For Example: The 7 card hand represents 11.67% of your starting 60 cards so it should - optimally - represent 11.67% of your total lands, creatures, and spells.
So, a deck that consists of 20 creatures, 20 spells, and 20 land should statistically have 2.33 creatures, 2.33 spells, and 2.33 land - or 2 creatures, 2 spells, 2 land and 1 mystery card (ohhhhhh...) in its opening hand.
Now, that was an easy example and only showed what an optimal hand looks like. My question is: how far can we deviate from that optimal hand and still have something that we should statistically keep?

Also, what are some rules we can establish to govern mulliganing?
Would it be fair to say that you'd want to auto
mulligan any hand with less than 5% or more than 20% of a deck's mana sources?
What about threats? When I play Aggro, I know I want so see at least 2 creatures - or roughly 10% of the deck's threats. Less than 10% is a mulligan, but I know that's not the case for something like Control that will keep hands without threats all day, but will toss any hand without enough control elements.
What about smaller hands? Once you've already thrown away 7 cards, what makes a keepable 6 card hand? Or 5? Or - God forbid - 4?
Thoughts?