Existing research indicates that students prefer to work with tutors who express politely in online human-human tutoring, but excessive polite expressions might lower tutoring efficacy. However, there is a shortage of understanding about the use of politeness in online tutoring and the extent to which the politeness of instructional strategies can contribute to students' achievement. To address these gaps, we conducted a study on a large-scale dataset (5,165 students and 116 qualified tutors in 18,203 online tutoring sessions) of both effective and ineffective human-human online tutorial dialogues. The study made use of a well-known dialogue act coding scheme to identify instructional strategies, relied on the linguistic politeness theory to analyse the politeness levels of the tutors' instructional strategies, and utilised Gradient Tree Boosting to evaluate the predictive power of these politeness levels in revealing students' problem-solving performance. The results demonstrated that human tutors used both polite and non-polite expressions in the instructional strategies. Tutors were inclined to express politely in the strategy of providing positive feedback but less politely while providing negative feedback and asking questions to evaluate students' understanding. Compared to the students with prior progress, tutors provided more polite open questions to the students without prior progress but less polite corrective feedback. Importantly, we showed that, compared to previous research, the accuracy of predicting student problem-solving performance can be improved by incorporating politeness levels of instructional strategies with other documented predictors (e.g., the sentiment of the utterances).