. In addition, it is shown that this method is fast enough to be used in real-time whereas MCMC is not.