In this work, we presented, in a didactic way, the Bayesian binary regression modeling for unbalanced data using new links functions. Under the Bayesian approach and using information criteria, predictive evaluation measures and introducing the analysis of residuals, we show that the models that use power and reverse power link functions are better than traditional models in the presence of unbalanced data, considering two applications. Additionally, codes with the procedures presented using the Stan package are made available in order to facilitate the use of these models. The work also contains a simulation study that shows how the unbalance in the response variable affects the estimation of the parameters of a logistic regression with respect to the bias, mean square error and standard deviation of the estimates, regardless of the sample size. At the same time, considering two applications, we show how binary regression models with the power and reverse power links recently formulated in the literature can be used to adequately estimate the parameters in the type of unbalance considered.