The prediction of the winner of a single tennis match and the estimation of a player's winning probability are interesting to tennis fans and are also important to sport lottery betters and bookmakers, since the betting odds for a tennis player are proportional to the reciprocal of her/his winning probability. In this presentation, we use three models to predict the winner as well as to estimate a player's winning probability of a men's single tennis match, using the difference of two players' ATP (Association of Tennis Professionals) official ranks as the predictor variable. The three models are logistic regression, ordered probit regression model with binary response and the ordered probit regression with multiple-level responses. The third method (the ordered probit regression with multiple-level responses) first predicts the real score in sets (say 0:2, 1:2, 2:1 and 2:0 for best of three matches) and then determines the winner of a tennis match based on the prediction. We split the 1992 match records of year 2019 ATP tournaments into two datasets of equal size 996, such that the first half of the records are used to estimate the above three models and the second is thus used to evaluate the accuracy of the three models. The results show the third model, namely the multilevel ordered probit model, has the best performance in predicting the winner. However, the historical match results show that roughly one third of the winners were the lower-ranked players than their opponents and such a counter-intuitive results occurred more often in practice when two players' ranks are closer, hindering prediction accuracies of the above three models considered. This suggests that the use of two players' rank difference alone has its limitations and that we need alternative mechanisms to rank the tennis players and that the above models should incorporate more (tennis skill based) explanatory variables to achieve more accurate predictions.