I'm starting to think that Roger isn't going to end up with the Slam record.
Slams: Roger 20, Rafa 18, Novak 15
Age: Roger almost 38, Rafa 33, Novak 32
Let's say Roger wins one more and finishes with 21. Do we really think that Rafa won't do what it takes to stick around and makes sure he gets those 4 more? And don't you think Novak will be motivated to stay around long enough to surpass Rafa?
My prediction is that Roger finishes with 20-21, Rafa with +1 (21-22), and Novak +2 (22-23). Its just the way of things.
Now if the situation was reversed and Roger was 5-6 years younger, I would predict him to finish with the highest Slam count. That's the benefit of coming after - you get to break older players' records.
The only way that doesn't happen is if either Rafa and/or Novak experience catastrophic injury, and/or one or two of the Next Genners rise to a level of greatness.