A year ago I voted for 12. I feel comfortable with that prediction, although might up it to 13-14. Here is what I posited then:
2014-15 (age 27-28): 2-3
2016-17 (age 28-29): 1-3
2018-20 (age 30-32): 0-2
Novak had just won his 7th. I predicted 2-3 more in 2014-15, which was five more Slams. So far he's won two--the AO and Wimb this year. So that's correct. Let's take another look:
Novak has six Slams before his 30th birthday in May of 2017. While turning 30 isn't some magical line that once a player crosses it, he'll start rapidly declining. But I'm going to use as the time during which Novak will continue at or near his absolute peak. Couple that with the rise of "Generation Kyrgios," and I see that as his best window for piling up Slams. I'm going to predict that he wins half of those six, which would bring him to a total of 12 by his 30th birthday.
After that, let's say he's got about 3 further years as a legit Slam contender - the rest of 2017, 2018, and 2019, the year he turns 32. After that he probably doesn't have much of a chance, but you never know. That's 11 more Slams. Let's say he wins 1-3 of those, or 2 to average it out. That brings him to 14, tied with Sampras, and possibly Nadal. Maybe he plays another year or two to try to get to 15, I don't know.
Regardless, 14 is my new prediction.