Calculating Baserunner RAA

Hi, I'm trying to replicate OpenWAR calculations on my own to potentially incorporate data that wasn't available when this project started, and I'm not understanding the following step in the Baserunner RAA portion:

Looking at line 550 of makeWAR.R, you create a function "getCDF" to compute the empirical probabilities of every possible # of bases advanced in a given situation. But then the _lagged_ cumulative probability is what gets merged back to the original dataset and used for the remainder of the RAA calculation.

Based on your journal article, I had thought **κ** was based on the probability of advancing _at least_ as many bases as the runner actually did, but to me it seems the lag would represent the probability of advancing strictly less than the number of bases. Any clarity would be much appreciated. Thanks a lot.