Science and Math Backing YAGNI?

I'm not a YAGNI purist, for experienced people can forecast certain events fairly reliably. However, I've recently bumped heads with a relatively young anti-YAGNI head architect: he is a feature & buzzword pack-rat.

I wonder if there is any strong science or math behind YAGNI, or at least some degree of it. Simple logic would dictate a linear relationship: that, for example, one devote about 50% of code to something that has a 50% chance of happening, compared to the total code if it were 100% (a requirement). But my experience tells me to devote more like 3%: light preparations. (A YAGNI purist would say 0%.) I would like to give a better case than mere experience.