In other words, unlike reddit, the rating of a story changes over time. Stories get one free upvote, so p-1 compensates for that (new stories have no points). Dividing by a power of time makes the number of upvotes that a story receives in its first few hours crucial to how likely the story is to stay on the front page.
In reddit's system, if you take a snapshot of the front page and then stop voting or submitting stories, the page will never change. At HN, stories might reorder themselves because a story with few points, which was given a boost from being very new, will lose rating compared to high-value stories that have been around a long time.