This year (2015), according to the AGA’s (American Gaming Association) research, nearly about 40 million people filled out about 70 million March Madness brackets (Moyer, 2015). Their objective is to correctly predict the winners of each game. This paper used the probability self-consistent (PSC) model (Shen, Hua, Zhang, Mu, Magel, 2015) to make the prediction of all 63 games in the NCAA Men's Division I Basketball Tournament. PSC model was first introduced by Zhang (2012). The Logit link was used in Zhang’s (2012) paper to connect only five covariates with the conditional probability of a team winning a game given its rival team. In this work, we incorporated fourteen covariates into the model. In addition to this, we used another link function, Cauchit link, in the model to make the predictions. Empirical results show that the PSC model with Cauchit link has better average performance in both simple and doubling scoring than Logit link during the last three years of tournament play. In the generalized linear model, maximum likelihood estimation is a popular method for estimating the parameters; however, convergence failuresmay happen when using large dimension covariates in the model (Griffiths, Hill, Pope, 1987). Therefore, in the second phase in this study, Bayesian inference is used for estimating in the parameters in the prediction model. Bayesian estimation incorporates prior information such as experts’ opinions and historical results in the model. Predictions from three years of March Madness using the model obtained from Bayesian estimation with Logit link will be compared to predictions using the model obtained from maximum likelihood estimation.