Researchers have demonstrated that dialogue-based intelligent tutoring systems (ITS) can be effective in assisting students in learning. However, little research has attempted to explore the necessity of equipping dialogue-based ITS with one of the most important capabilities of human tutors, that is, maintaining polite interactions with students, which is essential to provide students with a pleasant learning experience. In this study, we examined the role of politeness by analysing a large-scale real-world dataset consisting of over 14K online human-human tutorial dialogues. Specifically, we employed linguistic theories of politeness to characterise the politeness levels of tutor-student-generated utterances, investigated the correlation between the politeness levels of tutors' utterances and students' problem-solving performance and quantified the power of politeness in predicting students' problem-solving performance by applying Gradient Tree Boosting. The study results showed that: (i) in the effective tutorial sessions (ie, sessions in which students successfully solved problems), tutors tended to be very polite at the start of a tutorial session and become more direct to guide students as the session progressed; (ii) students with better performance in solving problems tended to be more polite at the beginning and the end of a tutorial session than their counterparts who failed to solve problems; (iii) the correlation between tutors' polite expressions and students' performance was not evident in non-instructional communication; and (iv) politeness alone cannot adequately reveal students' problem-solving performance, and thus other factors (eg, sentiment contained in utterances) should also be taken into account.