2000 Volume 45 Issue 6 Pages 719-738
One of the most important concerns in coaching activity and team management is to assess individual and/or team ability. One approach is to estimate ability by analyzing the outcome of an actual game. In most cases, the BT-model (Bradley & Terry, 1952), which was developed for preference analysis in psychometric studies, is popular in sports sciences because it readily allows ability to be estimated in terms of win-rate. However, this model is well known to have certain inherent problems. In this study, we developed a new model, the OD-model, which can assess not only offence and defence ability separately but also the stability of each performance. Maximum likelihood estimates of the parameters are obtained using scores, based on an ordinary additional normal error model and the local independent assumption. Moreover, a logistic model, principal component analysis model, timeseries model, and a model using win-loss data are also proposed. An illustrative application to data for the Japanese professional baseball league in 1994 is demonstrated. Finally, the relatioship to other models, and the advantages and limitations of the method relative to the BT-model are discussed.