The indirect impact a principal has relies on the influence the principal has on other people or features of the school. This would include the climate of the school. Does the principal create an inviting and professional community for the teachers and other staff members? In other words, the principal is influencing the influencers by creating a climate that allows them to become quality educators who have an impact on student achievement.
When principals take a stance that student achievement is central to their role the influence is greater. No matter how small that influence may be, it will be significant if the principal has a deep understanding of how students learn and continually advocates for these principles of learning. In fact, schools are unlikely to have a signifant impact on student achievement without highly effective principals.