[ethan]

First, it should be pretty clear to you that there's a difference between having a big stack in a tournament that lets you buy it, and having it in a tournament that doesn't.

A big stack does become more relevant later in the tournament; you're correct in that. That's because you're not really bullying the short stacks early on, because they're not _that_ short in terms # of BB. The big stack gives you leeway to gamble, and people are more afraid of gambling when they can see exactly what losing will cost them. (They've invested time in the tournament, maybe they've kept up with the average stack, and they're attached to those chips they've won. Losing all of those chips at once scares them. If they money's coming up, they're even more scared of missing out.) One nice thing about a big stack early is that it gives you a greater chance of having a big stack later on.

I'm not exactly sure what you're looking for in terms of "mathematical proof".