Difficulty arises when the number of units being compared is large.
In this case, likelihood-based analyses can be computationally too cumbersome to carry out on a regular basis as new data is obtained. This presents a problem for rating populations of chess players, and groups of online gamers, which often consist of tens of thousands of competitors. This talk develops computationally simple algorithms for fitting two particular dynamic paired comparison models. The second recognizes the possibility of sudden changes in the merits, so that the corresponding variances are themselves assumed to be stochastically time-varying. We explore the models and the developed algorithms on a data set consisting of all known chess game outcomes among 88 of the best players of all time.