That's some fancy math comparing his war to his Yankees years and then his BAPIP to his career average. Try comparing both to his Yankee years and you'll see that's where the whole decline came from. His peripherals are all the same. His line drive rate slightly up, pop up rate slightly down. Only difference between Yankees years and last year was BAPIP.
I'll make it easy for you - let's do career first. His career WAR is 27.7 over 10 years. That includes his first season in which he barely played at all and produced a WAR of 0. If you ignore that year his average WAR is over 3. So his WAR in 2013 was 20% below his career average while his BABIP was basically 1% below his career average - a negligible difference.
Now if you'd like to argue that the Yankee years are a better point of comparison because they're more recent, we can do that to. Using the number of ground balls and fly balls in each of his Yankee years (it's all on his Fan Graphs page) you can weight the BABIP listed to get his true BABIP for those 4 years. It comes out to .307, which means his BABIP was less than 10% worse this year than in his Yankee years. His Yankee WAR average was 3.6, which means his 2.4 WAR this year was more than 30% worse than in his Yankee years. You're going to have a hard time convincing anyone that his drop in overall production is due to bad luck on BIP.
We can sit here and break down the components from today until tomorrow, but you're going to find that this season was definitely a decline from both recent years and career averages, much more than any luck factors can explain. If you want to argue that it's one bad season and it doesn't constitute a decline, that's fine - though I don't buy it, especially at this later stage in his career.