Many studies have found a relationship between students' self-reported procrastination and their grades. Few studies have used learning analytic data as a behavioural measure of procrastination in order to predict performance, and there is no systematic research on how this relationship may differ across assessments or disciplines. In this study we analyse nine years' worth of institutional electronic submission records, a total of 73,608 assignment submissions, to examine the relationship between submission time and grades across assignments, students, courses, and disciplines in higher education. A significant negative relationship was found overall, with students who submitted closer to the deadline obtaining lower grades, however the size of the relationship was negligible, accounting for less than 1% of the variance in grades. The relationship varied significantly depending on student, assignment, course and discipline.