As promised, here is the chart for first time Unrestricted Free Agents. It includes only players who were 27 or younger who are Group III Free Agents. Bouwmeester is not 27 but earned his free agency with 7 years of service time. These are players who have never had a contract year where they would have been UFA the previous July - that would've have muddled the picture.
As we can see, even with Kurtis Foster's aberration included - his injury troubles have made it unclear whether he can be an effective NHL player - the average increase was still above 50%. This is coming in a year of almost no salary cap increase. We did not even include Johnny Oduya's contract which was signed on June 30 - his pay increased nearly sixfold.
Essentially, RFAs on 2nd contracts are 50% cheaper than UFAs, and players on entry-level contracts are far cheaper than that. It's a young man's game now; clubs need solid entry-level players in order to compete.