Hierarchical Bayesian Models for Rating Individual Players from Group Competitions

Providing direct and indirect contributions of more than $18 billion to the United States` gross output in 2004, the computer and video gaming industry is one of the fastest-growing sectors of entertainment. A significant portion of that market includes team-oriented online games. 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. The TrueSkill rating system is an example of one way to rate individuals from group competitions. This presentation presents a different model that also describes team abilities in terms of how well the individual players on the teams contribute to their team`s winning. In addition, the models presented include parameters that estimate other characteristics of the games themselves. The models are posed in a hierarchical Bayesian framework so the priors on the parameter variances can be inferred separately. The models are initially fit and evaluated using Markov-Chain Monte Carlo (MCMC) integration. Unfortunately, the amount of time it takes to fit the models using MCMC is longer than the average length of the competitions used to create the models, and therefore MCMC can not be used to rate the players real-time. The second part of this presentation gives an efficient recursive Newton-Raphson approximate Bayesian inference method to solve this problem. As with the TrueSkill system, the ratings and rankings derived can be used in order to improve gameplay in current matches and for helping players decide which matches to participate in. 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.