Egocentric means seeing things from only my point of view. It is something we get past in the Preoperational stage of development according to Piaget. That usually lasts from age 2 to 7. Anyway, I'm not sure what egocentrism has to do with this, but it let me showcase a bit of my knowledge on theories of development.
As for my guess when you get into the top 20 ... I'll have to get back to you on that. It not only depends on what those between you and the top 15 do, but whether some delete. Mathematically, should they quit playing right away, you'd have to find yourself with at least 800 villas. That's 146 more than you have right now. A good nobling rate for someone like F777 who doesn't use his resources for war in tribal wars would be about 3 villas per day. Since you are actually battling and losing some to enemy and yourself, I would say that you will do no better than an average long-term growth of 2 villas per day. I would think you will do a little less. Still, just for the sake of the numbers, you're going to need about 73 days to get to 800 villas. Shooting from the hip, you'll need about a half year if the current group between #15 and #38 slow up.