The method of Paired Comparisons (PC) is a technique used to prioritize items through subjective assessments. Stern (1990) develops gamma models for PC to comparing treatments on the basis of time taken in a point scoring competition. In this study, an effort is made to analyze gamma models for PC through Bayesian approach incorporating prior uncertainty existing in the model parameters. Uninformative and informative priors are used to serve the purpose. Hyperparameters of the informative priors are elicited. We use a real data set on five top-ranked one-day international cricket teams for illustration.