The second term in the brackets is the centroid of the time-series distribution. As the centroid increases, the STI increases. The maximum value for the centroid is N, and in that case STI = 1. If you add leading zeros to a time series, the STI value does not change; this is a useful property when comparing different time series, which could be of varied sizes (the centroid divided by N is another index but does not have this property).