I think the single biggest factor will be improved scheme familiarity for the players. Techniques improve to match the desired style of play. They gain awareness of when, where, and how they will be blocked, as well as how to defeat those blocks. They know where their teammates should be, allowing them to be more decisive in their movements. LBs and DBs will have a better understanding of run/pass reads. LBs (even the young ones) have been drilling Claeys' run fits non-stop.
Kill's teams don't get better magically. His teams get better as they get older and more familiar with the schemes. If a player knows his job, he will do the job much faster and more effectively than someone who is unsure.